(a + b) + c = a + (b + c) is called

\(({ 2 }^{ 0 }+{ 4 }^{ -1 })\times { 2 }^{ 2 }\) is equal to

The unit digit in the square of the number 27 is

Which of the following numbers is divisible by 5 ?

The one's digit of the cube of the number 123 is

Study the following frequency distribution table and answer the question given below:

The total number of workers is

Observe the  temperature time graph and answer the related question:

The coordinates of the origin are

The root of the equation 3y + 4 = 5y - 4 is

The measures of two angles of a quadrilateral are 110° and 100°. The remaining two angles are equal. The measure of each of the remaining two angles is

Which one of the following is a Pythagorian triplet?

Vimla purchased a watch for Rs. 500. She sold it at a loss of 20%. Find the selling price.

The area of a rectangle with length 2l²m and breadth 3lm² is

Which of the following is the number of faces of a solid sphere?

Two identical cubes each of total surface area of 6 cm² are joined end to end. Which of the following is the total surface area of the cuboid so formed?

120 copies of a book cost Rs.600. What will 400 copies cost?

The factorisation of 12a²b + 15ab² is

Write the rational number for each point labelled with a letter

Write each of the following in standard form: 0.0016

Write the square, making use of the above pattern 1111111²

Check the divisibility of the following numbers by 9: 294

Find the cube root of 46656 by estimation method.

Following are the number of members in 25 families of a village:
6, 8, 7, 7, 6, 5, 3, 2, 5, 6, 8, 7, 7, 4, 3, 6, 6, 6, 7, 5, 4, 3, 3, 2, 5.
Prepare a frequency distribution table for the data using class intervals 0 - 2, 2 - 4 etc.

A courier-person cycles from a town to a neighbouring Suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph:

Did the person stop on his way? Explain

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4, respectively and added then sum is 92. Find these integers.

What is the measure of each interior angle of a regular pentagon?

In a parallelogram, the lengths of adjacent sides are known. Do we still need measures of the angles to construct?

Given, P = Rs 40000 and R = 8% per annum compounded annually. Find the interest, if period is 1 yr.

Multiply these binomials:(2pq + 3q²) and (3pq - 2q²)

The actual width of a classroom is 900 cm. If the scale chosen to make it drawing is 1: 30. Then, what will be the width of the room in the drawing?

A cuboid is of dimensions 60 cm\(\times\)54 cm\(\times\)30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

In which of the following cases, there are direct variation between the two given quantities?
Your height and weight.

Divide as directed.
5 (2x+ 1)(3x+ 5) ÷ (2x+ 1)

Simplify 
\({3\over7}\times{28\over15}\div{14\over5}\)

Find the value of: \({ \left( \frac { 1 }{ 4 } \right) }^{ -2 }+{ \left( \frac { 1 }{ 3 } \right) }^{ -3 }+{ \left( \frac { 1 }{ 2 } \right) }^{ -4 }\)

Find the least number which must be added to the numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. 525

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad 4\quad A \\ +\quad 9\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad C\quad B\quad 3 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

What is the smallest number by which 288 must be multiplied so that the product is a perfect cube?

From a pack of well-shuffled cards, find the probability of getting an ace of club.

Draw the line graph using suitable scale to show the annual gross profit of a company for a period of five years.

Solve the following linear equation \(\frac { x }{ 2 } -\frac { 1 }{ 5 } =\frac { x }{ 3 } +\frac { 1 }{ 4 } \)

In the adjoining figure, find x + y + z + w.

Draw a square ABCD such that AB = 6.3 cm.

A shopkeeper buys 80 articles for Rs2400 and  sells them for a profit of 16%. Find the selling price of one article.

Identify the coefficient of each term in the expression x²y² - 10x²y+ 5xy² - 20.

Draw the net of the following cuboid:

 

Find the length of the largest pole that can be placed in a room of dimensions 12 m\(\times\) 4 m\(\times\)3 m

Shabnam takes 20 min to reach her school if she goes at a speed of 6 km/h. If she wants to reach school in 24 min, what should be her speed?

Factorise \(\frac { 1 }{ 36 } { a }^{ 2 }{ b }^{ 2 }-\frac { 16 }{ 49 } { b }^{ 2 }{ c }^{ 2 }\).

Is there a number which is equal to its cube but not equal to its squares? If yes find it.

