10th Standard CBSE Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 10 Session 2020 - 2021
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Class 10th Maths - Probability Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    Two friends Richa and Sohan have some savings in their piggy bank. They decided to count the total coins they both had. After counting they find that they have fifty \(\begin{equation} ₹ \end{equation} \) 1 coins, forty eight \(\begin{equation} ₹ \end{equation} \) 2 coins, thirty six \(\begin{equation} ₹ \end{equation} \) 5 coins, twenty eight \(\begin{equation} ₹ \end{equation} \)10 coins and eight \(\begin{equation} ₹ \end{equation} \) 20 coins. Now, they said to Nisha, their another friends, to choose a coin randomly.
    Find the probability that the coin chosen is

    (i)  \(\begin{equation} ₹ \end{equation} \)5 coin

    (a) \(\begin{equation} \frac{17}{55} \end{equation}\) (b) \(\begin{equation} \frac{36}{85} \end{equation}\)
    (c) \(\begin{equation} \frac{18}{85} \end{equation}\) (d) \(\begin{equation} \frac{1}{15} \end{equation}\)

    (ii) \(\begin{equation} ₹ \end{equation} \) 20 coin

    (a) \(\begin{equation} \frac{13}{85} \end{equation}\) (b) \(\begin{equation} \frac{4}{85} \end{equation}\)
    (c) \(\begin{equation} \frac{3}{85} \end{equation}\) (d) \(\begin{equation} \frac{4}{15} \end{equation}\)

    (iii) not a  \(\begin{equation} ₹ \end{equation} \) 10 coin

    (a) \(\begin{equation} \frac{15}{31} \end{equation}\) (b) \(\begin{equation} \frac{36}{85} \end{equation}\)
    (c) \(\begin{equation} \frac{1}{5} \end{equation}\) (d)  \(\begin{equation} \frac{71}{85} \end{equation}\)

    (iv) of denomination of atleast  \(\begin{equation} ₹ \end{equation} \)10. 

    (a) \(\begin{equation} \frac{18}{85} \end{equation}\) (b) \(\begin{equation} \frac{36}{85} \end{equation}\)
    (c) \(\begin{equation} \frac{1}{17} \end{equation}\) (d) \(\begin{equation} \frac{16}{85} \end{equation}\)

    (v) of denomination of atmost \(\begin{equation} ₹ \end{equation} \) 5.

    (a) \(\begin{equation} \frac{67}{85} \end{equation}\) (b) \(\begin{equation} \frac{36}{85} \end{equation}\)
    (c) \(\begin{equation} \frac{4}{85} \end{equation}\) (d)  \(\begin{equation} \frac{18}{85} \end{equation}\)
  • 2)

    In a play zone, Nishtha is playing claw crane game which consists of 58 teddy bears, 42 pokemons, 36 tigers and 64 monkeys. Nishtha picks a puppet at random. Now, find the probability of getting

    (i) a tiger 

    (a) \(\begin{equation} \frac{3}{50} \end{equation}\) (b) \(\begin{equation} \frac{9}{50} \end{equation}\)
    (c)  \(\begin{equation} \frac{1}{25} \end{equation}\) (d) \(\begin{equation} \frac{27}{50} \end{equation}\)

    (ii) a monkey

    (a)  \(\begin{equation} \frac{8}{25} \end{equation}\) (b) \(\begin{equation} \frac{4}{25} \end{equation}\)
    (c)  \(\begin{equation} \frac{16}{25} \end{equation}\) (d)  \(\begin{equation} \frac{1}{5} \end{equation}\)

    (iii) a teddy bear

    (a) \(\begin{equation} \frac{41}{50} \end{equation}\) (b) \(\begin{equation} \frac{29}{50} \end{equation}\)
    (c) \(\begin{equation} \frac{29}{100} \end{equation}\) (d)  \(\begin{equation} \frac{41}{100} \end{equation}\)

    (iv) not a monkey 

    (a) \(\begin{equation} \frac{1}{25} \end{equation}\) (b) \(\begin{equation} \frac{8}{25} \end{equation}\)
    (c) \(\begin{equation} \frac{13}{25} \end{equation}\) (d) \(\begin{equation} \frac{17}{25} \end{equation}\)

    (v) not a pokemon 

    (a) \(\begin{equation} \frac{27}{100} \end{equation}\) (b) \(\begin{equation} \frac{43}{100} \end{equation}\)
    (c)  \(\begin{equation} \frac{61}{100} \end{equation}\) (d) \(\begin{equation} \frac{79}{100} \end{equation}\)
  • 3)

    Rohit wants to distribute chocolates in his class on his birthday. The chocolates are of three types: Milk chocolate, White chocolate and Dark chocolate. If the total number of students in the class is 54 and everyone gets a chocolate, then answer the following questions.

    (i) If the probability of distributing milk chocolates is 1/3, then the number of milk chocolates Rohit has, is

    (a) 18 (b) 20
    (c) 22 (d) 30

    (ii) If the probability of distributing dark chocolates is 4/9, then the number of dark chocolates Rohit has, is

    (a) 18 (b) 25
    (c) 24 (d) 36

    (iii) The probability of distributing white chocolates is

    (a) \(\begin{equation} \frac{11}{27} \end{equation}\) (b)\(\begin{equation} \frac{8}{21} \end{equation}\)
    (c)  \(\begin{equation} \frac{1}{9} \end{equation}\) (d) \(\begin{equation} \frac{2}{9} \end{equation}\)


    (iv) The probability of distributing both milk and white chocolates is

     

    (a) \(\begin{equation} \frac{3}{17} \end{equation}\) (b) \(\begin{equation} \frac{5}{9} \end{equation}\)
    (c) \(\begin{equation} \frac{1}{3} \end{equation}\) (d) \(\begin{equation} \frac{1}{27} \end{equation}\)

    (v) The probability of distributing all the chocolates is

    (a) 0 (b) 1
    (c) \(\begin{equation} \frac{1}{2} \end{equation}\) (d) \(\begin{equation} \frac{3}{4} \end{equation}\)
  • 4)

    In a party, some children decided to play musical chair game. In the game the person playing the music has been advised to stop the music at any time in the interval of 3 mins after he start the music in each turn. On the basis of the given information, answer the following questions.
    (i) What is the probability that the music will stop within first 30 sees after starting?

    (a) \(\begin{equation} \frac{1}{6} \end{equation}\) (b) \(\begin{equation} \frac{1}{5} \end{equation}\)
    (c) \(\begin{equation} \frac{1}{4} \end{equation}\) (d) \(\begin{equation} \frac{1}{3} \end{equation}\)

    (ii) The probability that the music will stop within 45 sees after starting is

    (a)  \(\begin{equation} \frac{1}{4} \end{equation}\) (b) \(\begin{equation} \frac{1}{5} \end{equation}\)
    (c)  \(\begin{equation} \frac{1}{6} \end{equation}\) (d) \(\begin{equation} \frac{1}{8} \end{equation}\)

    (iii) The probability that the music will stop after 2 mins after starting is

    (a) \(\begin{equation} \frac{1}{8} \end{equation}\) (b) \(\begin{equation} \frac{1}{5} \end{equation}\)
    (c) \(\begin{equation} \frac{1}{4} \end{equation}\) (d) \(\begin{equation} \frac{1}{3} \end{equation}\)

    (iv) The probability that the music will not stop within first 60 sees after starting is

    (a) \(\begin{equation} \frac{1}{3} \end{equation}\) (b) \(\begin{equation} \frac{2}{3} \end{equation}\)
    (c) \(\begin{equation} \frac{4}{5} \end{equation}\) (d) \(\begin{equation} \frac{8}{9} \end{equation}\)

    (v) The probability that the music will stop within first 82 sees after starting is

    (a) \(\begin{equation} \frac{11}{30} \end{equation}\) (b) \(\begin{equation} \frac{41}{90} \end{equation}\)
    (c) \(\begin{equation} \frac{31}{35} \end{equation}\) (d) \(\begin{equation} \frac{41}{93} \end{equation}\)
  • 5)

    Three persons toss 3 coins simultaneously and note the outcomes. Then, they ask few questions to one another. Help them in finding the answers of the following questions.

    (i) The probability of getting atmost one tail is

    (a)  0 (b)  1
    (c)  \(\begin{equation} \frac{1}{2} \end{equation}\) (d) \(\begin{equation} \frac{1}{4} \end{equation}\)

    (ii) The probability of getting exactly 1 head is

    (a)  \(\begin{equation} \frac{1}{2} \end{equation}\) (b) \(\begin{equation} \frac{1}{4} \end{equation}\)
    (c)  \(\begin{equation} \frac{1}{8} \end{equation}\) (d) \(\begin{equation} \frac{3}{8} \end{equation}\)

    (iii) The probability of getting exactly 3 tails is 

    (a) 0 (b)  1
    (c) \(\begin{equation} \frac{1}{4} \end{equation}\) (d) \(\begin{equation} \frac{1}{8} \end{equation}\)

    (iv) The probability of getting atmost 3 heads is 

    (a)  0 (b)  1
    (c)  \(\begin{equation} \frac{1}{2} \end{equation}\) (d) \(\begin{equation} \frac{1}{8} \end{equation}\)

    (v) The probability of getting atleast two heads is

    (a)  0 (b) 1
    (c)  \(\begin{equation} \frac{1}{2} \end{equation}\) (d) \(\begin{equation} \frac{1}{4} \end{equation}\)

Class 10th Maths - Statistics Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    An agency has decided to install customised playground equipments at various colony parks. For that they decided to study the age-group of children playing in a park of the particular colony. The classification of children according to their ages, playing in a park is shown in the following table

    Age group of children (in years) 6-8 8-10 10-12 12-14 14-16
    Number of children 43 58 70 42 27

    Based on the above information, answer the following questions.
    (i) The maximum number of children are of the age-group

    (a) 12-14 (b) 10-12 (c) 14-16 (d) 8-10

    (ii) The lower limit of the modal class is

    (a) 10 (b) 12 (c) 14 (d) 8

    (iii) Frequency of the class succeeding the modal class is

    (a) 58 (b) 70 (c) 42 (d) 27

    (iv) The mode of the ages of children playing in the park is

    (a) 9 years (b) 8 years (c) 11.5 years (d) 10.6 years

    (v) If mean and mode of the ages of children playing in the park are same, then median will be equal to

    (a) Mean (b) Mode
    (c) Both (a) and (b) (d) Neither (a) nor (b)
  • 2)

    As the demand for the products grew, a manufacturing company decided to hire more employees. For which they want to know the mean time required to complete the work for a worker. The following table shows the frequency distribution of the time required for each worker to complete a work.

     

    Time (in hours) 15-19 20-24 25-29 30-34 35-39
    Number of workers 10 15 12 8 5

    Based on the above information, answer the following questions.
    (i) The class mark of the class 25-29 is

    (a) 17 (b) 22 (c) 27 (d) 32

    (ii) If xi's denotes the class marks and fi's denotes the corresponding frequencies for the given data, then the value of \(\sum x_{i} f_{i}\) equals to

    (a) 1200 (b) 1205 (c) 1260 (d) 1265

    (iii) The mean time required to complete the work for a worker is

    (a) 22 hrs (b) 23 hrs (c) 24 hrs (d) none of these

    (iv) If a worker works for 8 hrs in a day, then approximate time required to complete the work for a worker is

    (a) 3 days (b) 4 days (c) 5 days (d) 6 days

    (v) The measure of central tendency is

    (a) Mean (b) Median (c) Mode (d) All of these
  • 3)

    On a particular day, National Highway Authority ofIndia (NHAI) checked the toll tax collection of a particular toll plaza in Rajasthan.

    The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.

    Toll tax (in Rs) 30-40 40-50 50-60 60-70 70-80
    Number of vehicles 80 110 120 70 40

    Based on the above information, answer the following questions.
    (i) If A is taken as assumed mean, then the possible value of A is

    (a) 32 (b) 42 (c) 85 (d) 55

    (ii) If xi's denotes the class marks and fi's denotes the deviation of assumed mean (A) from xi's, then the minimum value of |di| is

    (a) -200 (b) -100 (c) 0 (d) 100

    (iii) The mean of toll tax received. by NHAI by assumed mean method is

    (a) Rs 52 (b) Rs 52.14 (c) Rs 52.50 (d) Rs 53.50

    (iv) The mean of toll tax received by NHAI by direct method is

    (a) equal to the mean of toll tax received by NHAI by assumed mean method
    (b) greater than the mean of toll tax received by NHAI by assumed mean method
    (c) less than the mean of toll tax received by NHAI by assumed mean method
    (d) none of these

    (v) The average toll tax received by NHAI in a day, from that particular toll plaza, is

    (a) Rs 21000 (b) Rs 21900 (c) Rs 30000 (d) none of these
  • 4)

    Transport department of a city wants to buy some Electric buses for the city. For which they wants to analyse the distance travelled by existing public transport buses in a day.

    The following data shows the distance travelled by 60 existing public transport buses in a day.

    Daily distance travelled (in km) 200-209 210-219 220-229 230-239 240-249
    Number of buses 4 14 26 10 6

    Based on the above information, answer the following questions.
    (i) The upper limit of a class and lower limit of its succeeding class is differ by

    (a) 9 (b) 1 (c) 10 (d) none of these

    (ii) The median class is

    (a) 229.5-239.5 (b) 230-239 (c) 220-229 (d) 219.5-229.5

    (iii) The cumulative frequency of the class preceding the median class is

    (a) 14 (b) 18 (c) 26 (d) 10

    (iv) The median of the distance travelled is

    (a) 222 km (b) 225 km (c) 223 km (d) none of these

    (v) If the mode of the distance travelled is 223.78 km, then mean of the distance travelled by the bus is

    (a) 225 km (b) 220 km (c) 230.29 km (d) 224.29 km
  • 5)

    A group of 71 people visited to a museum on a certain day. The following table shows their ages.

    Age (in years) Number of persons
    Less than 10 3
    Less than 20 10
    Less than 30 22
    Less than 40 40
    Less than 50 54
    Less than 60 71

    Based on the aboxe information, answer the following questions.
    (i) If true class limits have been decided by making the classes of interval 10, then first class must be

    (a) 5-15 (b) 0-10
    (c) 10-20 (d) none of these

    (ii) The median class for the given data will be

    (a) 20-30 (b) 10-20 (c) 30-40 (d) 40-50

    (iii) The cumulative frequency of class preceding the median class is

    (a) 22 (b) 13 (c) 25 (d) 35

    (iv) The median age of the persons visited the museum is

    (a) 30 years (b) 32.5 years (c) 34 years (d) 37.5 years

    (v) If the price of a ticket for the age group 30-40 is Rs 30, then the total amount spent by this age group is

    (a) Rs 360 (b) Rs 420 (c) Rs 540 (d) Rs 340

Class 10th Maths - Surface Areas and Volumes Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    Arun a 10th standard student makes a project on corona virus in science for an exhibition in his school. In this project, he picks a sphere which has volume 38808 cm3 and 11 cylindrical shapes, each of volume 1540 cm3 with length 10 cm.

    Based on the above information, answer the following questions.
    (i) Diameter of the base of the cylinder is

    (a) 7 cm (b) 14 cm (c) 12 cm (d) 16 cm

    (ii) Diameter of the sphere is

    (a) 40 cm (b) 42 cm (c) 21 cm (d) 20 cm

    (iii) Total volume of the shape formed is

    (a) 85541 cm3 (b) 45738 cm3 (c) 24625 cm3 (d) 55748 cm3

    (iv) Curved surface area of the one cylindrical shape is

    (a) 850 cm2 (b) 221 cm2 (c) 440 cm2 (d) 540 cm2

    (v) Total area covered by cylindrical shapes on the surface of sphere is

    (a) 1694 cm2 (b) 1580 cm2 (c) 1896 cm2 (d) 1470 cm2
  • 2)

    Ajay is a Class X student. His class teacher Mrs Kiran arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top. Path around Anda is known as Pradakshina Path.

    Based on the above information, answer the following questions.
    (i) Find the lateral surface area of the Hermika, if the side of cubical part is 8 m.

    (a) 128 m2 (b) 256 m2 (c) 512 m2 (d) 1024 m2

    (ii) The diameter and height of the cylindrical base part are respectively 42 m and 12 m. If the volume of each brick used is 0.01 m3, then find the number of bricks used to make the cylindrical base.

    (a) 1663200 (b) 1580500 (c) 1765000 (d) 1865000

    (iii) If the diameter of the Anda is 42 m, then the volume of the Anda is

    (a) 17475 m3 (b) 18605 m3 (c) 19404 m3 (d) 18650 m3

    (iv) The radius of the Pradakshina path is 25 m. If Buddhist priest walks 14 rounds on this path, then find the distance covered by the priest.

    (a) 1860 m (b) 3600 m (c) 2400 m (d) 2200 m

    (v) The curved surface area of the Anda is

    (a) 2856 m2 (b) 2772 m2 (c) 2473 m2 (d) 2652 m2
  • 3)

    One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24 ern and base radius is 7 cm. While watching this, some questions came into Rinkus mind. Help Rinku to find the answer of the following questions.

    (i) After carving out cone from the cylinder,

    (a) Volume of the cylindrical wood will decrease.
    (b) Height of the cylindrical wood will increase.
    (c) Volume of cylindrical wood will increase.
    (d) Radius of the cylindrical wood will decrease.

    (ii) Find the slant height of the conical cavity so formed.

