Question Set C

CBSE 7th Standard Mathematics Data Handling Important Questions And Answers Study Material - QB365

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Questions:

Generic 2

7 x 2 = 14

If \(12 \frac{4}{4}\) is divided by \(\frac{2}{4}\),then find the simplified value.

Evaluate the following, using the distributive property. (-85) \(\times\) 43 + 43 \(\times\) (-15)

A bag contains 3 black balls and 2 white balls. A ball is drawn without looking into the bag. What is the probability that the colour of the ball will be white?

Find \(\frac{3}{4}\)of (i) 16 (ii) 36

In the following figure, find the value of x.

Solve the following equation \(2y+\frac{5}{2}=\frac{37}{2}\)

Add the following integers using number line: -2 and 5

Generic 3

6 x 3 = 18

Find the value of the angles x, y and z in each of the following:

Arushi deposits Rs 2000 per month in her account for six months as saving. But when she is in need, she withdraw Rs 1600 and once again she withdraw Rs 5,000 from her account.
(a) If withdrawal of amount is represented by (-ve) sign and deposition by (+ve) sign, what is the present position (balance) of her account?
(b) Which mathematical concept is used in this problem?
(c) What is its value?

10.

Calculate the value of \([3\frac{6}{9}\times 4\frac{1}{5}]\div [4\frac{1}{45}]\)

11.

A multistorey building has 25 floors above the ground level each of height 5 m. It also has 3 floors in the basement each of height 5 m. A lift in building moves at the rate of 1m/s. If a man starts from 50 m above the ground, how long will it take him to reach at the 2nd floor of the basement?

12.

What happens to the value of the product, when we multiply two improper fractions?

\(\frac{7}{3}\times \frac{5}{2}=\frac{35}{6}\)	\(\frac{35}{6}>\frac{7}{3},\frac{35}{6}>\frac{5}{2}\)	Product is greater than each of the fractions
\(\frac{6}{5}\times \frac{\boxed {}}{3}=\frac{24}{15}\)
\(\frac{9}{2}\times \frac{7}{\boxed {}}=\frac{63}{8}\)
\(\frac{3}{\boxed {}}\times \frac{8}{7}=\frac{24}{14}\)

13.

Take the data giving the minimum and the maximum temperature of various cities given in the below table. Plot a double bar graph using the data and answer the following:

A temperature of cities as on 20.06.2006
City	maximum	Minimum
Ahmedabad	38⁰C	29⁰C
Amritsar	27⁰C	26⁰C
Bangalore	28⁰C	21⁰C
Chennai	36⁰C	27⁰C
Delhi	38⁰C	28⁰C
Jaipur	39⁰C	29⁰C
Jammu	41⁰C	26⁰C
Mumbai	32⁰C	27⁰C

Which city has the largest difference in the minimum and maximum temperatures on the given date?

Fill up / 1 Marks

8 x 1 = 8

14.

\(42.47 \div =\)________0.4247

15.

30% of 300 =________________

16.

In an isosceles triangle, angles opposite to equal sides are______________.

17.

If we multiply ____________ number of negative integers, then the resulting integer is positive.

18.

In the adjacent figure, if I and m are two straight lines, then \(\angle \)1 and \(\angle \)2 are ____________ angles.

19.

If \(\frac{9}{5}x=\frac{18}{5}\) then x = ________.

20.

In the given figure, ΔARO ≅ Δ _____

21.

Replace the blank with an integer to make it a true statement. (-3) x _____ =27

Multiple Choice Question

14 x 1 = 14

22.

The ascending arrangement of\(\frac { 2 }{ 3 } ,\frac { 6 }{ 7 } ,\frac { 14 }{ 21 } \)is

(a)

\(\frac { 1 }{ 5 } ,\frac { 3 }{ 7 } ,\frac { 7 }{ 10 } \)

(b)

\(\frac { 13 }{ 21 } ,\frac { 2 }{ 3 } ,\frac { 6 }{ 7 } \)

(c)

\(\frac { 6 }{ 7 } ,\frac { 13 }{ 21 } ,\frac { 2 }{ 3 } \)

(d)

\(\frac { 2 }{ 3 } ,\frac { 6 }{ 7 } ,\frac { 13 }{ 21 } \)

23.