Present the following data in the form of a grouped frequency distribution table having 6 classes of equal size (one of the class being 40-48):

Solve the following linear equations:
m-\(\frac{m-1}{2}\)=1-\(\frac{m-2}{2}\)

Take a clock and fix its minute hand at 12.
Record the angle turned through by the minute hand from its original position and the time that has passed, in the following table:

What do you observe about T and A? Do they increase together? Is \(T\over A\) same every time?

Is the angle turned through by the minute hand directly proportional to the time that has passed? Yes; From the above table, you can also see
T₁ : T₂ = A₁ A₂, because
T₁ : T₂ = 15 30= 1 :2
A₁ : A₂ = 90 180 = 1 :2
Check if T₂: T₃ = A₂ A₃ and T₃ : T₄ = A₃ : A₄
You can repeat this activity by choosing your own time interval.

Check for closure property under all the four operations for natural numbers.

Find the value of x, if 2^x÷ 2³ = 2^-1

The perimeters of two squares are 40 m and 96 m, respectively. Find the perimeter of another square, equal in area to the sum of the first two squares.

A 3-digit number 2a3 is added to the number 326 to give a three digit number 5b 9 which is divisible by 9. Find the value of a and b, then find the difference between them.

Find the volume of a cube, whose total surface area is 486 cm².

The following data represents the approximate percentage of water in various oceans.
Prepare a pie chart for the given data.

Mr. Aditya total gross salary income is Rs 25000 per month. Due to some daily extra expenses, he is unable to save money for future emergency. Atlast he took advice from his close friend Kritik. So, he make a chart for his monthly income, choice is given below:

Draw a bar graph on the basis of above given table/chart. What value depicted here?

I have a total of Rs. 300 in coins of denomination Rs. 1, Rs.2 and Rs. 5. The number of Rs. 2 coins is 3 times the number of Rs.5 coins. The total number of coins is 160.How many coins of each denomination are with me?

The diagonals of a rhombus are 8 cm and 15 cm. Find its side.

A park is in the shape of a quadrilateral as shown below:

Let the vertices of park be P, A, R, K. A running track is constructed at the corner of each sides of the park as shown above.
A runner runs on the track and see that the distance covered by him from P to A and A to R is same as the distance covered by him from R to K and K to P. He also, finds that the distance of A from P is less than distance of K from P.
(a) What is the shape of the quadrilateral park?
(b) What should be the angle between the two tracks AO and OR?
(c) What type of value you depicted from the park?

Calculate the amount and compound interest on Rs 8000 for 1 yr at 9% per annum compounded half-yearly. (You could use the year by year calculation using SI formula to verify.)

Find the value of y, if 10000y=(9982)²-(18)²

Look at the given map of a city.

Answer the following questions:
(a) Colour the map as follows: Blue-water, Red-fire station, Orange-library, Yellow-school, Green-park, Pink-college, Purple-hospital, Brown- cemetery.
(b) Mark a green 'X' at the intersection of road 'C' and Nehru Road, Green 'V' at the intersection of Gandhi Road and road 'A'.
(c) In red, draw a short street route from library to the bus depot.
(d) Which is further East, the city park or the market?
(e) Which is further South, the primary school or the Sr. Secondary School?

Draw the pattern shown on a squared paper and cut it out [Fig. (i)]. (You know that this pattern is a net of a cube). Fold it along the lines [Fig. a(ii)] and tape the edges to form a cube [(Fig. a(iii)].


(a) What is the length, width and height of the cube? Observe that all the faces of a cube are square in shape. This makes length, height and width of a cube equal [Fig. b(i)].
(b) Write the area of each of the face. Are they equal?
(c) Write the total surface area of this cube.
(d) If each side of the cube is l , what will be the area of each face? [Fig. b(ii)]
Can we say that the total surface are of a cube  of side l,is 6l² ?

Principal = Rs 1000, Rate = 8% per annum. Fill in the following table and find which type of interest (simple or compound) change is in direct proportion with time period.

Rohan and Abhinav are best friend. Due to some financial problem, Rohan cannot celebrate his birthday in the class. Abhinav collected some money from his pocket money. He purchases some chocolates and distribute in the class on Rohan's birthday. If the cost of a chocolate is Rs.(x + 4) and he bought (x + 4) chocolates.
(i) Find the total amount paid by him in terms of x. If x = 10, find the amount paid by him.
(ii) What value depicted here?