    (a) 28 cm (b) 38 cm (c) 35 cm (d) 25 cm

    (iii) The curved surface area of the conical cavity so formed is

    (a) 250 cm2 (b) 550 cm2 (c) 350 cm2 (d) 450 cm2

    (iv) External curved surface area of the cylinder is

    (a) 876 cm2 (b) 1250 cm2 (c) 1056 cm2 (d) 1025 cm2

    (v) Volume of conical cavity is

    (a) 1232 cm3 (b) 1248 cm3 (c) 1380 cm3 (d) 999 cm3
  • 4)

    To make the learning process more interesting, creative and innovative, Amayras class teacher brings clay in the classroom, to teach the topic - Surface Areas and Volumes. With clay, she forms a cylinder of radius 6 ern and height 8 cm. Then she moulds the cylinder into a sphere and asks some questions to students.

    (i) The radius of the sphere so formed is 

    (a) 4 cm (b) 6 cm (c) 7 cm (d) 8 cm

    (ii) The volume of the sphere so formed is

    (a) 905.14 cm3 (b) 903.27 cm3 (c) 1296.5 cm3 (d) 1156.63 cm3

    (iii) Find the ratio of the volume of sphere to the volume of cylinder.

    (a) 2:1 (b) 1:2 (c) 1:1 (d) 3: 1

    (iv) Total surface area of the cylinder is 

    (a) 528 cm2 (b) 756 cm2 (c) 625 cm2 (d) 636 cm2

    (v) During the conversion of a solid from one shape to another the volume of new shape will 

    (a) be increase (b) be decrease (c) remain unaltered (d) be double
  • 5)

    A carpenter used to make and sell different kinds of wooden pen stands like rectangular, cuboidal, cylindrical, conical. Aarav went to his shop and asked him to make a pen stand as explained below. Pen stand must be of the cuboidal shape with three conical depressions, which can hold 3 pens. The dimensions of the cuboidal part must be 20 cm x 15 cm x 5 cm and the ffrlog radius and depth of each conical depression must be 0.6 cm and 2.1 cm respectively.

    Based on the above information, answer the following questions.
    (i) The volume of the cuboidal part is

    (a) 1250 cm3 (b) 1500 cm3 (c) 1625 cm3 (d)  1500 cm3

    (ii) Total volume of conical depressions is 

    (a) 2.508 cm3 (b) 1.5 cm3 (c) 2.376 cm3 (d)  3.6 cm3

    (iii) Volume of the wood used in the entire stand is

    (a) 631.31 cm3 (b) 3564 cm3 (c) 1502.376 cm3 (d)  1497.624 cm3

    (iv) Total surface area of cone of radius r is given by

    \((a) \pi r l+\pi r^{2}\) \((b) 2 \pi r l+\pi r^{2}\) \((c) \pi r^{2} l+\pi r^{2}\) \((d) \pi r l+2 \pi r^{3}\)

    (v) If the cost of wood used is Rs 5 per cm3, then the total cost of making the pen stand is

    (a) Rs 8450.50  (b) Rs 7480 (c) Rs 9962.14 (d)  Rs 7488.12

Class 10th Maths - Areas Related to Circles Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    In a pathology lab, a culture test has been conducted. In the test, the number of bacteria taken into consideration in various samples is all3-digit numbers that are divisible by 7, taken in order.

    On the basis of above information, answer the following questions.
    (i) How many bacteria are considered in the fifth sample?

    (a) 126 (b) 140 (c) 133 (d) 149

    (ii) How many samples should be taken into consideration?

    (a) 129 (b) 128 (c) 130 (d) 127

    (iii) Find the total number of bacteria in the first 10 samples.

    (a) 1365 (b) 1335 (c) 1302 (d) 1540

    (iv) How many bacteria are there in the 7th sample from the last?

    (a) 952 (b) 945 (c) 959 (d) 966

    (v) The number of bacteria in 50th sample is

    (a) 546 (b) 553 (c) 448 (d) 496
  • 2)

    In a class the teacher asks every student to write an example of A.P. Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions. Help students to find the answers of the questions.

    (i) Find the 34th term of the progression written by Madhuri.

    (a) 286 (b) 88 (c) -99 (d) 190

    (ii) Find the sum of common difference of the two progressions.

    (a) 6 (b) -6 (c) 1 (d) 0

    (iii) Find the 19th term of the progression written by Geeta.

    (a) 49 (b) 59 (c) 52 (d) 62

    (iv) Find the sum of first 10 terms of the progression written by Geeta.

    (a) 85 (b) 95 (c) 110 (d) 200

    (v) Which term of the two progressions will have the same value?

    (a) 31 (b) 33 (c) 32 (d) 30
  • 3)

    Meenas mother start a new shoe shop. To display the shoes, she put 3 pairs of shoes in 1st row,S pairs in 2nd row, 7 pairs in 3rd row and so on.

    On the basis of above information, answer the following questions.
    (i) If she puts a total of 120 pairs of shoes, then the number of rows required are

    (a) 5 (b) 6 (c) 7 (d) 10

    (ii) Difference of pairs of shoes in 17th row and 10th row is

    (a) 7 (b) 14 (c) 21 (d) 28

    (iii) On next day, she arranges x pairs of shoes in 15 rows, then x =

    (a) 21 (b) 26 (c) 31 (d) 42

    (iv) Find the pairs of shoes in 30th row.

    (a) 61 (b) 67 (c) 56 (d) 59

    (v) The total number of pairs of shoes in 5th and 8th row is

    (a) 7 (b) 14 (c) 28 (d) 56
  • 4)

    Anuj gets pocket money from his father everyday. Out of the pocket money, he saves Rs 2.75 on first day, Rs 3 on second day, Rs 3.25 on third day and so on.
    On the basis of above information, answer the following questions .

    (i) What is the amount saved by Anuj on 14th day?

    (a) Rs 6.25 (b) Rs 6 (c) Rs 6.50 (d) Rs 6.75

    (ii) What is the total amount saved by Anuj in 8 days?

    (a) Rs 18 (b) Rs 33 (c) Rs 24 (d) Rs 29

    (iii) What is the amount saved by Anuj on 30th day?

    (a) Rs 10 (b) Rs 12.75 (c) Rs 10.25 (d) Rs 9.75

    (iv) What is the total amount saved by him in the month of June, if he starts savings from 1st June?

    (a) Rs 191 (b) Rs 191.25 (c) Rs 192 (d) Rs 192.5

    (v) On which day, he save tens times as much as he saved on day-I?

    (a) 9th (b) 99th (c) 10th (d) 100th
  • 5)

    In a board game, the number of sea shells in various cells forms an A.P. If the number of sea shells in the 3rd and 11th cell together is 68 and number of shells in 11th cell is 24 more than that of 3rd cell, then answer the following
    questions based on this data.
    (i) What is the difference between the number of sea shells in the 19th and 20th cells?

    (a) 2 (b) 3 (c) 8 (d) 7

    (ii) How many sea shells are there in the first cell?

    (a) 52 (b) 18 (c) 16 (d) 54

    (iii) How many total sea shells are there in first 13 cells?

    (a) 442 (b) 221 (c) 204 (d) Can't be determined

    (iv) Altogether, how many sea shells are there in the first 5 cells?

    (a) 220 (b) 125 (c) 96 (d) 110

    (v) What is the sum of number of sea shells in the 7th and 9th cell?

    (a) 42 (b) 32 (c) 74 (d) 80

     

     

Class 10th Maths - Circles Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    In a park, four poles are standing at positions A, B, C and D around the fountain such that the cloth joining the poles AB, BC, CD and DA touches the fountain at P, Q, Rand S respectively as shown in the figure.

    Based on the above information, answer the following questions.
    (i) If 0 is the centre of the circular fountain, then \(\angle\)OSA = 

    (a) 60° (b) 90°
    (c) 45° (d) None of these

    (ii) Which of the following is correct?

    (a) AS = AP (b) BP= BQ (c) CQ = CR (d) All of these

    (iii) If DR = 7 cm and AD = 11 ern, then AP =

    (a) 4 cm (b) 18 cm (c) 7 cm (d) 11 cm

    (iv) If O is the centre of the fountain, with \(\angle\)QCR = 60°, then \(\angle\)QOR

    (a) 60° (b) 120° (c) 90° (d) 30°

    (v) Which of the following is correct?

    (a) AB + BC = CD + DA (b) AB + AD = BC + CD
    (c) AB + CD = AD + BC (d) All of these
  • 2)

    Smita always finds it confusing with the concepts of tangent and secant of a circle. But this time she has determined herself to get concepts easier. So, she started listing down the differences between tangent and secant of a circle along with their relation. Here, some points in question form are listed by Smita in her notes. Try answering them to clear your concepts also.

    (i) A line that intersects a circle exactly at two points is called

    (a) Secant (b) Tangent (c) Chord (d) Both (a) and (b)

    (ii) Number of tangents that can be drawn on a circle is

    (a) 1 (b) 0 (c) 2 (d) Infinite

    (iii) Number of tangents that can be drawn to a circle from a point not on it, is

    (a) 1 (b) 2 (c) 0 (d) Infinite

    (iv) Number of secants that can be drawn to a circle from a point on it is

    (a) Infinite (b) 1 (c) 2 (d) 0

    (v) A line that touches a circle at only one point is called

    (a) Secant (b) Chord (c) Tangent (d) Diameter
  • 3)

    A backyard is in the shape of a triangle with right angle at B, AB = 6 m and BC = 8 m. A pit was dig inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that AP = x m.

    Based on the above information, answer the following questions.
    (i) The value of AR =

    (a) 2x m (b) x/2 m (c) x m (d) 3x m

    (ii) The value of BQ =

    (a) 2x m (b) (6-x) m (c) (2 - x) cm (d) 4x m

    (iii) The value of CQ =

    (a) (4+x)m (b) (10 - x) m (c) (2+x)m (d) both (b) and (c)

    (iv) Which of the following is correct?

    (a) Quadrilateral AROP is a square. (b) Quadrilateral BROQ is a square.
    (c) Quadrilateral CQOP is a square. (d) None of these

    (v) Radius of the pit is

    (a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm
  • 4)

    In a maths class, the teacher draws two circles that touch each other externally at point K with centres A and B and radii 5 em and 4 em respectively as shown in the figure.

    Based on the above information, answer the following questions.
    (i) The value of PA =

    (a) 12 cm (b) 5 cm (c) 13 cm (d) Can't be determined

    (ii) The value of BQ =

    (a) 4 cm (b) 5 cm (c) 6 cm (d) None of these

    (iii) The value of PK =

    (a) 13 cm (b) 15 cm (c) 16 cm (d) 18 cm

    (iv) The value of QY =

    (a) 2 cm (b) 5 cm (c) 1 cm (d) 3 cm

    (v) Which of the following is true?

    (a) PS2=PA.PK (b) TQ2=QB.QK (c) PS2=PX.PK (d) TQ2 = QA.QB
  • 5)

    Prem did an activity on tangents drawn to a circle from an external point using 2 straws and a nail for maths project as shown in figure.

    Based on the above information, answer the following questions.
    (i) Number of tangents that can be drawn to a circle from an external point is

    (a) 1 (b) 2 (c) infinite (d) any number depending on radius of circle

    (ii) On the basis of which of the following congruency criterion,\(\Delta \mathrm{OAP} \cong \Delta \mathrm{OBP} ?\)

    (a) ASA (b) SAS (c) RHS (d) SSS

    (iii) If \(\angle\)AOB = 150°, then \(\angle\)APB =

    (a) 75° (b) 30°  (c) 60° (d) 100°

    (iv) If \(\angle\)APB = 40°, then \(\angle\)BAO =

    (a) 40° (b) 30°  (c) 50° (d) 20°

    (v) If \(\angle\)ABO = 45°, then which of the following is correct option?

    (a) \(A P \perp B P\) (b) PAOB is square (c) \(\angle\)AOB = 90° (d) All of these

Class 10th Maths - Some Applications of Trigonometry Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing on the top of 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30° and 60° respectively. (Take \(\sqrt{3}\) = 1.73)

    Based on the above information, answer the following questions.
    (i) Measure of \(\angle\)ADF is equal to 

    (a) 45° (b) 60° (c) 30° (d) 90°

    (ii) Measure of \(\angle\)ACB is equal to

    (a) 45° (b) 60° (c) 30° (d) 90°

    (iii) Width of the river is 

    (a) 28.90 m (b) 26.75 m (c) 25 m (d) 27 m

    (iv) Height of the other temple is

    (a) 32.5 m (b) 35 m (c) 33.33 m (d) 40 m

    (v) Angle of depression is always

    (a) reflex angle (b) straight
    (c) an obtuse angle (d) an acute angle
  • 2)

    There are two windows in a house. First window is at the height of 2 m above the ground and other window is 4 m vertically above the lower window. Ankit and Radha are sitting inside the two windows at points G and F respectively. At an instant, the angles of elevation of a balloon from these windows are observed to be 60° and 30° as shown below

    Based on the above information, answer the following questions.
    (i) Who is more closer to the balloon?

    (a) Ankit (b) Radha
    (c) Both are at equal distance (d) Can't be determined

    (ii) Value of DF is equal to

    \((a) \frac{h}{\sqrt{3}} \mathrm{~m}\) \((b) h \sqrt{3} \mathrm{~m}\) \((c) \frac{h}{2} \mathrm{~m}\) \((d) 2 h \mathrm{~m}\)

    (iii) Value of h is

    (a) 2 (b) 3 (c) 4 (d) 5

    (iv) Height of the balloon from the ground is

    (a) 4 m (b) 6 m (c) 8 m (d) 10 m

    (v) If the balloon is moving towards the building, then both angle of elevation will

    (a) remain same (b) increases (c) decreases (d) can't be determined
  • 3)

    A circus artist is climbing through a 15 m long rope which is highly stretched and tied from the top of a vertical pole to the ground as shown below. Based on the above information, answer the following questions.

    (i) Find the height of the pole, if angle made by rope to the ground level is 45°.

    \((a) 15 \mathrm{~m}\) \((b) 15 \sqrt{2} \mathrm{~m}\)
    \((c) \frac{15}{\sqrt{3}} \mathrm{~m}\) \((d) \frac{15}{\sqrt{2}} \mathrm{~m}\)

    (ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

    \((a) \frac{15}{\sqrt{2}} \mathrm{~m}\) \((b) 15 \sqrt{2} \mathrm{~m}\) \((c) 15 \mathrm{~m}\) \((d) {15}{\sqrt{3}} \mathrm{~m}\)

    (iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

    (a) 2.5 m (b) 5 m (c) 7.5 m (d) 10 m

    (iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

    (a) 2m (b) 4m (c) 5m (d) 6m

    (v) Which mathematical concept is used here?

    (a) Similar Triangles (b) Pythagoras Theorem
    (c) Application of Trigonometry (d) None of these
  • 4)

    There is fire incident in the house. The house door is locked so, the fireman is trying to enter the house from the window. He places the ladder against the wall such that its top reaches the window as shown in the figure .

    Based on. the above information, answer the following questions.
    (i) If window is 6 m above the ground and angle made by the foot ofladder to the ground is 30°, then length of the ladder is

    (a) 8m  (b) 10m  (c) 12m  (d) 14m

    (ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length of the ladder is

    (a) 5 m \((b) \frac{10}{\sqrt{3}} \mathrm{~m}\) \((c) \frac{15}{\sqrt{2}} \mathrm{~m}\) (d) 20 m

    (iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find the height of the window. (Take \(\sqrt{3}\) = 1.73)

    (a) 4.325 m  (b) 5.5 m  (c) 6.3 m  (d) 2.5 m

    (iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is

    (a) 2 m  (b) 4 m  (c) 6 m  (d) 8 m

    (v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?

    (a) 5 m  (b) 3\(\sqrt{5}\)m  (c) 3 m  (d) 4 m
  • 5)

    An electrician has to repair an electric fault on the pole of height of8 m. He needs to reach a point 2 m below the top of the pole to undertake the repair work.

    Based on the above information, answer the following questions.
    (i) Length of BD is

    (a) 10 m (b) 6 m (c) 4 m (d) 4 m

    (ii) What should be the length of ladder, so that it makes an angle of 60° with the ground?

    \((a) 4\sqrt{3} {~m}\) \((b) 2\sqrt{3} {~m}\) \((c) 3\sqrt{3} {~m}\) \((d) 5\sqrt{3} {~m}\)

    (iii) The distance between the foot ofladder and pole is

    \((a) 6\sqrt{3} {~m}\) \((b) 4\sqrt{3} {~m}\) \((c) 3\sqrt{3} {~m}\) \((d) 2\sqrt{3} {~m}\)

    (iv) What will be the measure of \(\angle\)BCD when BD and CD are equal?

    (a) 30° (b) 45° (c) 60° (d) 75°

    (v) Find the measure of \(\angle\)DBC.

    (a) 15° (b) 60° (c) 30° (d) 45°

Class 10th Maths - Introduction to Trigonometry Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    Three friends - Anshu, Vijay and Vishal are playing hide and seek in a park. Anshu and Vijay hide in the shrubs and Vishal have to find both of them. If the positions of three friends are at A, Band C respectively as shown in the figure and forms a right angled triangle such that AB = 9 m, BC = 3\(\sqrt{3}\) m and \(\angle\)B = 90°, then answer the following questions.