Madhre is standing in the middle of a bridge which is 20 m above the water level of a river. If a 35m deep river is flowing under the bridge, then the vertical distance between the foot of Madhre and bottom level of the river is:

(a)

55 m

(b)

35 m

(c)

20 m

(d)

15 m

24.

How many pieces of 13.2 cm can be cut from a 330 cm long rod?

(a)

(b)

(c)

(d)

25.

The product of \(\frac{11}{13}\) and 4 is

(a)

\(3 \frac{5}{13}\)

(b)

\(5\frac{3}{13}\)

(c)

\(13\frac{5}{5}\)

(d)

\(13\frac{5}{3}\)

26.

In the given figure, find the value of x.

(a)

75°

(b)

90°

(c)

120°

(d)

60°

27.

If \(\bigotimes \) , O and \(\bullet\) represent some integers on the number line, then descending order of these numbers is

(a)

\(\bullet ,\bigotimes ,\oslash ,O\)

(b)

\(\bigotimes ,\bullet ,\oslash ,O\)

(c)

\(O,\oslash ,\bigotimes ,\bullet \)

(d)

\(O,\bullet ,\bigotimes ,\oslash \)

28.

In the following figure, the value of x is

(a)

110°

(b)

46°

(c)

64°

(d)

150°

29.

Angles which are both supplementary and vertically opposite are

(a)

95°,85°

(b)

90°,90°

(c)

100°,80°

(d)

45°,45°

30.

A bag is having 4 red balls and 6 yellow balls. If a ball is pulled out without seeing them, then find the probability of getting a red ball.

(a)

\(\frac { 2 }{ 5 } \)

(b)

\(\frac { 3 }{ 5 } \)

(c)

\(\frac { 9 }{ 12 } \)

(d)

\(\frac { 2 }{ 3 } \)

31.

The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. The mode of this data is

(a)

(b)

(c)

(d)

32.

If k + 7 = 16, then the value of 8k - 72 is equal to

(a)

(b)

(c)

112

(d)

33.

If a and b are positive integers, then the solution of the equation ax = b will always be a

(a)

positive number

(b)

negative number

(c)

(d)

34.

Which congruence criterion do you use in the following?
Given, ZX = RP, RQ =ZY, ㄥPRQ = ㄥXZY. So, ΔPOR ≅ ΔXYZ

(a)

ASA rule

(b)

SSS rule

(c)

RHS rule

(d)

SAS rule

35.

If * represents 3 mangoes, then 18 mangoes are represented by

(a)

***

(b)

****

(c)

******

(d)

None of these

Generic 5

2 x 5 = 10

36.

In the following figure, X and Y are the points on sides PO and PR of \(\triangle PQR\).such that XY II OR. If \(\angle Q=40^0,\angle P=30^0\),find the angle (i) \(\angle a\) (ii) \(\angle b\) (iii) \(\angle c\).

37.

In the given figure, ΔPQR is a right angled at P, V and T are the points on line QRT, if QP II ST and US II RP, find ㄥS.

True or False

8 x 1 = 8

38.

0 is called the additive identity of integers.

(a)

False

(b)

True

39.

Product of two fractions =\(\frac { Product\ of\ their\ denominators }{ Product\ of\ their\ numerators } \)

(a)

True

(b)

False

40.

A linear pair may have two acute angles.

(a)

True

(b)

False

41.

Two supplementary angles always from a linear pair.

(a)

False

(b)

True

42.

a ÷ b = b ÷ a

(a)

True

(b)

False

43.

5 - (- 8) is same as 5 + 8.

(a)

False

(b)

True

44.

Range of the data is always from the data.

(a)

True

(b)

False

45.

The mode of the observation 23, 26,15,12,28,38,19, 23, 26, 23 is 28.

(a)

True

(b)

False

Generic 4

2 x 4 = 8

46.

If \(\frac { 2x-3 }{ 5 } +\frac { x+3 }{ 4 } =\frac { 4x+1 }{ 7 } \) , find the value of x.

47.

Find:
(a) 9% of Rs.700
(b) 6\(\frac { 2 }{ 3 } \)% of 75 m
(c) 7'5% of 80 kg
(d) 8% of 5 litres

1 Marks

6 x 1 = 6

48.