    (i) The measure of \(\angle\)A is 

    (a) 30° (b) 45° (c) 60° (d) None of these

    (ii) The measure of  \(\angle\)C is

    (a) 30° (b) 45° (c) 60° (d) None of these

    (iii) The length of AC is 

    \((a) 2 \sqrt{3} \mathrm{~m}\) \((b) \sqrt{3} \mathrm{~m}\) \((c) 4 \sqrt{3} \mathrm{~m}\) \((d) 6 \sqrt{3} \mathrm{~m}\)

    (iv) cos2A =

    (a) 0 \((b) \frac{1}{2}\) \((c) \frac{1}{\sqrt{2}}\) \((d) \frac{\sqrt{3}}{2}\)

    (v) sin \(\left(\frac{C}{2}\right)\) =

    (a) 0 \((b) \frac{1}{2}\) \((c) \frac{1}{\sqrt{2}}\) \((d) \frac{\sqrt{3}}{2}\)
  • 2)

    Two aeroplanes leave an airport, one after the other. After moving on runway, one flies due North and other flies due South. The speed of two aeroplanes is 400 km/hr and 500 km/hr respectively. Considering PQ as runway and A and B are any two points in the path followed by two planes, then answer the following questions.

    (i) Find \(\tan \theta ; \text { if } \angle A P Q=\theta\)

    \((a) \frac{1}{2}\) \((b) \frac{1}{\sqrt{2}}\) \((c) \frac{\sqrt{3}}{2}\) \((d) \frac{3}{4}\)

    (ii) Find cot B

    \((a) \frac{3}{4}\) \((b) \frac{15}{4}\) \((c) \frac{3}{8}\) \((d) \frac{15}{8}\)

    (iii) Find tanA.

    \((a) 2\) \((b) \sqrt{2}\) \((c) \frac{4}{3}\) \((d) \frac{2}{\sqrt{3}}\)

    (iv) Find secA.

    \((a) 1\) \((b) \frac{2}{3}\) \((c) \frac{4}{3}\) \((d) \frac{5}{3}\)

    (v) Find cosecB.

    \((a) \frac{17}{8}\) \((b) \frac{12}{5}\) \((c) \frac{5}{12}\) \((d) \frac{8}{17}\)
  • 3)

    Anita, a student of class 10th, has to made a project on 'Introduction to Trigonometry' She decides to make a bird house which is triangular in shape. She uses cardboard to make the bird house as shown in the figure. Considering the front side of bird house as right angled triangle PQR, right angled at R, answer the following questions.

    (i) If \(\angle P Q R=\theta, \text { then } \cos \theta=\)

    \((a) \frac{12}{5}\) \((b) \frac{5}{12}\) \((c) \frac{12}{13}\) \((d) \frac{13}{12}\)

    (ii) The value of sec \(\theta\) =

    \((a) \frac{5}{12}\) \((b) \frac{12}{5}\) \((c) \frac{13}{12}\) \((d) \frac{12}{13}\)

    (iii) The value of \(\frac{\tan \theta}{1+\tan ^{2} \theta}=\)

    \((a) \frac{5}{12}\) \((b) \frac{12}{5}\) \((c) \frac{60}{169}\) \((d) \frac{169}{60}\)

    (iv) The value of \(\cot ^{2} \theta-\operatorname{cosec}^{2} \theta=\) 

    (a) -1 (b) 0 (c) 1 (d) 2

    (v) The value of \(\sin ^{2} \theta+\cos ^{2} \theta=\)

    (a) 0 (b) 1 (c) -1 (d) 2
  • 4)

    Ritu's daughter is feeling so hungry and so thought to eat something. She looked into the fridge and found some bread pieces. She decided to make a sandwich. She cut the piece of bread diagonally and found that it forms a
    righ.t angled triangle with sides 4 cm, 4\(\sqrt{3}\) cm and 8 cm.

    On the basis of above information, answer the following questions.
    (i) The value of \(\angle\)M = 

    (a) 30° (b) 60° (c) 45° (d) None of these

    (ii) The value of \(\angle\)K =

    (a) 45° (b) 30 ° (c) 60° (d) None of these

    (iii) Find the value of tanM.

    \((a) \sqrt{3}\) \((b) \frac{1}{\sqrt{3}}\) (c) 1 (d) None of these

    (iv) sec2M - 1 =

    (a) tanM (b) tan2M (c) tan2M (d) None of these

    (v) The value of \(\frac{\tan ^{2} 45^{\circ}-1}{\tan ^{2} 45^{\circ}+1}\) is

    (a) 0 (b) 1 (c) 2 (d) -1
  • 5)

    Aanya and her father go to meet her friend Juhi for a party. When they reached to [uhi's place, Aanya saw the roof of the house, which is triangular in shape. If she imagined the dimensions of the roof as given in the figure, then answer the following questions.

    (i) If D is the mid point of AC, then BD =

    (a) 2m (b) 3m (c) 4m (d) 6m

    (ii) Measure of \(\angle\)A =

    (a) 30° (b) 60° (c) 45° (d) None of these

    (iii) Measure of \(\angle\)C =

    (a) 30° (b) 60° (c) 45° (d) None of these

    (iv) Find the value of sinA + cosC.

    (a) 0 (b) 1 (c) \(\frac{1}{2}\) (d) \(\sqrt{2}\)

    (v) Find the value of tan2C + tan2 A.

    (a) 0 (b) 1 (c) 2 (d) \(\frac{1}{2}\)

Class 10th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    The Chief Minister of Delhi launched the, 'Switch Delhi: an electric vehicle mass awareness campaign in the National Capital. The government has also issued tenders for setting up 100 charging stations across the city. Each station will have five charging points. For demo charging station is set up along a straight line and has charging points at \(A\left(\frac{-7}{3}, 0\right), B\left(0, \frac{7}{4}\right)\)C(3, 4), D(7, 7) and E(x, y). Also, the distance between C and E is 10 units.

    Based on the above information, answer the following questions.
    (i) The distance DE is

    (a) 5 units (b) 10 units (c) 4 units (d) 6units

    (ii) The value of x + y is 

    (a) 20 (b) 21 (c) 22 (d) 23

    (iii) Which of the following is true?

    (a) The points C, D and E are vertices of a triangle
    (b) The points C, D and E are collinear
    (c) The points C, D and E lie on a circle
    (d) None of these

    (iv) The ratio in which B divides AC is

    (a) 9:7 (b) 4:7 (c) 7:4 (d) 7:9

    (v) Which of the following equations is satisfied by the given points?

    (a) x + y = 0 (b) x - y = 0 (c) 3x - 4y + 7 = 0 (d) 3x+4y+7=0
  • 2)

    Alia and Shagun are friends living on the same street in Patel Nagar. Shaguns house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point 0, i.e., the origin, Alia's house is at A. Shaguns house is at B and library is at C. Based on the above information, answer the following questions.

    (i) How far is Alia's house from Shaguns house?

    (a) 3 units (b) 4 units (c) 5 units (d) 2 units

    (ii) How far is the library from Shaguns house?

    (a) 3 units (b) 2 units (c) 5 units (d) 4 units

    (iii) How far is the library from Alia's house?

    (a) 2 units (b) 3 units (c) 4 units (d) (d) None of these

    (iv) Which of the following is true?

    (a) ABC forms a scalene triangle (b) ABC forms an isosceles triangle
    (c) ABC forms an equilateral triangle (d) None of these

    (v) How far is the school from Alia's house than Shaguns house?

    (a) \(\sqrt(13)\) units (b) \(\sqrt(5)\) units (c) (\(\sqrt(13)\) + \(\sqrt(5)\) )units (d) (\(\sqrt(13)\) - \(\sqrt(5)\) ) units
  • 3)

    A person is riding his bike on a straight road towards East from his college to city A and then to city B. At some point in between city A and city B, he suddenly realises that there is not enough petrol for the journey. Also, there is no petrol pump on the road between these two cities.

    Based on the above information, answer the following questions.
    (i) The value of y is equal to

    (a) 2 (b) 3 (c) 4 (d) 5

    (ii) The value of x is equal to

    (a) 4 (b) 5 (c) 8 (d) 7

    (iii) If M is any point exactly in between city A and city B, then coordinates of M are

    (a) 3,3 (b) 4,4 (c) 5,5 (d) 6,6

    (iv) The ratio in which A divides the line segment joining the points O and M is

    (a) 1:2 (b) 2.1 (c) 3.2 (d) 2.3

    (v) If the person analyse the petrol at the point M(the mid point of AB), then what should be his decision?

    (a) Should he travel back to college (b) Should try his luck to move towards city B
    (c) Should be travel back to city A (d) None of these
  • 4)

    Satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of x and y-axes. If we go 2 em east and 3 em north from the house, then we reach to a Grocery store. If we go 4 em west and 6 em south from the house, then we reach to a Electrician's shop. If we go 6 em east and 8 em south from the house, then we reach to a food cart. If we go 6 em west and 8 em north from the house, then we reach to a bus stand.

    Based on the above information, answer the following questions.
    (i) The distance between grocery store and food cart is

    (a) 12 cm (b) 15 cm (c) 18 cm (d) none of these

    (ii) The distance of the bus stand from the house is

    (a) 5 cm (b) 10 cm (c) 12 cm (d) 15 cm

    (iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is

    (a) 3.2 (b) 2.3 (c) 1.2 (d) 2.1

    (iv) The ratio of distances of house from bus stand to food cart is

    (a) 1.2 (b) 2.1 (c) 1.1 (d) none of these

    (v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a

    (a) rectangle (b) parallelogram (c) square  (d) none of these
  • 5)

    A round clock is traced on a graph paper as shown below. The boundary intersect the coordinate axis at a distance of 4/3 units from origin.

    Based on the above information, answer the following questions .
    (i) Circle intersect the positive y-axis at 

    \(A\left(\frac{2}{3}, 0\right),\) \((b) \left(0, \frac{2}{3}\right)\) \((c) \left(0, \frac{4}{3}\right)\) \((d) \left(\frac{4}{3}, 0\right)\)

    (ii) The centre of circle is the

    (a) mid-point of points of intersection with x-axis (b) mid-point of points of intersection with y-axis
    (c) both (a) and (b) (d) none of these

    (iii) The radius of the circle is

    \((a) \frac{4}{3} units\) \((b) \frac{3}{2} units\) \((c) \frac{2}{3} units\) \((d) \frac{3}{4} units\)

    (iv) The area of the circle is

    \((a) 16 \pi^{2} sq. units\) \((b) \frac{16}{9} \pi sq. units\) \((c) \frac{4}{9} \pi^{2} sq. units\) \((d) 4 \pi sq. units\)

    (v) If \(\left(1, \frac{\sqrt{7}}{3}\right)\) is one of the ends of a diameter, then its other end is

    \((a) \left(-1, \frac{\sqrt{7}}{3}\right)\) \((b) \left(1,-\frac{\sqrt{7}}{3}\right)\) \((c) \left(1, \frac{\sqrt{7}}{3}\right)\) \((d) \left(-1,-\frac{\sqrt{7}}{3}\right)\)

Class 10th Maths - Triangles Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    In a classroom, students were playing with some pieces of cardboard as shown below.

    All of a sudden, teacher entered into classroom. She told students to arrange all pieces. On seeing this beautiful image, she observed that \(\Delta\) ADH is right angled triangle, which contains.

    (i) right triangles ABJ and IGH.
    (ii) quadrilateral GFJI
    (iii) squares JKLM and LCBK
    (iv) rectangles MLEF and LCDE.
    After observation, she ask certain questions to students. Help them to answer these questions.
    (i) If an insect (small ant) walks 24 m from H to F, then walks 6 m to reach at M, then walks 4 m to reach at L and finally crossing K, reached at J. Find the distance between initial and final position of insect.

    (a) 25m (b) 26m (c) 27m (d) 28m

    (ii) If m, n and r are the sides of right triangle ABJ, then which of the following can be correct?

    (a) m2+n2= r2 (b) m2+n2+r2-=0
    (c) m2 + n2 = 2r2 (d) none of these

    (iii) If \(\Delta\)ABJ ~ \(\Delta\)ADH, then which similarity criterion is used here?

    (a) AA (b) SAS (c) AAS (d) SSS

    (iv) If  \(\angle\)ABJ = 90° and B, J are mid points of sides AD and AH respectively and BJ || DH, then which of the following option is false?

    \((a) \triangle A B J \sim \triangle A D H\) \((b) 2 B J=D H\) \((c) A J^{2}=J B^{2}+A B^{2}\) \((d) \frac{A B}{B D}=\frac{A J}{A H}\)

    (v) If \(\Delta\)PQR is right triangle with QM \(\perp\) PR, then which of the following is not correct?

    \((a) \Delta P M Q \sim \Delta P Q R\)
    \((b) Q R^{2}=P R^{2}-P Q^{2}\)
    \((c) P R^{2}=P Q+Q R\)
    \((d) \Delta P M Q \sim \Delta Q M R\)
  • 2)

    An aeroplane leaves an airport and flies due north at a speed of 1200km /hr. At the same time, another aeroplane leaves the same station and flies due west at the speed of 1500 km/hr as shown below. After \(1 \frac{1}{2}\) hr both the aeroplanes reaches at point P and Q respectively.

    (i) Distance travelled by aeroplane towards north after \(1 \frac{1}{2}\) hr is

    (a) 1800 km (b) 1500 km (c) 1400km (d) 1350 km

    (ii) Distance travelled by aeroplane towards west after  \(1 \frac{1}{2}\) hr is

    (a) 1600 km (b) 1800 km (c) 2250km (d) 2400 km

    (iii) In the given figure,\(\angle\)POQ is 

    (a) 70° (b) 90° (c) 80° (d) 100°

    (iv) Distance between aeroplanes after \(1 \frac{1}{2}\) hr is

    \((a) 450 \sqrt{41} \mathrm{~km}\) \((b) 350 \sqrt{31} \mathrm{~km}\) \((c) 125 \sqrt{12} \mathrm{~km}\) \((d) 472 \sqrt{41} \mathrm{~km}\)

    (v) Area of \(\Delta\)POQ is

    (a) 185000km2 (b) 179000km2
    (c) 186000km2 (d) 2025000 km2
  • 3)

    Rohit's father is a mathematician. One day he gave Rohit an activity to measure the height of building. Rohit accepted the challenge and placed a mirror on ground level to determine the height of building. He is standing at a certain distance so that he can see the top of the building reflected from mirror. Rohit eye level is at 1.8m above ground. The distance of Rohit from mirror and that of building from mirror are 1.5 m and 2.5 m respectively.

    Based on the above information, answer the following questions.
    (i) Two similar triangles formed in the above figure is

    \((a) \Delta A B M and \Delta C M D\) \((b) \Delta A M B and \Delta C D M\) \((c) \Delta A B M and \Delta C D M\) (d) None of these

    (ii) Which criterion of similarity is applied here?

    (a) AA similarity criterion (b) SSS similarity criterion
    (c) SAS similarity criterion (d) ASA similarity criterion

    (iii) Height of the building is

    (a) 1m (b) 2m (c) 3m (d) 4m

    (iv) In \(\Delta\)ABM, if LBAM = 30°, then LMCD is equal to 

    (a) 40° (b) 30° (c) 65° (d) 90°

    (v) If \(\Delta\)ABM and \(\Delta\)CDMare similar where CD = 6 ern, MD = 8 cm and BM = 24 ern, then AB is equal to 

    (a) 16cm (b) 18cm (c) 12cm (d) 14cm
  • 4)

    Meenal was trying to find the height of tower near his house. She is using the properties of similar triangles. The height of Meenal's house is 20 m. When Meenal's house casts a shadow of 10m long on the ground, at the same time, tower casts a shadow of 50 m long and Arun's house casts a shadow of 20 m long on the ground as shown below.

    Based on the above information, answer the following questions.
    (i) What is the height of tower?

    (a) 100 m (b) 50 m (c) 15 m (d) 45 m

    (ii) What will be the length of shadow of tower when Meenal's house casts a shadow of 15 m? 

    (a) 45 m (b) 70 m (c) 75 m (d) 72 m

    (iii) Height of Aruns house is 

    (a) 80 m (b) 75 m (c) 60 m (d) 40 m

    (iv) If tower casts a shadow of 40 rn, then find the length of shadow of Arun's house 

    (a) 18 m (b) 17 m (c) 16 m (d) 14 m

    (v) If tower casts a shadow of 40 m, then what will be the length of shadow of Meenal's house? 

    (a) 7 m (b) 9 m (c) 4 m (d) 8 m
  • 5)

    In the backyard of house, Shikha has some empty space in the shape of a \(\Delta\)PQR. She decided to make it a garden. She divided the whole space into three parts by making boundaries AB and CD using bricks to grow flowers and
    vegetables where ABIICDIIQR as shown in figure.

    Based on the above information, answer the following questions.
    (i) The length of AB is

    (a) 3m (b) 4m (c) 5m (d) 6m

    (ii) The length of CD is 

    (a) 4m (b) 5m (c) 6m (d) 7m

    (iii) Area of whole empty land is 

    (a) 90 m2 (b) 60m2 (c) 32m2 (d) 72m2

    (iv) Area of \(\Delta\)PAB is 

    \((a) \frac{45}{4} \mathrm{~m}^{2}\) \((b) \frac{45}{8} \mathrm{~m}^{2}\) \((c) \frac{8}{45} \mathrm{~m}^{2}\) \((d) \frac{4}{45} \mathrm{~m}^{2}\)

    (v) Area of \(\Delta\)PCD is

    \((a) \frac{12}{245} \mathrm{~m}^{2}\) \((b) \frac{245}{12} \mathrm{~m}^{2}\) \((c) \frac{243}{8} \mathrm{~m}^{2}\) \((d) \frac{245}{8} \mathrm{~m}^{2}\)

     

Class 10th Maths - Arithmetic Progressions Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    In a pathology lab, a culture test has been conducted. In the test, the number of bacteria taken into consideration in various samples is all3-digit numbers that are divisible by 7, taken in order.

    On the basis of above information, answer the following questions.
    (i) How many bacteria are considered in the fifth sample?

    (a) 126 (b) 140 (c) 133 (d) 149

    (ii) How many samples should be taken into consideration?

    (a) 129 (b) 128 (c) 130 (d) 127

    (iii) Find the total number of bacteria in the first 10 samples.

    (a) 1365 (b) 1335 (c) 1302 (d) 1540

    (iv) How many bacteria are there in the 7th sample from the last?

    (a) 952 (b) 945 (c) 959 (d) 966

    (v) The number of bacteria in 50th sample is

    (a) 546 (b) 553 (c) 448 (d) 496
  • 2)

    In a class the teacher asks every student to write an example of A.P. Two friends Geeta and Madhuri writes their progressions as -5, -2, 1,4, ... and 187, 184, 181, .... respectively. Now, the teacher asks various students of the class the following questions on these two progressions. Help students to find the answers of the questions.

    (i) Find the 34th term of the progression written by Madhuri.

    (a) 286 (b) 88 (c) -99 (d) 190

    (ii) Find the sum of common difference of the two progressions.

    (a) 6 (b) -6 (c) 1 (d) 0

    (iii) Find the 19th term of the progression written by Geeta.

    (a) 49 (b) 59 (c) 52 (d) 62

    (iv) Find the sum of first 10 terms of the progression written by Geeta.

    (a) 85 (b) 95 (c) 110 (d) 200

    (v) Which term of the two progressions will have the same value?

    (a) 31 (b) 33 (c) 32 (d) 30
  • 3)

    Meenas mother start a new shoe shop. To display the shoes, she put 3 pairs of shoes in 1st row,S pairs in 2nd row, 7 pairs in 3rd row and so on.

    On the basis of above information, answer the following questions.
    (i) If she puts a total of 120 pairs of shoes, then the number of rows required are

    (a) 5 (b) 6 (c) 7 (d) 10

    (ii) Difference of pairs of shoes in 17th row and 10th row is

    (a) 7 (b) 14 (c) 21 (d) 28

    (iii) On next day, she arranges x pairs of shoes in 15 rows, then x =

    (a) 21 (b) 26 (c) 31 (d) 42

    (iv) Find the pairs of shoes in 30th row.

    (a) 61 (b) 67 (c) 56 (d) 59

    (v) The total number of pairs of shoes in 5th and 8th row is

    (a) 7 (b) 14 (c) 28 (d) 56
  • 4)

    Anuj gets pocket money from his father everyday. Out of the pocket money, he saves Rs 2.75 on first day, Rs 3 on second day, Rs 3.25 on third day and so on.
    On the basis of above information, answer the following questions .

    (i) What is the amount saved by Anuj on 14th day?

    (a) Rs 6.25 (b) Rs 6 (c) Rs 6.50 (d) Rs 6.75

    (ii) What is the total amount saved by Anuj in 8 days?

    (a) Rs 18 (b) Rs 33 (c) Rs 24 (d) Rs 29

    (iii) What is the amount saved by Anuj on 30th day?

    (a) Rs 10 (b) Rs 12.75 (c) Rs 10.25 (d) Rs 9.75

    (iv) What is the total amount saved by him in the month of June, if he starts savings from 1st June?

    (a) Rs 191 (b) Rs 191.25 (c) Rs 192 (d) Rs 192.5

    (v) On which day, he save tens times as much as he saved on day-I?

    (a) 9th (b) 99th (c) 10th (d) 100th
  • 5)

    In a board game, the number of sea shells in various cells forms an A.P. If the number of sea shells in the 3rd and 11th cell together is 68 and number of shells in 11th cell is 24 more than that of 3rd cell, then answer the following
    questions based on this data.
    (i) What is the difference between the number of sea shells in the 19th and 20th cells?

    (a) 2 (b) 3 (c) 8 (d) 7

    (ii) How many sea shells are there in the first cell?

    (a) 52 (b) 18 (c) 16 (d) 54

    (iii) How many total sea shells are there in first 13 cells?

    (a) 442 (b) 221 (c) 204 (d) Can't be determined

    (iv) Altogether, how many sea shells are there in the first 5 cells?

    (a) 220 (b) 125 (c) 96 (d) 110

    (v) What is the sum of number of sea shells in the 7th and 9th cell?

    (a) 42 (b) 32 (c) 74 (d) 80

     

     

Class 10th Maths - Quadratic Equations Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    A quadratic equation can be defined as an equation of degree 2. This means that the highest exponent of the polynomial in it is 2. The standard form of a quadratic equation is ax2+ bx + c = 0, where a, b, and c are real numbers and \(a \neq 0\) Every quadratic equation has two roots depending on the nature of its discriminant, D = b2 - 4ac.Based on the above information, answer the following questions.
    (i) Which of the following quadratic equation have no real roots?

    \((a) -4 x^{2}+7 x-4=0\) \((b) -4 x^{2}+7 x-2=0\)
    \((c) -2 x^{2}+5 x-2=0\) \((d) 3 x^{2}+6 x+2=0\)

    (ii) Which of the following quadratic equation have rational roots?

    \((a) x^{2}+x-1=0\) \((b) x^{2}-5 x+6=0\)
    \((c) 4 x^{2}-3 x-2=0\) \((d) 6 x^{2}-x+11=0\)

    (iii) Which of the following quadratic equation have irrational roots?

    \((a) 3 x^{2}+2 x+2=0\) \((b) 4 x^{2}-7 x+3=0\)
    \((c) 6 x^{2}-3 x-5=0\) \((d) 2 x^{2}+3 x-2=0\)

    (iv) Which of the following quadratic equations have equal roots?

    \((a) x^{2}-3 x+4=0\) \((b) 2 x^{2}-2 x+1=0\)
    \((c) 5 x^{2}-10 x+1=0\) \((d) 9 x^{2}+6 x+1=0\)

    (v) Which of the following quadratic equations has two distinct real roots?

    \((a) x^{2}+3 x+1=0\) \((b) -x^{2}+3 x-3=0\)
    \((c) 4 x^{2}+8 x+4=0\) \((d) 3 x^{2}+6 x+4=0\)
  • 2)

    In our daily life we use quadratic formula as for calculating areas, determining a product's profit or formulating the speed of an object and many more.
    Based on the above information, answer the following questions.
    (i) If the roots of the quadratic equation are 2, -3, then its equation is

    (a) x2 - 2x + 3 = 0 (b) x+ x - 6 = 0 (c) 2x2 - 3x + 1 = 0 (d) x2 - 6x - 1= 0

    (ii) If one root of the quadratic equation 2x2 + kx + 1 = 0 is -1/2, then k =

    (a) 3 (b) -5 (c) -3 (d) 5

    (iii) Which of the following quadratic equations, has equal and opposite roots?

    (a) x- 4=0 (b) 16x- 9=0 (c) 3x+ 5x - 5=0 (d) Both (a) and (b)

    (iv) Which of the following quadratic equations can be represented as (x - 2)2 + 19 = 0?

    (a) x+ 4x+15=0 (b) x- 4x+15=0 (c) x2 - 4x+23=0 (d) x2 + 4x+23=0

    (v) If one root of a qua drraattiic equation is \(\frac{1+\sqrt{5}}{7}\),then I.ts other root is

    \((a) \frac{1+\sqrt{5}}{7}\) \((b) \frac{1-\sqrt{5}}{7}\) \((c) \frac{-1+\sqrt{5}}{7}\) \((d) \frac{-1-\sqrt{5}}{7}\)
  • 3)

    Quadratic equations started around 3000 B.C. with the Babylonians. They were one of the world's first civilisation, and came up with some great ideas like agriculture, irrigation and writing. There were many reasons why Babylonians needed to solve quadratic equations. For example to know what amount of crop you can grow on the square field;
    Based on the above information, represent the following questions in the form of quadratic equation.
    (i) The sum of squares of two consecutive integers is 650.

    (a) x2 + 2x - 650=0 (b) 2x2 + 2x - 649=0 (c) x2 - 2x - 650=0 (d) 2x2 + 6x - 550=0

    (ii) The sum of two numbers is 15 and the sum of their reciprocals is 3/10.

    (a) x2+ 10x-150=0 (b) 15x2-x + 150=0 (c) x2-15x + 50=0 (d) 3x2 - 10x + 15 = 0

    (iii) Two numbers differ by 3 and their product is 504.

    (a) 3x2- 504=0 (b) x2- 504x+3=0 (c) 504x2+3=x (d) x2 + 3x - 504 = 0

    (iv) A natural number whose square diminished by 84 is thrice of 8 more of given number.

    (a) x2 + 8x-84=0 (b) 3x2 - 84x+3=0 (c) x2 -3x-108=0 (d) x2 -11x+60=0

    (v) A natural number when increased by 12, equals 160 times its reciprocal.

    (a) x2 - 12x + 160 = 0 (b) x2 - 160x + 12 = 0 (c) 12x2 - x - 160 = 0 (d) x2 + 12x - 160 = 0

     

     

     

  • 4)

    Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of \(a x^{2}+b x+c \text { be }(p x+q) \text { and }(r x+s)\)
    \(\therefore a x^{2}+b x+c=(p x+q)(r x+s)=p r x^{2}+(p s+q r) x+q s .\)

    Now, factorize each of the following quadratic equations and find the roots.
    (i) 6x2 + x - 2 = 0

    \((a) 1,6\) \((b) \frac{1}{2}, \frac{-2}{3}\) \((c) \frac{1}{3}, \frac{-1}{2}\) \((d) \frac{3}{2},-2\)

    (ii) 2x2-+ x - 300 = 0

    \((a) 30, \frac{2}{15}\) \((b) 60, \frac{-2}{5}\) \((c) 12, \frac{-25}{2}\) (d) None of these

    (iii) x2-  8x + 16 = 0

    (a) 3,3 (b) 3,-3 (c) 4,-4 (d) 4,4

    (iv) 6x2-  13x + 5 = 0

    \((a) 2, \frac{3}{5}\) \((b) -2, \frac{-5}{3}\) \((c) \frac{1}{2}, \frac{-3}{5}\) \((d) \frac{1}{2}, \frac{5}{3}\)

    (v) 100x2- 20x + 1 = 0

    \((a) \frac{1}{10}, \frac{1}{10}\) \((b) -10,-10\) \((c) -10, \frac{1}{10}\) \((d) \frac{-1}{10}, \frac{-1}{10}\)

     

  • 5)

    If p(x) is a quadratic polynomial i.e., p(x) = ax2- + bx + c, \(a \neq 0\), then p(x) = 0 is called a quadratic equation. Now, answer the following questions.
    (i) Which of the following is correct about the quadratic equation ax2- + bx + c = 0 ?

    (a) a, band c are real numbers, \(c \neq 0\) (b) a, band c are rational numbers, \(a \neq 0\)
    (c) a, band c are integers, a, band \(c \neq 0\) (d) a, band c are real numbers, \(a \neq 0\)

    (ii) The degree of a quadratic equation is

    (a) 1 (b) 2 (c) 3 (d) other than 1

    (iii) Which of the following is a quadratic equation?

    (a) x(x + 3) + 7 = 5x - 11 (b) (x - 1)2 - 9 = (x - 4)(x + 3)
    (c) x2-(2x + 1) - 4 = 5x2- 10 (d) x(x - 1)(x + 7) = x(6x - 9)

    (iv) Which of the following is incorrect about the quadratic equation ax2- + bx + c = 0 ?

    (a) If a\(\alpha\)2 + b\(\alpha\). + c = 0, then x = -\(\alpha\) is the solution of the given quadratic equation.
    (b)The additive inverse of zeroes of the polynomial ax2- + bx + c is the roots of the given equation.
    (c) If a is a root of the given quadratic equation, then its other root is -\(\alpha\).
    (d) All of these

    (v) Which of the following is not a method of finding solutions of the given quadratic equation?

    (a) Factorisation method (b) Completing the square method
    (c) Formula method (d) None of these

Class 10th Maths - Pair of Linear Equation in Two Variables Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    A part of monthly hostel charges in a college is fixed and the remaining depends on the number of days one has taken food in the mess. When a student Anu takes food for 25 days, she has to pay Rs 4500 as hostel charges, whereas another student Bindu who takes food for 30 days, has to pay Rs 5200 as hostel charges.

    Considering the fixed charges per month by Rs x and the cost of food per day by Rs y, then answer the following questions.
    (i) Represent algebraically the situation faced by both Anu and Bindu.

    (a) x + 25y = 4500, x + 30y = 5200 (b) 25x + y = 4500, 30x + Y = 5200
    (c) x - 25y = 4500, x - 30y = 5200 (d) 25x - y = 4500, 30x - Y = 5200

    (ii) The system of linear equations, represented by above situations has

    (a) No solution (b) Unique solution
    (c) Infinitely many solutions (d) None of these

    (iii) The cost of food per day is

    (a) Rs 120 (b) Rs 130 (c) Rs 140 (d) Rs 1300

    (iv) The fixed charges per month for the hostel is

    (a) Rs 1500 (b) Rs 1200 (c) Rs 1000 (d) Rs 1300

    (v) If Bindu takes food for 20 days, then what amount she has to pay?

    (a) Rs 4000 (b) Rs 3500 (c) Rs 3600 (d) Rs 3800
  • 2)

    From Bengaluru bus stand, if Riddhima buys 2 tickets to Malleswaram and 3 tickets to Yeswanthpur, then total cost is Rs 46; but if she buys 3 tickets to Malleswaram and 5 tickets to Yeswanthpur, then total cost is Rs 74.

    Consider the fares from Bengaluru to Malleswaram and that to Yeswanthpur as Rs x and Rs y respectively and answer the following questions.
    (i) 1st situation can be represented algebraically as

    (a) 3x-5y=74 (b) 2x+5y=74 (c) 2x-3y=46 (d) 2x+3y=46

    (ii) 2nd situation can be represented algebraically as

    (a) 5x + 3y = 74 (b) 5x- 3y= 74 (c) 3x + 5y = 74 (d) 3x-5y=74

    (iii), Fare from Ben~aluru to Malleswaram is

    (a) Rs 6 (b) Rs 8 (c) Rs 10 (d) Rs 2

    (iv) Fare from Bengaluru to Yeswanthpur is

    (a) Rs 10 (b) Rs 12 (c) Rs 14 (d) Rs 16

    (v) The system oflinear equations represented by both situations has

    (a) infinitely many solutions (b) no solution
    (c) unique solution (d) none of these
  • 3)

    Points A and B representing Chandigarh and Kurukshetra respectively are almost 90 km apart from each other on the highway. A car starts from Chandigarh and another from Kurukshetra at the same time. If these cars go in the same direction, they meet in 9 hours and if these cars go in opposite direction they meet in 9/7 hours. Let X and Ybe two cars starting from points A and B respectively and their speed be x km/hr and y km/hr respectively.

    Then, answer the following questions.
    (i) When both cars move in the same direction, then the situation can be represented algebraically as

    (a) x - y = 10 (b) x + y = 10 (c) x + y = 9 (d) x - y = 9

    (ii) When both cars move in opposite direction, then the situation can be represented algebraically as

    (a) x - y=70 (b) x + y=90 (c) x + y=70 (d) x + y=10

    (iii) Speed of car X is

    (a) 30 km/hr (b) 40 km/hr (c) 50 km/hr (d) 60 km/hr

    (iv) Speed of car Y is

    (a) 50km//hr (b) 40 km/hr (c) 30 km/hr (d) 60 km/hr

    (v) If speed of car X and car Y, each is increased by 10 km/hr, and cars are moving in opposite direction, then after how much time they will meet?

    (a) 5 hrs (b) 4 hrs (c) 2 hrs (d) 1 hr
  • 4)

    Mr Manoj Jindal arranged a lunch party for some of his friends. The expense of the lunch are partly constant and partly proportional to the number of guests. The expenses amount to Rs 650 for 7 guests and Rs 970 for 11 guests .

    Denote the constant expense by Rs x and proportional expense per person by Rs y and answer the following questions.
    (i) Represent both the situations algebraically.

    (a) x + 7y = 650, x + 11y = 970 (b) x - 7y = 650, x - 11y = 970
    (c) x+ 11y=650,x+7y=970 (d) 11x + 7y = 650, 11x - 7y = 970

    (ii) Proportional expense for each person is

    (a) Rs 50 (b) Rs 80 (c) Rs 90 (d) Rs 100

    (iii) The fixed (or constant) expense for the party is

    (a) Rs 50 (b) Rs 80 (c) Rs 90 (d) Rs 100

    (iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

    (a) Rs 1500 (b) Rs 1300 (c) Rs 1200 (d) Rs 1290

    (v) The system of linear equations representing both the situations will have

    (a) unique solution (b) no solution
    (c) infinitely many solutions (d) none of these
  • 5)

    In a office, 8 men and 12 women together can finish a piece of work in 10 days, while 6 men and 8 women together can finish it in 14 days. Let one day's work of a man be l/x and one day's work of a woman be 1/y.

    Based on the above information, answer the following questions.
    (i) 1st situation can be represented algebraically as

    \((a) \frac{80}{x}-\frac{120}{y}=1\) \((b) \frac{120}{x}-\frac{80}{y}=1\) \((c) \frac{120}{x}+\frac{80}{y}=1\) \((d) \frac{80}{x}+\frac{120}{y}=1\)

    (ii) 2nd situation can be represented algebraically as

    \((a) \frac{112}{x}-\frac{84}{y}=1\) \((b) \frac{84}{x}-\frac{112}{y}=1\) \((c) \frac{84}{x}+\frac{112}{y}=1\) \((d) \frac{112}{x}+\frac{84}{y}=1\)

    (iii) One woman alone can finish the work in

    (a) 220 days (b) 140 days (c) 280 days (d) 160 days

    (iv) One man alone can finish the work in

    (a) 140 days (b) 220 days (c) 160 days (d) 280 days

    (v) If 14 men and 28 women work together, then in what time, the work will be completed?