In the figure, identify:

Two pairs of vertically opposite angles

49.

What value of x will make \(\angle \)AOB and \(\angle \)BOC a linear pair?

50.

Find each of the following and classify the result as whole numbers, proper or improper fraction:
14\(\div\)4\(\frac{3}{4}\)

51.

Pankaj's age is 5 years more than three times the Raju's age. Find the Raju's age if Pankaj's age is 44 years.

52.

What is the median of 10, 1, 9, 2, 8, 3, 7, 4, 6,5?

53.

If 15x = 27 + 6x, find x.

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Answers Key:

Generic 2

7 x 2 = 14

-4300

\(\frac { 2 }{ 5 } \)

(i) We have, \(\frac{3}{4}\)of 16=\(\frac{3}{4}\times 16\)=\(\frac{3\times 16}{4}=\frac{48}{4}=12\)
(ii) We have, \(\frac{3}{4}\)of 27=\(\frac{3}{4}\times 36\)=\(\frac{3\times 36}{3}=\frac{108}{4}=27\)

x = 30°

We have, \(2y+\frac{5}{2}=\frac{37}{2}\)
On transposing \((+\frac{5}{2})\) from LHS to RHS, we get
\(2y=\frac{37}{2}-\frac{5}{2}\quad \Rightarrow 2y=\frac{1}{2}(37-5)\) [taking \(\frac{1}{2}\) as common]
\(\Rightarrow \quad 2y=\frac{32}{2}=16\)
On dividing both sides by 2, we get
\(\frac{2y}{2}=\frac{16}{2}\quad \Rightarrow y=8\)
Hence, y = 8 is a solution of the given equation.

We have, -2 and 5
In this case, firstly we go to (-2) and then move (5) step to the right of (-3).
Thus, we reached to (3), i.e. (-2) + (5) = 3

Generic 3

6 x 3 = 18

Since 40° and z are vertically opposite angles,
∴ z=40°
Again y and 40° form a linear pair.
∴ y + 40° = 180°
[Transposing 40° to R.H.S]
or y = 180° - 40°
or y = 140°
∵ y and (x + 25°) are vertically opposite angles
∴ (x + 25°) = y = 140°
[∵ y = 140^o]
or x = 140° - 25°
[Transposing 25° to R.H.S.]
or x = 115°
Thus, x = 115°, y = 140° and z = 40°

(a) Since, she deposits Rs 2000 per month
∴ Amount deposit by her in six months
= Rs 2000 \(\times\) (6)
= Rs 12,000
She withdraw Rs 1600 and Rs 5000 in need.
So, withdrawal = - (1600 + 5000)
So, present position of account
= 12000- (1600 + 5000)
= 12000- 6600
= 5400
So, she has balance Rs 5400 in her account.
(b) Multiplication and subtraction of integers.
(c) If you save the money you can use it in need.

10.

\(3\frac{150}{181}\)

11.

In the following figure, we can clearly see that man will have to cover 60 m to reach the second floor of the basement.

Since lift moves with a speed of 1 m/s.
Hence, time taken to reach the second floor of basement = \(\frac { Distance }{ Speed } =\frac { 60m }{ 1{ m }/{ s } } \) = 60 s or 1 min

12.

\(\frac{7}{3}\times \frac{5}{2}=\frac{35}{6}\)	\(\frac{35}{6}>\frac{7}{3},\frac{35}{6}>\frac{5}{2}\)	Product is greater than each of the fractions
\(\frac{6}{5}\times \frac{\boxed {}}{3}=\frac{24}{15}\)	\(\frac{24}{15}>\frac{6}{5},\frac{24}{15}>\frac{4}{3}\)	Product is greater than each of the fractions
\(\frac{9}{2}\times \frac{7}{\boxed {}}=\frac{63}{8}\)	\(\frac{63}{8}>\frac{9}{2},\frac{63}{8}>\frac{7}{4}\)	Product is greater than each of the fractions
\(\frac{3}{\boxed {}}\times \frac{8}{7}=\frac{24}{14}\)	\(\frac{24}{14}>\frac{3}{2},\frac{24}{14}>\frac{8}{7}\)	Product is greater than each of the fractions

13.