    (a) 2 days (b) 3 days (c) 4 days (d) 5 days

Class 10th Maths - Polynomials Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    ABC construction company got the contract of making speed humps on roads. Speed humps are parabolic in shape and prevents overspeeding, mini mise accidents and gives a chance for pedestrians to cross the road. The mathematical representation of a speed hump is shown in the given graph.

    Based on the above information, answer the following questions.
    (i) The polynomial represented by the graph can be _______polynomial.

    (a) Linear (b) Quadratic
    (c) Cubic (d) Zero

    (ii) The zeroes of the polynomial represented by the graph are

    (a) 1,5 (b) 1,-5
    (c) -1,5 (d) -1,-5

    (iii) The sum of zeroes of the polynomial represented by the graph are

    (a) 4 (b) 5 (c) 6 (d) 7

    (iv) If a and β are the zeroes of the polynomial represented by the graph such that \(\beta>\alpha, \text { then }|8 \alpha+\beta|=\)

    (a) 1 (b) 2 (c) 3 (d) 4

    (v) The expression of the polynomial represented by the graph is

    \(\text { (a) }-x^{2}-4 x-5\) \((b) x^{2}+4 x+5\) \((c) x^{2}+4 x-5\) \((d) -x^{2}+4 x+5\)
  • 2)

    While playing in garden, Sahiba saw a honeycomb and asked her mother what is that. She replied that it's a honeycomb made by honey bees to store honey. Also, she told her that the shape of the honeycomb formed is parabolic. The mathematical representation of the honeycomb structure is shown in the graph.

    Based on the above information, answer the following questions.
    (i) Graph of a quadratic polynomial is in___________shape.

    (a) straight line (b) parabolic
    (c) circular (d) None of these

    (ii) The expression of the polynomial represented by the graph is

    (a) x2-49 (b) x2-64 (c) x2-36 (d) x2-81

    (iii) Find the value of the polynomial represented by the graph when x = 6.

    (a) -2 (b) -1 (c) 0 (d) 1

    (iv) The sum of zeroes of the polynomial x2 + 2x - 3 is

    (a) -1 (b) -2 (c) 2 (d) 1

    (v) If the sum of zeroes of polynomial at2 + 5t + 3a is equal to their product, then find the value of a.

    (a) -5 (b) -3 \(\text { (c) } \frac{5}{3}\) \(\text { (d) } \frac{-5}{3}\)
  • 3)

    Just before the morning assembly a teacher of kindergarten school observes some clouds in the sky and so she cancels the assembly. She also observes that the clouds has a shape of the polynomial. The mathematical representation of a cloud is shown in the figure.

    (i) Find the zeroes of the polynomial represented by the graph.

    (a) -1/2,7/2 (b) 1/2, -7/2 (c) -1/2, -7/2 (d) 1/2,7/2

    (ii) What will be the expression for the polynomial represented by the graph?

    \((a) p(x)=12 x^{2}-4 x-7\) \((b) p(x)=-x^{2}-12 x+3\) \((c) p(x)=4 x^{2}+12 x+7\) \((d) p(x)=-4 x^{2}-12 x+7\)

    (iii) What will be the value of polynomial represented by the graph, when x = 3?

    (a) 65 (b) -65 (c) 68 (d) -68

    (iv) If a and \(\beta\) are the zeroes of the polynomial \(f(x)=x^{2}+2 x-8 \text { , then } \alpha^{4}+\beta^{4}=\)

    (a) 262 (b) 252 (c) 272 (d) 282

    (v) Find a quadratic polynomial where sum and product of its zeroes are 0,\(\sqrt (7)\) respectively.

    \((a) k\left(x^{2}+\sqrt{7}\right)\) \((b) k\left(x^{2}-\sqrt{7}\right)\) \((c) k\left(x^{2}+\sqrt{5}\right)\) (d) none of these
  • 4)

    Pankaj's father gave him some money to buy avocado from the market at the rate of p(x) = x- 24x + 128. Let a , \(\beta\) are the zeroes of p(x).
    Based on the above information, answer the following questions.

    (i) Find the value of a and \(\beta\), where a < \(\beta\).

    (a) -8, -16 (b) 8,16 (c) 8,15 (d) 4,9

    (ii) Find the value of \(\alpha\) + \(\beta\)\(\alpha\)\(\beta\).

    (a) 151 (b) 158 (c) 152 (d) 155

    (iii) The value of p(2) is

    (a) 80 (b) 81 (c) 83 (d) 84

    (iv) If \(\alpha\) and \(\beta\) are zeroes of \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)

    (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/5

    (v) If sum of zeroes of \(q(x)=k x^{2}+2 x+3 k\) is equal to their product, then k =

    (a) 2/3 (b) 1/3 (c) -2/3 (d) -1/3
  • 5)

    Two friends Trisha and Rohan during their summer vacations went to Manali. They decided to go for trekking. While trekking they observes that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph.

    Based on the above information, answer the following questions.
    (i) The zeroes of the polynomial whose graph is given, are

    (a) 4,7  (b) -4,7  (c) 4,3 (d) 7,10

    (ii) What will be the expression of the given polynomial p(x)?

    \((a) x^{2}-3 x+\mathbf{3} 8\) \((b) -x^{2}+4 x+28\) \((c) x^{2}-4 x+28\) \((d) -x^{2}+3 x+28\)

    (iii) Product of zeroes of the given polynomial is

    (a) -28  (b) 28 (c) -30 (d) 30

    (iv) The zeroes of the polynomial 9x2 - 5 are

    \((a) \frac{3}{\sqrt{5}}, \frac{-3}{\sqrt{5}}\) \((b) \frac{2}{\sqrt{5}}, \frac{-2}{\sqrt{5}}\) \((c) \frac{\sqrt{5}}{3}, \frac{-\sqrt{5}}{3}\) \((d) \frac{\sqrt{5}}{2}, \frac{-\sqrt{5}}{2}\)

    (v) If f(x) = x2 - 13x + 1, then f(4) =

    (a) 35  (b) -35 (c) 36 (d) -36

Class 10th Maths - Real Number Case Study Questions and Answers 2022 - 2023 - by Study Materials - View & Read

  • 1)

    Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.
    (i) For what value of n, 4ends in 0?

    (a) 10 (b) when n is even
    (c) when n is odd (d) no value of n

    (ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, an is a rational number?

    (a) when n is any even integer  (b) when n is any odd integer
    (c) for all n > 1  (d) only when n = 0

    (iii) If x and yare two odd positive integers, then which of the following is true?

    (a) x2 + y2 is even (b) x2 + y2 is not divisible by 4
    (c) x2 + y2 is odd (d) both (a) and (b)

    (iv) The statement 'One of every three consecutive positive integers is divisible by 3' is

    (a) always true (b) always false
    (c) sometimes true (d) None of these

    (v) If n is any odd integer, then n2 - 1 is divisible by

    (a) 22 (b) 55 (c) 88 (d) 8

     

  • 2)

    Real numbers are extremely useful in everyday life. That is probably one of the main reasons we all learn how to count and add and subtract from a very young age. Real numbers help us to count and to measure out quantities of different items in various fields like retail, buying, catering, publishing etc. Every normal person uses real numbers in his daily life. After knowing the importance of real numbers, try and improve your knowledge about them by answering the following questions on real life based situations.
    (i) Three people go for a morning walk together from the same place. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance travelled when they meet at first time after starting the walk assuming that their walking speed is same?

    (a) 6120 cm (b) 12240 cm (c) 4080 cm (d) None of these

    (ii) In a school Independence Day parade, a group of 594 students need to march behind a band of 189 members. The two groups have to march in the same number of columns. What is the maximum number of columns in which they can march?

    (a) 9 (b) 6 (c) 27 (d) 29

    (iii) Two tankers contain 768litres and 420 litres of fuel respectively. Find the maximum capacity of the container which can measure the fuel of either tanker exactly.

    (a) 4litres (b) 7litres (c) 12litres (d) 18litres

    (iv) The dimensions of a room are 8 m 25 cm, 6 m 75 crn and 4 m 50 cm. Find the length of the largest measuring rod which can measure the dimensions of room exactly.

    (a) 1 m 25cm (b) 75cm (c) 90cm (d) 1 m 35cm

    (v) Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads

    (a) 3 and 2 (b) 2 and 5 (c) 3 and 4 (d) 4 and 5

     

  • 3)

    In a classroom activity on real numbers, the students have to pick a number card from a pile and frame question on it if it is not a rational number for the rest of the class. The number cards picked up by first 5 students and their questions on the numbers for the rest of the class are as shown below. Answer them.
    (i) Suraj picked up \(\sqrt{8}\) and his question was - Which of the following is true about \(\sqrt{8}\)?

    (a) It is a natural number (b) It is an irrational number
    (c) It is a rational number (d) None of these

    (ii) Shreya picked up 'BONUS' and her question was - Which of the following is not irrational?

    (a) 3-4\(\sqrt{5}\) (b) \(\sqrt{7}\) -6 (c) 2+2\(\sqrt{9}\) (d) 4\(\sqrt{11}\)-6

    (iii) Ananya picked up \(\sqrt{5}\)  -.\(\sqrt{10}\) and her question was - \(\sqrt{5}\)  -.\(\sqrt{10}\) _________is number.

    (a) a natural (b) an irrational (c) a whole (d) a rational

    (iv) Suman picked up \(\frac{1}{\sqrt{5}}\) and her question was - \(\frac{1}{\sqrt{5}}\) is __________ number.

    (a) a whole (b) a rational (c) an irrational (d) anatural

    (v) Preethi picked up \(\sqrt{6}\) and her question was - Which of the following is not irrational?

    (a) 15 + 3\(\sqrt{6}\) (b) \(\sqrt{24}\)- 9 (c) 5.\(\sqrt{150}\) (d) None of these

     

  • 4)

    Decimal form of rational numbers can be classified into two types.
    (i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form \(\frac{p}{\sqrt{q}}\) where p and q are co-prime and the prime faetorisation of q is of the form 2n·5m, where n, mare non-negative integers and vice-versa.
    (ii) Let x = \(\frac{p}{\sqrt{q}}\) be a rational number, such that the prime faetorisation of q is not of the form 2n 5m, where n and m are non-negative integers. Then x has a non-terminating repeating decimal expansion.
    (i) Which of the following rational numbers have a terminating decimal expansion?

    (a) 125/441 (b) 77/210 (c) 15/1600 (d) 129/(22 x 52 x 72)

    (ii) 23/(23 x 52) =

    (a) 0.575 (b) 0.115 (c) 0.92 (d) 1.15

    (iii) 441/(22 x 57 x 72) is a_________decimal.

    (a) terminating (b) recurring
    (c) non-terminating and non-recurring (d) None of these

    (iv) For which of the following value(s) of p, 251/(23 x p2) is a non-terminating recurring decimal?

    (a) 3 (b) 7 (c) 15 (d) All of these

    (v) 241/(25 x 53) is a _________decimal.

    (a) terminating (b) recurring
    (c) non-terminating and non-recurring (d) None of these

     

  • 5)

    HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. Based on the above information answer the following questions.
    (i) If two positive integers x and yare expressible in terms of primes as x = p2q3 and y = p3 q, then which of the following is true?

    (a) HCF = pq2 x LCM (b) LCM = pq2 x HCF
    (c) LCM = p2q x HCF (d) HCF = p2q x LCM

    (ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p?

    (a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

    (iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.

    (a) 3 (b) 1 (c) 34 (d) 17

    (iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600.

    (a) 12600 (b) 12599 (c) 12601 (d) 12500

    (v) If A, Band C are three rational numbers such that 85C - 340A :::109, 425A + 85B = 146, then the sum of A, B and C is divisible by

    (a) 3 (b) 6 (c) 7 (d) 9

10th standard CBSE Mathematics Public Model Question Paper IV 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    If ax2 + bx + c , a≠0 is factorizable into product of two linear factors, then roots of ax2 + bx + c = 0 can be found by equating each factor to

  • 2)

    If p, q, r, s, t are the terms of an A.P. with common difference -1 the relation between p and t is

  • 3)

    From a point A, the length of a tangent to a circle is 8cm and distance of A from the circle is 10cm. The length of the diameter of the circle is

  • 4)

    In which of the following ratios a line segment cannot be divided using ruler and compass?

  • 5)

    If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is

10th standard CBSE Mathematics Public Model Question Paper III 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    If the length of the rectangle is one more than the twice its width, and the area of the rectangle is 300 square meter. What is the measure of the width of the rectangle?

  • 2)

    How many terms of AP 54, 51, 48… are required to give a sum of 513

  • 3)

    The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:

  • 4)

    In the figure, P divides AB internally in the ratio

  • 5)

    The ——– is the line drawn from the eye of an observer to the point in the object viewed by the observer

10th standard CBSE Mathematics Public Model Question Paper II 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    The same value of x satisfies the equations 4x + 5 = 0 and 4x2 + (5 + 3p)x + 3p2=0, then p is

  • 2)

    The nth term of the AP 9, 13, 17, 21, 25, ………….. is:

  • 3)

    If radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle which is tangent to the other circle, is

  • 4)

    If TP and TQ are two tangents to a circle with centre O so that angle POQ = 110o then angle PTQ is equal to

  • 5)

    In the following figure α is

10th standard CBSE Mathematics Public Model Question Paper I 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    The solution of x2 + 4x + 4 = 0 is

  • 2)

    The 8th term of 117, 104, 91, 78, …….is.....

  • 3)

    In fig., two circles with centres A and B touch each other externally at k. The length of PQ (in cm) is

  • 4)

    In drawing triangle ABC, it is given that AB = 3 cm, BC = 2 cm and AC = 6 cm. It is not possible to draw the triangle as:

  • 5)

    The figure shows the observation of point C from point A. The angle of depression from A is:

10th standard CBSE Mathematics Public Model Question Paper V 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    The roots of quadratic equation x2 – 9 = 0 are

  • 2)

    The first and last terms of an AP are 1 and 11. If the sum of all its terms is 36, then the number of terms will be

  • 3)

    in figure , if ㄥAOB = 125o, then ㄥCOD is equal to

  • 4)

    In the given figure, AC: CB is

  • 5)

    An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is

10th standard CBSE Mathematics Public Model Question Paper IV 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    If  1/2 is a root of the equation x+ kx-5/4 = 0 then the other root of the quadratic equation is

  • 2)

    A tree in each year grows 4cm less than it grew in previous year. If it grew 1 metre in the first year, in how many years will it have ceased growing and what will be its height then,

  • 3)

    The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:

  • 4)

    PT and PS are tangents drawn to a circle, with cantre C, from a point P. If ∠TPS = 50° , then the measure of ΔTCS is

  • 5)

    If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is

10th standard CBSE Mathematics Public Model Question Paper III 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    The roots of quadratic equation x2 – 9 = 0 are

  • 2)

    Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011

  • 3)

    In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to

  • 4)

    Given a triangle with side AB = 8 cm. To get a line segment AB’ = 3/4 of AB, it is required to divide the line segment AB in the ratio:

  • 5)

    Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

10th standard CBSE Mathematics Public Model Question Paper II 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    The roots of quadratic equation x2 – 9 = 0 are

  • 2)

    Which term of the A.P. 1, 4, 7 … is 88?

  • 3)

     PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120°, then ∠OPQ is

  • 4)

    If four sides of a quadrilateral ABCD are tangential to a circle, then

  • 5)

    Find AB in the given figure

10th standard CBSE Mathematics Public Model Question Paper I 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    The equation 4x2 = 4x has following solution/solutions

  • 2)

    If p, q, r, s, t are the terms of an A.P. with common difference -1 the relation between p and t is

  • 3)

    A circle can pass through

  • 4)

    Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

    \(\frac { A'B }{ AB } =\frac { A'C }{ AC } =\frac { BC' }{ BC } =\frac { 3 }{ 4 } \)
    \(\frac { A'B }{ AB } =\frac { A'C' }{ AC } =\frac { BC' }{ BC' } =\frac { 3 }{ 4 } \)
    \(\frac { A'B }{ AB } =\frac { A'C' }{ AC } =\frac { BC' }{ BC } =\frac { 4 }{ 3 } \)
    \(\frac { A'B }{ AB } =\frac { A'C' }{ AC } =\frac { BC }{ BC' } =\frac { 4 }{ 2 } \)

  • 5)

    If the angle of elevation of a cloud from a point 100 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is

10th standard CBSE Mathematics Board Exam Model Question Paper IV 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    In the triangles PQR and NLM, angle M will be

  • 2)

    Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?

  • 3)

    A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, total surface area which is exposed to the surroundings is

  • 4)

    A rational number can be expressed as a terminating decimal if its denominator has factors

  • 5)

    To construct a triangle similar to a given triangle as per given scale factor which may be __________ than or may be __________ than 1.

10th standard CBSE Mathematics Board Exam Model Question Paper II 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    In the triangles PQR and NLM, angle M will be

  • 2)

    Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?

  • 3)

    A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, total surface area which is exposed to the surroundings is

  • 4)

    A rational number can be expressed as a terminating decimal if its denominator has factors

  • 5)

    To construct a triangle similar to a given triangle as per given scale factor which may be __________ than or may be __________ than 1.

10th standard CBSE Mathematics Board Exam Model Question Paper III 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    In the figure, AE is the bisector of exterior angle CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then CE is equal to

  • 2)


    In the above fig Q and α respectively are

     

  • 3)

    A bucket is in the form of a frustum of a cone ad holds 28.490 liters of water. The radii of the top and bottom are 28cm and 21cm respectively. Find the height of the bucket.

  • 4)

    Which of the following rational numbers has a denominator that can be expressed as a product of powers of 2 and 5?

  • 5)

    Find the next term of the series \(\sqrt { 2 } ,\sqrt { 8 } ,\sqrt { 18 } ,\sqrt { 32 } ....\)

10th standard CBSE Mathematics Board Exam Model Question Paper IV 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    If four sides of a quadrilateral ABCD are tangential to a circle, then

  • 2)

    Find AB in the given figure

  • 3)

    In the figure, the shape of a solid copper piece (made of two pieces) with dimensions as shown. The face ABCDEFA has uniform cross section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece.

  • 4)

    The prime factorization of 184 is

  • 5)

    The sum of all the angles of a triangle is________________

10th standard CBSE Mathematics Board Exam Model Question Paper V 2019-2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    In the triangles PQR and NLM, angle M will be

  • 2)

    The angle formed by the line of sight with the horizontal, when the point being viewed is above the horizontal level is called:

  • 3)

    If the curved surface area of a right circular cylinder is 1760 cm2 and its radius is 10 cm, then what is its height?

  • 4)

    What is the HCF of 1076 and 584

  • 5)

    A Segment AB is divided at point P such that \(\frac { PB }{ AB } =\frac { 3 }{ 7 } \) then find the radio AP : PB.

10th standard CBSE Mathematics Board Exam Model Question Paper I 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    PT and PS are tangents drawn to a circle, with cantre C, from a point P. If ∠TPS = 50° , then the measure of ΔTCS is

  • 2)

    The length of shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of sun is :

  • 3)

    If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

  • 4)

    There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?

  • 5)

    The difference of any two sides of a triangle is always __________ than the third side.

10th standard CBSE Mathematics Board Exam Model Question Paper II 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    Given a triangle with side AB = 8 cm. To get a line segment AB’ = 3/4 of AB, it is required to divide the line segment AB in the ratio:

  • 2)

    If sun’s elevation is 60° then a pole of height 6 m will cast a shadow of length

  • 3)

    What is \(1-\sqrt { 3 } \)?

  • 4)

    A school has three sections of Class 10. They need to have enough books in the class library so that they can be distributed equally in the three sections . What is the minimum number of books required if the number of students in section A , B and C are 30, 32 and 36 respectively?

  • 5)

    The sum of any two sides of a triangle is always _____________ than the third side.

10th standard CBSE Mathematics Board Exam Model Question Paper III 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    In the triangles PQR and NLM, angle M will be

  • 2)

    The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60 m then, the height of the first tower is

  • 3)

    A sequence a1, a2, a3,.......... an, an+1,..... is called an A.P. If there exists constant d such that

  • 4)

    In the figure, if AB, AC and line I are tangents to the circle and semi-perimeter of  \(\triangle APQ\)= 14 cm, then AC = ___________cm.

  • 5)

    When are the two triangles said to be similar?

10th standard CBSE Mathematics Board Exam Model Question Paper IV 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is an acute angle and then points  are located at equal distances on the ray AX and the point B is joined to

  • 2)

    An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is

  • 3)

    If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is

  • 4)

    ‘a’ and ‘b’ are two prime numbers . What is their HCF

  • 5)

    The sum of all the angles of a triangle is________________

CBSE 10th Mathematics - Public Model Question Paper 2019 - 2020 - by QB365 - Question Bank Software - View & Read

  • 1)

    In the figure, P divides AB internally in the ratio

  • 2)

    Write the HCF of the smallest composite number and the smallest even number

  • 3)

    In reduced scale-factor, the geometric figure to be constructed is .______________in size.

  • 4)

    Three points A, B and C are collinear, if any one of the following takes place:
    ........... + AB = CB

  • 5)

    A right circular cylinder of radius r cm and height h cm (h>2r) just enclosed a sphere of diameter

CBSE 10th Mathematics - Arithmetic Progressions Model Question Paper - by QB365 - Question Bank Software - View & Read

  • 1)

    Amit starts his exercise regime with 25 push ups on Monday. He plans to increase 5 push ups every following Monday. How many push ups will he be doing on the 3rd Monday since he started?

  • 2)

    Which term of the A.P 10,8,6,… will be the first negative term?

  • 3)

    An AP has first term -3 and a common difference -1. Find the 3rd term of the A.

  • 4)

    Find the fifth term of an A.P whose first term is -1 and common difference is -3.

  • 5)

    If for an A.P sn= + 3n What is the nth term?

10th Standard CBSE Mathematics - Quadratic Equations Model Question Paper - by QB365 - Question Bank Software - View & Read

  • 1)

    The roots of quadratic equation x2 – 9 = 0 are

  • 2)

    If x = -2 is a root of equation x2 – 4x + K = 0 then value of K is

  • 3)

    Which of the following is not a quadratic equation?

  • 4)

    The condition for equation ax2 + bx + c = 0 to be quadratic is

  • 5)

    Solve 9x2= 36

CBSE 10th Mathematics - Full Syllabus One Mark Question Paper with Answer Key - by QB365 - Question Bank Software - View & Read

  • 1)

    If x = 1 is a root of equation x2 – Kx + 5 = 0 then value of K is

  • 2)

    Solve 9x2= 36

  • 3)

    The roots of quadratic equation x2 – 9 = 0 are

  • 4)

    The roots of quadratic equation ax² + bx + c = 0 is given by

  • 5)

    If 4 is a root of the equation x2 + 3x + k = 0 , then k is

Second quarter exam 2019 - by Ramu tuition centre - View & Read

  • 1)

    If the perimeter and area of a circle are numerically equal, then the radius of the circle is

  • 2)

    If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is

  • 3)

    The ratio of radii of two circles is in the ratio of 1:5. Calculate the ratio of their perimeters

  • 4)

    The area of a sector of a circle of radius 5 cm is 5 cm2. The angle contained by the sector will be

  • 5)

    The inner circumference of a circular track is 440m, and the track is 14m wide. The cost of levelling the track at 25 paise/m2 will be

SECOND QUARTERLY EXAM 2019 - by Ramu tuition centre - View & Read

  • 1)

    In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.

  • 2)

    in figure , if ㄥAOB = 125o, then ㄥCOD is equal to

  • 3)

    The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :

  • 4)

    Number of tangents, that can be drawn to a circle, parallel to a given chord is

  • 5)

    A circle can pass through

CBSE 10th Mathematics - Full Portion Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A motor boat whose speed is 24km/h in still water takes 1 hour more to go 32 km upstream than no return downstream to the same spot. Find the speed of the steam.

  • 2)

    If the pth terms of an AP is \(\frac{1}{q}\) and the qth term is \(\frac{1}{p}\), show that the sum of pq terms is \(\frac{1}{2}\) (pq + 1).

  • 3)

    Check graphically, whether the following pair of linear equations is consistent. If yes, solve it graphically.
    2x-y=0, x+y=0

  • 4)

    Solve the following pair of linear equations graphically:
    2x + 3y = 12 and x - y = 1.
    Find the area of the region bounded by the two lines representing the above equations and Y-axis.

CBSE 10th Mathematics - Full Portion Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Using quadratic formula, solve the following quadratic equation for x: 
    p2x2+(p2-q2)x-q2=0

  • 2)

    Find the roots of the following quadratic equation (if they exist) by the method of completing square \(5x^{2} - 6x-2 = 0\) .

  • 3)

    Find the numbers of terms in A.P.: 5, 12, 19, 28, ....., 159.

  • 4)

    In the given figure, TBP and TCQ are tangents to the circle whose centre isO.Also \(\angle PBA=60^0\ and \ \angle ACQ=70^0.\)Determine \(\angle BAC\ and \ \angle BTC.\)

  • 5)

    In the given figure, if AB = AC, then prove that BC = 2CE.

CBSE 10th Mathematics - Full Portion Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Check whether the following are quadratic equations: x2-2x=(-2)(3-x)

  • 2)

    Check whether the following are quadratic equations: (2x-1)(x-3)=(x+5)(x-1)

  • 3)

    Find the roots of the following quadratic equation, if they exist, by the method of completing the square: 2x2+x+4=0

  • 4)

    Out of a group of children, \({7\over 2}\) times the square root of the number are creative, the two remaining ones are visionary. What is the total number of children ? How many persons in the group are creative?
    Write one-one characteristics each of creativity and vision.

  • 5)

    Solve for x : \(\sqrt { 6x+7 } -(2x-7)=0\)

10th Standard CBSE Mathematics - Triangles Five Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    If \(\triangle ABC\sim \triangle DFE\)\(\angle A={ 30 }^{ ° }\)\(\angle C={ 50 }^{ ° }\) , AB = 5 cm, AC = 8 cm and DF = 75 cm, then find DE and \(\angle F\)

  • 2)

    If the areas of two similar triangles are respectively 81 cm2 and 49 cm Find the ratio of their corresponding medians.

  • 3)

    If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.

  • 4)

    E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR. PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

  • 5)

    A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

10th CBSE Mathematics - Introduction to Trigonometry Four Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    If sinA=\(\frac {12}{13}\) , what is the value of cos A?

  • 2)

    If \(\sqrt { 3 } \sin { \theta } =\cos { \theta } \), find the value of \(\frac { \tan { \theta } (1+\cot { \theta } ) }{ \sin { \theta } +\cos { \theta } } .\)

  • 3)

    Find the value of \((\sin { { 30 }^{ 0 } } +\cos { { 30 }^{ 0 } } )-(\sin { { 60 }^{ 0 } } +\cos { { 60 }^{ 0 } } ).\)

  • 4)

    Evaluate \({ \left( \frac { \sin { { 25 }^{ 0 } } }{ \cos { { 65 }^{ 0 } } } \right) }^{ 2 }+{ \left( \frac { \tan { { 65 }^{ 0 } } }{ \cot { { 25 }^{ 0 } } } \right) }^{ 2 }-2\cos ^{ 2 }{ { 45 }^{ 0 } } .\)

  • 5)

    Prove that \(\frac { \sec ^{ 2 }{ \theta } -\sin ^{ 2 }{ \theta } }{ \tan ^{ 2 }{ \theta } } =1+\cot ^{ 2 }{ \theta } -\cos ^{ 2 }{ \theta } \)

10th CBSE Mathematics - Statistics Four Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    Find the mean of the following distribution by direct method.

    Class interval 0-10 10-20 20-30 30-40 40-50
    Number of workers 7 10 15 8 10
  • 2)

    Using assumed mean method find the mean of the following frequency distribution.

    Class 63-65 66-68 69-71 72-74 75-77
    Frequency 4 3 7 8 3
  • 3)

    Find the mode of given data.

    Marks 0-10 10-20 20-30 30-40 40-50
    Frequency 20 24 40 36 20
  • 4)

    On sports day of a school, agewise participation of students is shown in the following distribution:

    Age in years 5-7 7-9 9-11 11-13 13-15 15-17 17-19
    Number of students x 15 18 30 50 48 x

    Find the mode of the data. Also, find missing frequencies when sum of frequencies is 181. 

  • 5)

    The following table gives the literacy rate (in %) of 25 cities.

    Literacy rate 50-60 60-70 70-80 80-90
    Number of cities 9 6 8 2

    Find the median class and modal class. 

10th Standard CBSE Mathematics - Pair of Linear Equation in Two Variables Four Marks Model Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    Five years ago, Jacob's age was seven times that of his son. After five years, the age of Jacob will be three times that of his son. Represent this situation algebraically and graphically.

  • 2)

    Solve graphically the following pair of equations.
    2x-y+3=0 and 3x-5y+1=0

  • 3)

    Two straight paths are represented by the lines 7x-5y=3 and 21x-15y=5. Check whether the paths cross each other.

  • 4)

    Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

  • 5)

    In \(\triangle ABC,\quad \angle C=5\angle B=3(\angle A+\angle B)\) find all angles of \(\triangle ABC\) .

10th CBSE Mathematics - Polynomials Four Marks Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    Find the degree of the following polynomial
    (i) \(7y^{ 5 }+6y^{ 2 }-1\)
    (ii) \(\frac { y^{ 4 }+3y^{ 2 }+y }{ y } \)

  • 2)

    If 2 is a zero of polynomial f(x)=ax2-3(a-1)x-1, then find the value of a.

  • 3)

    Find the zeroes of quadratic polynomial y2+92y+1920.

  • 4)

    If α and β are the zeroes of the polynomial 2y2+7y+5, then find the value of α+β+αβ.

  • 5)

    Find the quadratic polynomial, whose sum of zeroes is 8 and their products is 12. Then, find the zeroes of the polynomial.

10th Standard CBSE Mathematics - Surface Areas and Volumes Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A tent is in the shape of a cylinder surmounted by a conical top.If the height and diameter of the cylindrical part are 2.1m and 4m respectively, and the slant height of the top is 2.8m, find the area of the canvas used for making the tent.Find the cost of the canvas of the tent at the rate of Rs.500 per m2.Also find the volume air enclosed in the tent.

  • 2)

    A juice seller serves his customers using a glass as shown in figure.The inner diameter of the cylindrical glass is 5cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass.If the height of the glass is 10cm, find the apparent capacity of the glass and its actual capacity.[\(\pi\)=3.14]

  • 3)

    A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

  • 4)

    Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?

  • 5)

    Metal spheres, each of radius 2 cm are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of the liquid. [Use \(\pi\) = 3.14]

10th Standard CBSE Mathematics - Real Number Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Show that the square of an odd positive integer is of the form 8m + 1, where m is some whole number.

  • 2)

    Use Euclid's division algorithm to the HCF of the following three numbers.
    (i) 441, 567 and 693
    (ii) 1620, 1725 and 255

  • 3)

    If the LCM of 26 and 91 is 182. find their HCF.

  • 4)

    If the HCF of 150 and 100 is 50, find the LCM of 150 and 100.

  • 5)

    Without actually performing the long division, state whether \(\frac{543}{225}\) has a terminating decimal expansion or non-terminating recurring decimal expansion.

10th Standard CBSE Mathematics - Polynomials Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find the zeroes of quadratic polynomial y2+92y+1920.

  • 2)

    If zeroes α and β of a polynomial x2-7x+k are such that α-β=1, then find the value of k.

  • 3)

    If α and β are the zeroes of the quadratic polynomial f(x)=3x2-5x-2, then evaluate α33.

  • 4)

    If α and β are zeroes of the quadratic polynomial p(x)=6x2+x-1, then find the value of \(\frac { \alpha }{ \beta } +\frac { \alpha }{ \alpha } +2\left( \frac { 1 }{ \alpha } +\frac { 1 }{ \beta } \right) +3\alpha \beta \)

  • 5)

    On dividing polynomial p(x) by 3x+1, the quotient is 2x-3 and the remainder is -2. Find p(x).

CBSE 10th Mathematics - Pair of Linear Equation in Two Variables Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Solve graphically, the pair of linear equations x-y=-1 and 2x+y-10=0. Also, find the vertices of the triangle formed by these lines and X-axis.

  • 2)

    Solve graphically, the pair of linear equations 3x+y-11=0,x-y-1=0. Also, find the vertices of the triangle formed by these lines and Y-axis.

  • 3)

    Two straight paths are represented by the lines 7x-5y=3 and 21x-15y=5. Check whether the paths cross each other.

  • 4)

    The sum of the digits of a two-digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

  • 5)

    The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, then the area is increased by 50 q units. Find the length and the breadth of the rectangle.

10th Standard CBSE Mathematics - Triangles Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.

  • 2)

    For going to city B from city A, there is a route via city C such that \(AC\bot CB\) , AC = 2x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway, which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction on the highway?

  • 3)

    Find the third side of a right angled triangle whose hypotenuse is of length p cm, one side of length q cm and p - q = 1.

  • 4)

    Find the value of unknown variables, if \(\triangle ABC\) and \(\triangle PQR\)are similar.
          

  • 5)

    In \(\triangle PQR\) and \(\triangle MST\) , \(\angle P={ 55 }^{ ° }\)\(\angle Q={ 25 }^{ ° }\)\(\angle M={ 100 }^{ ° }\) and \(\angle S={ 25 }^{ ° }\). Is \(\triangle QPR\sim \triangle TSM\) ? Why?

10th Standard CBSE Mathematics - Introduction to Trigonometry Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    If sin C=\(\frac {15}{17}\) , find the value of sin A.

  • 2)

    In a \(\triangle ABC,\angle B={ 90 }^{ 0 }\) If AB=2 cm and AC=3 cm, find the value of sin A,

  • 3)

    If 17 cosA = 8, find 15 cosecA - 8 sec B.

  • 4)

    Find the value of
    (i) \(\sin { \theta } \cos { \theta } \)   for \(\theta ={ 30 }^{ 0 }\)
    (ii) \(3\tan ^{ 2 }{ { 45 }^{ 0 } } +2\sin { { 45 }^{ 0 } } \cos { { 45 }^{ 0 } } \)

  • 5)

    If \(\sin { \theta } -\cos { \theta } =0,(0\le \theta \le { 90 }^{ 0 })\) find the value of \(\theta \) .

10th Standard CBSE Mathematics - Statistics Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Calculate the mean of the scores of 20 students in a Mathematics test.

    Marks 10-20 20-30 30-40 40-50 50-60
    Number of students 2 4 7 6 1
  • 2)

    Find the mode of given data.

    Marks 0-10 10-20 20-30 30-40 40-50
    Frequency 20 24 40 36 20
  • 3)

    Compute the median marks for the following data.

    Marks Number of students
    0 and above 50
    10 and above 46
    20 and above 40
    30and above 20
    40 and above 10
    50 and above 3
    60and above 0
  • 4)

    If the coordinates of the point of intersection of less than ogive and more than ogive is (12.5,20) then find the value of median.