Jammu is a city in which, there is largest difference in the minimum and maximum temperature

Fill up / 1 Marks

8 x 1 = 8

14.

()
100

15.

()
90

16.

()
equal

17.

()
even

18.

()
vertically opposite

19.

Given, \(\frac{9}{5}x=\frac{18}{5}\quad \Rightarrow x=\frac{18\times 5}{5\times 9}\)
\(\Rightarrow x=\frac{18\times 1}{1\times 9}=2\)
So, if \(\frac{9}{5}x=\frac{8}{5}\) then x = 2.

20.

()
PQO

21.

()
(- 3) x (- 9) = 27

Multiple Choice Question

14 x 1 = 14

22.

(b)
\(\frac { 13 }{ 21 } ,\frac { 2 }{ 3 } ,\frac { 6 }{ 7 } \)

23.

(a)
55 m

24.

(a)
25

25.

(a)
\(3 \frac{5}{13}\)

26.

27.

28.

(d)
150°

29.

(b)
90°,90°

30.

(a)
\(\frac { 2 }{ 5 } \)

31.

32.

(a)
0

33.

(a)
positive number

34.

(d)
SAS rule

35.

Generic 5

2 x 5 = 10

36.

a = 40° ,b = 110° ,c = 110°

37.

Given ㄥQPR = 90°, ORT is a line, OP II ST and US II PR, ㄥS=?
Now, we extend US up to U such that it intersects QP at U.
PR || US [given]
⇒ PR || U'S, U'P is a transversal.

So, ㄥP + ㄥU' = 180° [by the property, sum of two interior angles on the same side of a transversal]
90⁰ + ㄥU = 180°
ㄥU' = 180° - 90°
ㄥU = 90°
Similarly, OP II ST [given]
Then, US is a transversal.
So, ㄥU' + ㄥS =180° ⇒ 90° + ㄥS =180°
⇒ ㄥS=180⁰ - 90° ⇒ ㄥS = 90°.

True or False

8 x 1 = 8

38.

(a)
False

39.

(b)
False

40.

(b)
False

41.

(a)
False

42.

(b)
False

43.

(a)
False

44.

(b)
False

45.

(b)
False

Generic 4

2 x 4 = 8

46.

Given, \(\frac { 2x-3 }{ 5 } +\frac { x+3 }{ 4 } =\frac { 4x+1 }{ 7 } \)
\(\Rightarrow \quad \frac { 4(2x-3) }{ 5\times 4 } +\frac { 5(x+3) }{ 5\times 4 } =\frac { 4x+1 }{ 7 } \)
\(\Rightarrow \quad \frac { 8x-12 }{ 20 } +\frac { 5x+15 }{ 20 } =\frac { 4x+1 }{ 7 } \)
\(\Rightarrow \quad \frac { 8x-12+5x+15 }{ 20 } =\frac { 4x+1 }{ 7 } \)
\(\Rightarrow \quad \frac { 13x+3 }{ 20 } =\frac { 4x+1 }{ 7 } \)
\(\Rightarrow\) 7(13x + 3) = 20(4x + 1)
\(\Rightarrow\) 91x + 21 = 80x + 20
\(\Rightarrow\) 91x - 80x = 20 - 21
\(\Rightarrow\) 11x = -1
Thus, \(x=-\frac { 1 }{ 11 } \)

47.

(a) 9% of Rs.700= \(\frac { 9 }{ 100 } \times \)700
= 9 X 7
= Rs.63
(b) 6 \(\frac { 2 }{ 3 } \)% of 75m =\(\frac { 20 }{ 3 } \)% of 75 m
=\(\frac { 20 }{ 300 } \times \)75 m
=\(\frac { 1 }{ 15 } \times \)75 m
=5 m
(c) 7.5 % of 80 kg =\(\frac { 7.5 }{ 100 } \times \)80 kg
=\(\frac { 3 }{ 40 } \times \)80 = 6 kg
(d) 8% of 5 liters =\(\frac { 8 }{ 100 } \times \)5 litres
=\(\frac { 40 }{ 100 } \times \)0.4 litre.