  • 5)

    A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

    Number of days 0-6 6-10 10-14 14-20 20-28 28-38 38-40
    Number of students 11 10 7 4 4 3 1

10th Standard CBSE Mathematics - Areas Related to Circles Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. If bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s, then calculate the number of complete revolutions the wheel makes in raising the bucket.

  • 2)

    In fig., PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flowers beds (shaped parts).

  • 3)

    The long and short hands of a clock are 6 cm and 3 cm respectively. Find the sum of distance travelled by their tips in a day.

  • 4)

    A bus has wheels which are 112 cm in diameter. How many complete revolutions does each wheel make in 20 minutes, when the bus is travelling at a speed of 66 km/h?

  • 5)

    A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road.

CBSE Mathematics 10th - Coordinate Geometry Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find the points of trisection of the line segment determined by (7,5) and (16,-1).

  • 2)

    Find the coordinates of the points o trisection of the line segment joining the points A(2,-2) and B(-7,4)

  • 3)

    Find the coordinates of the points P,Q and R which divide the line segment joining A(5,4) and B(11,6) into four equal parts.

  • 4)

    In what ratio does the point (-4,6) divide the line segment joining the point A(-6,10) and B(3,-8)?

  • 5)

    Find the value of p for which the points (3,6), (7,p) and (-5,2) are collinear.

10th Standard CBSE Mathematics - Probability Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A coin is tossed. If it results in a head a coin is tossed, otherwise a die is thrown. Describe the following events:
    (i) A = getting atleast one head  
    (ii) B = getting an even number
    (iii) C = getting a tail  
    (iv) D = getting a tail and an odd number

  • 2)

    20 cards numbered 1, 2, 3, ...., 20 are put in a box and mixed thoroughly. Shashi draws a cards from the box. Find the probability that the number on the card is

    (i) odd    (ii) even  (iii) a prime

    (iv) divisible by 3    (v) divisible by 3 and 2 both.

  • 3)

    At a fete cards bearing numbers 1 to 500, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number the player wins prize.

    (i) What is the probability that the first player wins a prize?

    (ii) The second player wins prize, if the first has not won.

  • 4)

    A letter is at drawn at random from the word 'MATHEMATICS'.Find the probability of drawing each of the different letters in the given word.

  • 5)

    A box of 24 solar cells contain 8 defective cells.One cell is drawn at random.What is the probability that the cell is not defective and it is not replaced and a second cell is selected at random from the rest, what is the probability that second cell is defective?

10th Standard CBSE Mathematics - Some Applications of Trigonometry Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird, from a point on the ground is 45o . The bird flies away from the point of observation horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes 30o . Find the speed of flying of the bird.

  • 2)

    At the foot of a mountain, the elevation of its summit is 45o . After ascending 1000 m towards the mountain up a slope of 30o inclination, the elevation is found to be 60o . Find the height of the mountain.

  • 3)

    A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches a height of 90 m on the wall and makes an angle of 60o with the ground. If while resting at the same point on the path, it were made to lean against the other wall, it would have made an angle of 45o with the ground. Find the height it would have reached on the second wall.

  • 4)

    Two stations due south of a leaning tower which leans towards north are at distances a and b from its foot. If \(\alpha\) and \(\beta\) be the elevation  of the top of the tower from these stations, prove that its inclination \(\theta\) to the horizontal is given by \(cot\theta =\frac { b\quad cot\alpha -a\quad cot\beta }{ b-a } \).

  • 5)

    From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stones on the opposite sided of the aeroplane are found to be \(\alpha\) and \(\beta\), show that the height of the aeroplane is \(\frac { tan\alpha tan\beta }{ tan\alpha +tan\beta } \).

10th Standard CBSE Mathematics - Constructions Fours Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to \(\triangle ABC\) in which PQ = 8cm.  Also justify the construction.

  • 2)

    Draw a \(\Delta ABC\) with sides BC = 6cm, AB = 5cm and \(\angle ABC=60°\), Then, construct a triangle whose sides are 3/4 of the corresponding sides of the \(\Delta ABC\)

  • 3)

    Draw two equal circles with centres A and B and distance between A and B is 6 cm. Construct a pair of tangents from centres A and B to each other. Measure the lengths of the tangents. What type of 31. figure is enclosed by these four tangents?

  • 4)

    Draw a circle of radius 3.5 cm. Take a point T out side the circle at a distance of 7 cm from the centre and construct a pair of tangents from this point T to the circle and justify your construction.

10th Standard CBSE Maths - Real Number Four Mark Model Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    A number when divided by 53 gives 34 as quotient and 21 as remainder. Find the number.

  • 2)

    The product of two consecutive positive integers is divisible by 2. Is this statement true or false? Give reason.

  • 3)

    Use the Euclid's division algorithm to find the HCF of
    (i) 650 and 1170
    (ii) 870 and 225

  • 4)

    If two positive integers p and q can be expressed as p = ab2 and q = a3b; where a,b being prime numbers, find the LCM (p,q)

  • 5)

    Find the HCF and LCM of 60, 84 and 108 by using the prime factorisation method.

10th CBSE Mathematics - Surface Areas and Volumes Four Mark Model Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    A wooden article was made by scooping out a hemisphere from each end of a solid cylinder.If the height of the cylinder is 20cm and radius of the base is 3.5cm, find the total surface area of the article.

  • 2)

    A juice seller serves his customers using a glass as shown in figure.The inner diameter of the cylindrical glass is 5cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass.If the height of the glass is 10cm, find the apparent capacity of the glass and its actual capacity.[\(\pi\)=3.14]

  • 3)

    A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

  • 4)

    A tent consists of a frustum of cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum are 14 m and 26 m respectively, the height of the frustum is 8 m and the slant height of the surmounted conical portion is 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal.)

  • 5)

    A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled into it. The diameter of the pencil is 7 mm; the diameter of the graphite is 1 mm and the length of the pencil is 10 cm. Calculate the weight of the whole pencil if the specific gravity of the wood is 0.7 g/cm3 and that of the graphite is 2.1 g/cm3 .

10th Standard CBSE Mathematics - Circles Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    In figure, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.Prove that
    (i) AB + CQ = AC + BQ
    (ii)area (\(\Delta\)ABC) = \(1\over2\) (perimeter of \(\Delta\)ABC) x r

  • 2)

    Two circles touch each other externally at C.AB and CD are two common tangents.If D lies on AB such that CD=6cm, then find AB.

  • 3)

    QR is a tangent Q.PR||AQ, where AQ is a chord through A and P is a centre, the end point of the diameter AB.Prove that BR is tangent at B.

  • 4)

    In the given figure, the diameters, of two wheels have measures 4cm and 2cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.

  • 5)

    With the vertices of a triangle ABC as centres, three circles are described each touching the other two externally. If the sides of the triangle are 4 cm, 6 cm, and 8 cm, find the radii of the circles.

10th Standard CBSE Mathematics - Arithmetic Progressions Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find the sum of the integers between 100 and 200 that is not divisible by 9.

  • 2)

    The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

  • 3)

    150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed.

  • 4)

    Interior angles of a polygon are in AP. If the smallest angle is 120o and common difference is 5o , find the number of sides of the polygon.

  • 5)

    A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief?

10th Standard CBSE Mathematics - Quadratic Equations Four Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find three consecutive positive integers whose product is equal to sixteen times their sum.

  • 2)

    Solve for x \({x-2\over x-3}+{x-4\over x-5}={10\over 3}, x\ne3,5\)

  • 3)

    The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

  • 4)

    A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

  • 5)

    Solve for x : \(({{4x-3}\over2x+1})-10({2x+1\over4x-3})=3; x\ne{-1\over2};x\ne{3\over4}\)

CBSE 10th Standard Mathematics - Areas Related to Circles Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    The diameters of the front and rear wheels of tractor are 80 cm and 2 m respectively.  Find the number of revolutions that rear wheel will make to cover the distance which the front wheel covers in 1400 revolutions. [Use \(\pi={22\over 7}\)]

  • 2)

    An elastic belt is placed round the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm away from O. Find the length of the belt that is in contact with the rim of the pulley. Also find the shaded area . ( Use \(\pi =3.14,\sqrt { 3 } =1.73)\) 

  • 3)

    In fig., PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flowers beds (shaped parts).

  • 4)

    The long and short hands of a clock are 6 cm and 3 cm respectively. Find the sum of distance travelled by their tips in a day.

  • 5)

    Find the diameter of the circle, which has circumference equal to the sum of the circumference of two circles with radii 7 cm and 14 cm.

10th CBSE Mathematics - Coordinate Geometry Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    The three vertices of a parallelogram ABCD are A(3,-4), B(-1,-3) and C(-6,2). Find the coordinates of vertex D and find the area of ABCD.

  • 2)

    In \(\Delta PAB, \) PA=PB and area of \(\Delta PAB=10\)sq.units. Find the coordinates of P if coordinates of A and B are (1,2) and (3,8) respectively.

  • 3)

    A(0,3), B(-1,-2) and C(4,2) are vertices of a \(\Delta ABC\). D is a point on the side BC such that \({BD\over DC}={1\over2}\). P is a point on AD such that \(AP={2\sqrt5\over3}\)units. Find coordinates of P.

  • 4)

    If A(-3,5), B(-2,-7), C(1,-8) and D(6,3) are the vertices of a quadrilateral ABCD, find its area.

  • 5)

    Find the values of k so that the area of the triangle with vertices (1,-1), (-4,2k) and (-k,-5) in 24sq.units.

10th Standard CBSE Mathematics - Statistics Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find the mean of the following frequency distribution using assumed mean method.

    Class 2-8 8-14 14-20 20-26 26-32
    Frequency 6 3 12 11 8
  • 2)

    Find the mean of the following data, by using step deviation method.

    Class 10-20 20-30 30-40 40-50 50-60 60-70
    Frequency 4 28 15 20 17 16
  • 3)

    In a health checkup, the number of heart beats of  women were recorded in the following table

    Number of heart beats/minute 65-69 70-74 75-79 80-84
    Number of women 2 18 16 4

     Find the mean of the data.

  • 4)

    An NGO working for welfare of cancer patients, maintained its records as follows:

    Age of patients (in years) 0-20 20-40 40-60 60-80
    Number of patients 35 315 120 50

    find mode. 

  • 5)

    If the mode of the following series is 54, then find the value of f.

    Class 0-15 15-30 30-45 45-60 60-75 75-90
    Frequency 3 5 f 16 12 7

10th Standard CBSE Mathematics - Introduction to Trigonometry Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Evaluate cos230+ sin2450\(\frac {1}{3}\) tan600.

  • 2)

    Find the value of \(\frac { \cos { { 60 }^{ 0 } } +\sin { { 45 }^{ 0 } } -\cot { { 30 }^{ 0 } } }{ \tan { { 60 }^{ 0 } } +\sec { { 45 }^{ 0 } } -cosec{ 30 }^{ 0 } } .\)

  • 3)

    If \(2\cos { 3\theta } =\sqrt { 3 } \) find the value of \(\theta\) .

  • 4)

    If sin (A – B) = \(\frac{1}{2}\) cos (A + B) = \(\frac{1}{2}\) 0° < A + B \(\leq\) 90°, A > B, find A and B.

  • 5)

    If tan (3x + 300) = 1, find the value of x.

10th Standard CBSE Mathematics - Triangles Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    If \(\triangle ABC\sim \triangle PQR\), AB = 6.5 cm, PQ = 10.4 cm and perimeter of \(\triangle ABC\) = 60 cm, find the perimeter of \(\triangle PQR\).

  • 2)

    It is given that \(\triangle ABC\sim \triangle EDF\) such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

  • 3)

    Find the value of the height 'h' in the adjoining figure. at which the tennis ball must be hit, so that it will just pass over the net and land 6 m away from the base of the net.

  • 4)

    In the given figure of \(\triangle ABC\)\(DE\parallel AC\). If \(DC\parallel AP\), where point P lies on BC produced, then prove that \(\frac { BE }{ EC } =\frac { BC }{ CP } \).

  • 5)

    ABCD is a trapezium with \(AB\parallel DC\). E and F are two points on non-parallel sides AD and BC respectively, such that EF is parallel to AB. Show that
    \(\frac { AE }{ ED } =\frac { BF }{ FC } \)

CBSE 10th Mathematics - Pair of Linear Equation in Two Variables Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Solve the following pair of linear equations.
    41x+53y=135 and 53x+41y=147

  • 2)

    If the lines given by 2x+Ky=1 and 3x-5y=7 has unique solution, then find the value of K.

  • 3)

    Find the value of 'k' for which the system of equations kx-5y=2; 6x+2y=7 has no solution.

  • 4)

    For what value of k, will the following pair of linear equations have infinitely many solutions?
    2x+3y=4 and (k+2)x+6y=3k+2

  • 5)

    The sum of a two-digit number and number obtained by reversing the order of digits 99. If the digits of the number differ by 3, then find the numbers.

10th Standard CBSE Mathematics - Polynomials Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find the value of 'a' if X+a is a factor (zero) of the polynomial 2x2+2ax+5x+10.

  • 2)

    If zeros of the polynomial x2+(a+1)x+b are 2 and -3, then find the value of (a+b).

  • 3)

    Find the zeros of the quadratic polynomial x2 +7x+10 and verify relationship between the zeros and the coefficients.

  • 4)

    Find a quadratic polynomial whose one zero is 7 and sum of zeroes is -18.

  • 5)

    If a and β are the zeroes of the quadratic polynomial p(x)=ax2+bx+c, then evaluate a2β+aβ2 .

10th Standard CBSE Mathematics - Some Applications of Trigonometry Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60o . At a point Y, 40 m vertically above X, the angle of elevation is 45o . Find the height of the PQ and the distance XQ.

  • 2)

    The angle of elevation of a jet fighter from a point A on the ground is 60o . After a flight of 15 seconds, the angle of elevation changes to 30o. If the jet is flying at a speed of 720 km/hr, find the constant height. \((\sqrt { 3 } =1.732)\) .

  • 3)

    The angle of elevation of a cloud from a point 60 m above a lake is 30o and the angle of depression of the reflection of the cloud in the lake is 60o . Find the height of the cloud from the surface of the lake.

  • 4)

    At the foot of a mountain, the elevation of its summit is 45o . After ascending 1000 m towards the mountain up a slope of 30o inclination, the elevation is found to be 60o . Find the height of the mountain.

  • 5)

    The pilot of an aircraft flying horizontally at a speed of 1200 km/hr. observes that the angle of depression of a point on the ground changes from 30o to 45o in 15 seconds. Find the height at which the aircraft is flying.

10th CBSE Mathematics - Probability Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 2, 2 3, 3, 4 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting (i) sum 7 (ii) sum is a perfect  square.

  • 2)

    In a game, the entry fee is Rs. 5. The game consists of tossing a coin 3 times. If one or two heads show, Shweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she
    (i) loses the entry fee
    (ii) gets double entry fee
    (iii) just gets her entry fee

  • 3)

    A coin is tossed. If it results in a head a coin is tossed, otherwise a die is thrown. Describe the following events:
    (i) A = getting atleast one head  
    (ii) B = getting an even number
    (iii) C = getting a tail  
    (iv) D = getting a tail and an odd number

  • 4)

    At a fete cards bearing numbers 1 to 500, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number the player wins prize.

    (i) What is the probability that the first player wins a prize?

    (ii) The second player wins prize, if the first has not won.

CBSE 10th Mathematics - Real Number Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Write the HCF of the smallest composite number and the smallest prime number.

  • 2)

    Find the LCM and HCF of 120 and 144 by fundamental theorem of arithmetic.

  • 3)

    If HCF of two numbers is 2 and their product is 120, find their LCM.

  • 4)

    If the HCF of 35 and 45 is 5, LCM of 35 and 45 is 63 x a, then find the value of a.

  • 5)

    Show that \(3\sqrt { 2 } \) is an irrational number.

10th CBSE Mathematics - Surface Areas and Volumes Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A teak wood log is cut first in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m3. How many rectangular planks of size 2.3 m x 0.75 m x 0.04 m can be cut from the cuboid?

  • 2)

    A rectangular reservoir is 120 m long and 75 m wide. At what speed per hour must water flow into it through a square pipe of 20 cm wide so that the water rises by 2.4 m in 18 hours?

  • 3)

    The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm3, then find the value of r Use \(\pi=\frac{22}{7}\)

  • 4)

    An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at Rs.30 per litre. [ \(\pi=\frac{22}{7}\)]

  • 5)

    Water flows in a tank 150 m x 100 m at the base through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km/h. In what time will the water be 3 m deep?

CBSE 10th Mathematics - Areas Related to Circles Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    In fig., ABC is a right-angled triangle, right-angled at A.  Semicircles are drawn on Ab, Ac and BC as diameters.  Find the area of the shaded region.

  • 2)

    The area of an equilateral triangle in \(49\sqrt3\ cm^2\).  Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle.  Find the area of triangle not included in the circles.\([Take\ \sqrt3=1.73]\)

  • 3)

    Find the area of the shared region in figure, where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm, as centre.

  • 4)

    In given figure, an equilateral triangle has been inscribed in a circle of radius 6 cm.  Find the area of the shaded region.  \([Use\ \pi=3.14]\) 

  • 5)

    The inner perimeter of a racetrack is 400 m and the outer perimeter is 488 m.  The length of each straight portion is 90 m.  Find the cost of developing the track at the rate of \(Rs. \ 12.50/m^2\)

CBSE 10th Mathematics - Coordinate Geometry Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Show that the points (7,10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle.

  • 2)

    Show that points A(7,5),B(2,3) and C(6,-7) are the vertices of a right triangle. Also find its area.

  • 3)

    Point P divides the line segment joining the points A(2,1) and B(5,-8) such that \({AP\over AB}={1\over 3}\). If P lies on the 2x-y+k=0, find the value of k.

  • 4)

    The line segment AB joining the points A(3,-4) and B(1,2) is trisected at the points P(p,-2) and Q(5/3,q). Find the values of p and q.

  • 5)

    If R(x,y) is a point on the line segment joining the points P(a,b) and Q(b,a) then prove that x+y=a+b

10th Standard CBSE Mathematics - Probability Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.

  • 2)

    One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing : (i) an ace (ii) '2' spades  (iii) '10' of a black suit

  • 3)

    Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is
    (i) an even number    (ii) a number less than 14
    (iii) a number which is a perfect square  (iv) a prime number less than 20.

  • 4)

    A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. Find the probability that the selected number is their average.

  • 5)

    If a number x is chosen from the number 1, 2, 3 and a number y is selected from the numbers 1, 4, 9. Find the probability that xy = 10.

CBSE 10th Standard Mathematics - Constructions Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    Two line segments AB and AC include an angle of \(60^o\) where AB = 5 cm and AC = 7 cm.  Locate points P and Q on AB and AC, respectively such that \(AP={3\over 4}\) AB and \(AQ={1\over 4}AC.\) Join P and Q and measure the length PQ.

  • 2)

    Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to \(\triangle ABC\) in which PQ = 8cm.  Also justify the construction.

  • 3)

    Draw two tangents from the end points of the diameter of a circle of radius 4.0 cm. Are these tangents parallel?

  • 4)

    Draw a \(\triangle\)ABC with BC = 7 cm, \(\angle B=45°\)  and \(\angle C=60°\). Then, construct another triangle, whose sides are \(\frac { 3 }{ 5 } \)  times of the corresponding sides of \(\Delta ABC\) and justify your construction.

  • 5)

    Draw a right-angled triangle, in which the sides (other than the hypotenuse) are lengths 8 cm and 6 cm. Then, construct another triangle, whose sides are \(\frac { 3 }{ 4 } \)  times of the corresponding sides of  given triangle. Justify your construction.

10th Standard CBSE Mathematics - Circles Four Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    In the figure, AB is diameter of a circle with centre O and QC is a tangent to the circle at C.If \(\angle CAB=30^0,\ find \ \angle CQA\ and \angle CBA.\) 

  • 2)

    In figure, PA are two tangents drawn from an external point P to a circle with centre O.Prove that OP is the right bisector of line segment AB.

  • 3)

    AB is a chord of length 24cm of a circle of radius 13cm.The tangents at A and B intersect at a point C.Find the length AC.

  • 4)

    Two circles with centres O and O' of radii 3cm and 4cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles.Find the length of the common chord PQ.

  • 5)

    In figure, the common tangent, AB and CD are tangents to two circles with centres O and O' intersect at E. Prove that the points O, E, O' are collinear.

10th Standard CBSE Mathematics - Arithmetic Progressions Five Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

  • 2)

    Find the sum: \(\frac{a - b}{a + b}+\frac{3a - 2b}{a + b}+\frac{5a - 3b}{a + b}+...\) to 11 terms.

  • 3)

    In the following A.P., find the missing term: 9, ...., ...., ....., 25

  • 4)

    Find the sum of the first 50 odd natural numbers.

  • 5)

    If the sum of first p terms of an AP is q and the sum of first q terms is p, then find the sum of first (p + q) terms.

10th Standard CBSE Mathematics - Quadratic Equations Five Mark Question Paper - by Kajal Puri - Chandigarh - View & Read

  • 1)

    If \(\alpha, \beta\) are roots of the equation 2x2-6x+a=0 and \(2\alpha+5\beta=12\) find the value of a.

  • 2)

    Solve for x: \(x^2+5x-(a^2+a-6)=0\)

  • 3)

    If twice the area of a smaller square is subtracted from the area of the larger square.the result is \(14cm^{ 2 }\) However, if twice the area of the larger square is added to three times the area of the smaller square. the result is \(203cm^{ 2 }\) .Find the sides of the two square.

  • 4)

    In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in maths and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.

  • 5)

    In a flight of 2800km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100km/h and time increased by 30 minutes. Find the original duration of the flight.

10th Standard CBSE Mathematics - Some Applications of Trigonometry Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A statue 1.46 m tall stand on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60o and from the same point, the angle of elevation of the top of the pedestal is 45o . Find the height of the pedestal. \((\sqrt { 3 } =1.73)\) .

  • 2)

    On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angles of elevation of the top and bottom of the flag pole are 60o and 30o respectively. Find the heights of the tower and flag pole mounted on it.

  • 3)

    A ladder of length 6 m makes an angle of 45o with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60o with the floor. Find the distance between these two walls of the room.

  • 4)

    The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30o . If the height of the second pole is 24 m, find the height of the first pole. \((Use\sqrt { 3 } =1.732)\)

  • 5)

    The length of the shadow of a tower standing on level ground is found to 2 x metre longer when the sun's altitude is 30o than when it was 45o. Prove that the height of tower is \(x(\sqrt { 3 } +1)\) metres.

10th Standard CBSE Mathematics - Constructions Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Draw an isosceles \(\triangle ABC\) in which \(BC=5.5cm\) and altitude AL = 3cm.  Then construct another triangle whose sides are \(3\over 4\) of the corresponding sides of \(\triangle ABC\).

  • 2)

    Draw a line segment AB of length 7 cm.  Taking A as centre, draw a circle of radius 3 cm and taking B as Centre, draw another circle of radius 2 cm.  Construct tangents to each circle from the centre of the other circle.

  • 3)

    Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.

  • 4)

    Draw an equilateral \(\Delta ABC\) of each side 4 cm.Construct a triangle similar to it and of scale factor \(\frac{3}{5}\).Is the new triangle also an equilateral?

CBSE 10th Mathematics - Circles Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

  • 2)

    In the given figure, ABC is a right-angled triangle, right angled at A, with AB =6cm and AC=8cm.A circle with centre O has been inscribed inside the triangle Calculate the value of r, the radius of the inscribed circle.

  • 3)

    ABC is a right-angled triangle, right angled at A.A circle is inscribed in it.The lengths of two sides containing the angle are 24cm and 10cm.Find the radius of the incircle.

  • 4)

    In two concentric circles, a chord of length 24 cm of larger circle becomes a tangent to the smaller circle whose radius is 5 cm. Find the radius of the larger circle.

  • 5)

    AB is a diameter of a circle. AH and BK are perpendicular from A and B respectively to the tangent at P.Prove that AH + BK = AB.

CBSE 10th Mathematics - Arithmetic Progressions Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    If 9th term of an AP is zero, prove that its 29th term is double of its 19th term.

  • 2)

    Find the value of the middle term of the following AP: -6, -2, 2, ....., 58

  • 3)

    Determine the AP whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.

  • 4)

    How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

  • 5)

    The 2nd, 31st and the last term of an AP are 7\(\frac{3}{4}\)\(\frac{1}{2}\) and -6\(\frac{1}{2}\), respectively. Find the first term and number of terms. 

CBSE 10th Mathematics - Quadratic Equations Three Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

     A 2-digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

  • 2)

    If the price of a book is reduced by Rs.5, a person can buy 5 more books for Rs.300. Find the original list price of a book.

  • 3)

    If a and b are roots o the equation 2x2+7x+5=0 then write a quadratic equation whose roots are 2a+3 and 2b+3

  • 4)

    Find the positive value of k, for which the equations x2+kx+64=0 and x2-8x+k=0 will both have real roots.

  • 5)

    In the following equations determine the set of values of p for which the given equation has real roots: px2+4x+1=0

10th Standard CBSE Mathematics - Polynomials Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    If the product of the zeroes of the polynomial (ax2-6x-6) is 4, then find the value of a.

  • 2)

    If one zero of the polynomial (a2+9)x2+13x+6a is a reciprocal of the other, then find the value of a.

  • 3)

    Find the zeroes of the quadratic polynomial 3x2+11x-4, then find the value of  \(\frac { m }{ n } +\frac { n }{ m } \) .

  • 4)

    If m and n are the zeroes of the polynomial 3x2+11x-4, then find the value of \(\frac { m }{ n } +\frac { n }{ m } \) .

  • 5)

    The sum and the product of a zeroes of the polynomial f(x)=4x2-27x+3k2 are equal. Find the value of k.

10th CBSE Mathematics - Pair of Linear Equation in Two Variables Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find a, if the line 3x+ay=8 passes through the intersection of lines represented by equations 3x-2y=10 and 5x+y=8.

  • 2)

    There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.

  • 3)

    If the angles of a triangle are x, y and 400 and the difference between the two angles x and y is 300 . Then, find the values of x and y.

  • 4)

    Solve the following pair of equations by elimination method.
    2x+3y-5=0; 3x-2y-14=0

  • 5)

    Solve the following pair of equations by elimination method.
    3x+2y=7; 2x-5y+8=0

10th CBSE Mathematics - Triangles Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    In the given figure, \(\triangle ACB={ 90 }^{ ° }\) and \(CD\bot AB\) . Prove that \(\frac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\frac { BD }{ AD } \)

  • 2)

    A girl of height 100 cm is walking away from the base of a lamppost at a speed of 1.9 m/s. If the lamp is 5 m above the ground, find the length of her shadow after 4s.
     

  • 3)

    In an equilateral triangle of side\(3\sqrt { 3 } cm,\) find the length of the altitude.

  • 4)

    In the given figure, OA = 3 cm, OB = 4 cm, \(\angle\)AOB = 90\(\unicode{xb0} \), AC = 12 cm and BC = 13 cm, prove that \(\angle\)CAB = 90\(\unicode{xb0} \).

  • 5)

    In an equilateral triangle of side 24 cm, find the length of the altitude.

CBSE 10th Mathematics - Introduction to Trigonometry Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    If \(\sec ^{ 2 }{ \theta } =x+\frac { 1 }{ 4x } ,\) find the value of \(\sec { \theta } +\tan { \theta } .\)

  • 2)

    Prove that \(\sqrt { \sec ^{ 2 }{ \theta } +{ cosec }^{ 2 }\theta } =\tan { \theta } +\cot { \theta } .\)

  • 3)

    Eliminate  \(\theta\) from the following equation. \(x=a\sec { \theta } ,y=b\tan { \theta } \)

  • 4)

    Using the formula, \(\cos { A } =\sqrt { \frac { 1+\cos { 2A } }{ 2 } } ,\) find the value of \(\cos { { 15 }^{ 0 } } \)

  • 5)

    If \(\sqrt { 3 } \cot ^{ 2 }{ \theta } -4\cot { \theta } +\sqrt { 3 } =0,\) find the value of the \(\tan ^{ 2 }{ \theta } +\cot ^{ 2 }{ \theta } .\)

10th Standard CBSE Mathematics - Statistics Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Construct the frequency distribution table for the given data.

    Marks Number of students
    Less than 10 14
    Less than 20 22
    Less than 30 37
    Less than 40 58
    Less than 50 67
    Less than 60 75
  • 2)

    Find the mean of the data using an empirical formula when it is given that mode is 50.5 and median in 45.5

  • 3)

    The regarding marks obtained by 48 students of a class in a class test is given below. Calculate the modal marks of students.

    Marks Obtained 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50
    Number of students 1 0 2 0 0 10 25 7 2 1
  • 4)

    Given below is the distribution of weekly pocket money received by students of a class. Calculate the pocket money that is received by most of the students.

    Pocket Money (in Rs) 0-20 20-40 40-60 60-80 80-100 100-120 120-140
    Number of students 2 2 3 12 18 5 2
  • 5)

    Find the mean of the following distribution

    Class Interval 0-6 6-12 12-18 18-24 24-30
    Frequency 5 4 1 6 4

10th Standard CBSE Mathematics - Real Number Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Write the HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number p divides q2, then will it divide q3 also? Explain.

  • 2)

    A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.

  • 3)

    If n is an odd integer, then show that n2 - 1 is divisible by 8.

  • 4)

    Find the LCM of x and y, if xy = 180 and HCF of (x, y) = 5

  • 5)

    Find (HCF x LCM) for the numbers 100 and 190.

10th Standard CBSE Mathematics - Surface Areas and Volumes Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    A cubical block of side 7cm is surmounted by a hemisphere.What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

  • 2)

    A tent is in the shape of a cylinder surmounted by a conical top.If the height and diameter of the cylindrical part are 2.1m and 4m respectively, and the slant height of the top is 2.8m, find the area of the canvas used for making the tent.Also, find the cost of the canvas of the tent at the rate of Rs.500 per m2.(Note that the base of the tent will not be covered with canvas.)

  • 3)

    From a solid cylindrical whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out.Find the total surface area of the remaining solid to the nearest cm2 .

  • 4)

    Rachel, an engineering student, was asked make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet.The diameter of the model is 3cm and its length is 12cm.If each cone has a height of 2cm, find the volume of air contained in the model that Rachel made.(Assume the outer and inner dimensions of the model to be nearly the same.)

  • 5)

    The sum of the radius of the base and the height of a solid cylinder is 37cm.If the total surface area of the of the solid cylinder is 1628cm2, find the volume of the cylinder.\([\pi=22/7]\)

10th Standard CBSE Mathematics Unit 8 Areas Related to Circles Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Find the area of  a quadrant of a circle whose circumference is 22cm.

  • 2)

    The length of the minute hand of a clock is 14 cm.  Find the area swept by the minute hand in 5 minutes.

  • 3)

    Find the area of \(\Delta\)PQR such that \(\angle\)=900, PR=10cm and \(\angle\) PRQ=300.[Take \(\sqrt{3}=1.73\)]

  • 4)

    Find the area of the shaded region with adjoining figure.

  • 5)

    A circular is of diameter 1.5m.It is surrounded by a 2m wide path.Find the cost of constructing the path at the rate of Rs.25 per m2 .

CBSE 10th Mathematics Coordinate Geometry Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer. (4,5), (7,6), (4,3), (1,2)

  • 2)

    What point on the x-axis is equidistant from (7,6) and (-3,4)?

  • 3)

    Show that the following points are collinear: (2,-2),(-3,8) and (-1,4).

  • 4)

    An equilateral triangle has two vertices at the points (3,4) and (-2,3). Find the coordinates of the third vertex.

  • 5)

    Find the centre of a circle passing through (5,-8), (2,-9) and (2,1).

CBSE 10th Mathematics - Probability Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

  • 2)

    It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

  • 3)

    A die is thrown once. Find the probability of getting
    (i) a prime number.
    (ii) a number lying between 2 and 6.
    (iii) an odd number

  • 4)

    A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that is bears
    (i) a two digit number
    (ii) a perfect square number
    (iii) a number divisible by 5

  • 5)

    A die is thrown twice. What is the probability that
    (i) 5 will not come up either time?
    (ii) 5 will come up at least once?
    [Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment.]

10th Standard CBSE Mathematics - Some Applications of Trigonometry Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30o . Find the height of the tower.

  • 2)

    From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45o and 60o respectively. Find the height of the tower.

  • 3)

    The angle of elevation of the top of a building from the foot of a tower is 30o and the angle of elevation of the top of the tower from the foot of the building is 60o. If the tower is 50 m high, find the height of the building.

  • 4)

    From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60o and the angle of depression of its foot is 45o. Determine the height of the tower.

  • 5)

    A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30o , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60o . Find the time taken by the car to reach the foot of the tower from this point.

CBSE 10th Mathematics - Constructions Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Draw a triangle ABC with side BC = 7 cm,  Then, construct a triangle whose sides are \({4\over 3}\) times the corresponding sides of \(\triangle ABC\)

  • 2)

    Construct a triangle ABC in which  \(AB=5\ cm, BC=6\ cm\) and \(AC=7cm.\) Construct another triangle similar to \(\triangle ABC\) such that its sides are \(3\over 5\) of the corresponding sides of \(\triangle ABC\).

  • 3)

    Draw line segment AB of length 8 cm.  Taking A as centre, draw a circle of radius 4cm and taking B as centre, draw another circle of radius 3cm.  Construct tangents to each circle from the centre of the other circle.

  • 4)

    Construct tangents to a circle of radius 3 cm from a point on concentric circle of radius 5 cm and measure its length.

  • 5)

    Draw two tangents from the end points of the diameter of a circle of radius 3.5 cm. After these tangents parallel?

10th Standard CBSE Mathematics - Circles Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

  • 2)

    Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

  • 3)

    In figure, \(\Delta ABC\) is circumscribing a circle.Find the length of BC.

  • 4)

    In the given figure, RS is the tangent to the circle at L and MN is a diameter. If, determine \(\angle RLM.\)

CBSE 10th Mathematics Arithmetic Progressions Two Marks Questions - by QB365 - Question Bank Software - View & Read

  • 1)

    Write first four terms of the AP, when the first term a and the common difference d are given as follows: a = -1, d = \(\frac{1}{2}\)

  • 2)

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.. 2, \(\frac{5}{2}\) , 3, \(\frac{7}{2}\).......

  • 3)

    Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
    a, a2, a3, a4.......

  • 4)

    In the following APs, find the missing terms in the blanks:
    ........., 13, ..........., 3

  • 5)

    For what value of n, are the nth terms of two APs: 63, 65, 67,....... and 3, 10, 17,............ equal?

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CBSE Education Study Materials

10th CBSE Mathematics 2019 - 2020 Academic Syllabus - by QB365 - Question Bank Software Aug 21, 2019

Mathematics 2019 - 2020 Academic Syllabus 

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CBSEStudy Material - Sample Question Papers with Solutions for Class 10 Session 2020 - 2021

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