Wisechamps Grade 7 Exponents and Powers (Session 5)

Exponents

and

Power

Multiple Choice

9. There are three places A, B, C in a straight line as shown below. If distance between place A and B is $$\left(2.4\times10^6\right)$$ m and distance between place B and C is $$\left(5.2\times10^5\right)$$ m, then find the distance between place A and C in

standard form.

• $$292\times10^6\ km$$

• $$2.92\times10^6\ km$$

• $$292\times10^5\ m$$

• $$2.92\times10^4\ m$$

12. State ‘T’ for true and ‘F’ for false.

W. If x and y are zero rational numbers and m is a positive integer, then xm ✖ ym = (xy)2m and xm÷ ym=

X. Standard from of 38000000 is 3.8 ✖ 107.

Y. The base and power in (— 16 ✖ 2)4 is — 32 and 44 respectively.

Z. 62is greater than 26.

(W)

(X)

(Y)

(Z)

A.

T

F

F

T

B.

F

T

T

F

C.

F

T

F

T

D.

T

F

T

F

Ans. B

Solution:

W. False; If a and b are rational numbers, then

xm ✖ ym= (ab)m

xm✖ ym= (xy)m= (x ✖ y)m

Hence, xm✖ ym≠ (x ✖ y)2m

And xm÷ ym ≠

X. True;

Y. True;

Z. False; 62= 36 is less than 26= 2 ✖ 2 ✖ 2 ✖ 2 ✖ 2 ✖ 2 = 64
So, statement Z is false.

13. Match the following and select the correct option.

Column - I

Column - II

(i)

(ii)

(iii)

(iv)

A.

S

P

R

Q

B.

P

Q

S

R

C.

R

S

P

Q

D.

R

P

Q

S

14. Fill in the blanks.

(i) If x = (6—1 — 8—1)—1 and y = (2— 1— 3—1)—1, then x + y = _________.
(ii) The value of 100150÷ 10146is _______.
(iii) In the standard form, there is only one digit to the ________ of decimal point.
(iv) 30+ 60 + _______ + 70 = 6

(i)

(ii)

(iii)

(iv)

A.

24

10024

right

1

B.

30

10077

left

3

C.

6

1077

left

2

D.

30 right

2

Ans. B

Solution: We have

(ii) We have, 100150÷ 10146
(102)150÷ 10146= 10300 ÷ 10146

10300 — 146= 10154

102 ✖ 77 = (102)77= 10077

(iii) In the standard form, there is only one digit to the left of the decimal points.

(iv) 30+ 60+ _______ + 70= 6

1 + 1 + ______ + 1 = 6
1 + 1 + 3 + 1 = 6

15. Read the statements carefully and select the correct option.

Statement - I: If 8x + 1 .= 64, then the value of (— 1)2x + 1= 1.

Statement- II:

A. Both Statement - I and Statement - II are true.
B. Both Statement - I and Statement - II are False.
C. Statement -I is true but Statement - II is false.
D. Statement - I is false but Statement - II is true.

Ans. D

Solution:
Statement - I: 8x + 1 = 64 = 8x + 1 = 82
x + 1 = 2, x = 1
Now, (— 1) 2x + 1= (—1) 2 + 1= — 1
So ,Statement - I is false.

Statement - II: We have,

9. 3/20 of delegation are from India, ¼ are from Britain, 3/10 are from Germany ad the rest are
Americans. If there are 1200 members in the delegation, calculate how may Americans there?
A. 460
B. 400
C. 360
D. 300

Ans. 9. B. 360

Solution: Fraction of delegates from India = 3/20
Fraction of delegates from Britain = 1/4

Fraction of delegates from Germany = 3/10

Given that the rest of the delegates are American
⇒ Delegates from America = 1 − 3/20 -¼ - 3/10 = 20−3−5−6/20 = 6/20

Total members in the delegation =1200
∴ Number of American delegates = 6/20 ×1200=360

10. In an examination, a student was asked to find 5/17 of certain number. By mistake he found 17/5 of
that number. If his answer was 264/119 more than correct answer, then find the number
A. 7/5
B. 5/7
C. 3/7
D. 7/3

Ans. 10. B. 5/7

Solution: Let the number be x.
Answer obtained by the student = 17/5 x X

According to the question, we have
(17/5)x – (5/17)x = 264/119

= 289x -25x/ 85 = 264/119
= 264x / 85 = 264 /119
x = 5/7

11. Evaluate :

A.

B.

C.

D.

Ans. 11. B.

Solution: Consider,

Now,

12. Which of the following rational numbers satisfies 4(a+b) = 10(b + c)?

A. a = -2,

B. a = -10,

C.

D.

Ans. 12. A

Solution: 4(a + b) =

13. Read the statements carefully and state ‘T’ for true and ‘F’ for False.

(i)

(ii)

(iii) There are finite rational numbers between two rational numbers.

(iv) If the numerator equivalent fraction of

is ー16 then the denominator is ー20.

(i)

(ii)

(iii)

(iv)

A.

T

F

F

T

B.

T

T

T

T

C.

F

T

F

T

D.

T

F

T

F

Ans. 13. A.

T

F

F

T

Solution:
(i). True;

(ii). False;

(iii) False; There are infinite rational numbers between two rational numbers.

(iv) True;

, which is a positive rational number.

14. Study the following statements carefully and select the correct option.
Statement - I. Number 0 is neither a positive nor a negative rational number.

Statement - II. If Ravi from a point A towards North and then from there towards South, then

he is at from point A towards south.

A. Both Statement - I and Statement - II are true.
B. Both Statement - I and Statement - II are false.
C. Statement - I is false but Statement - II is true
D. Statement - I is True but Statement - II is False

Ans. 14. D. Statement - I is false but Statement - II is true

Solution:
Statement - I. Number 0 is neither a positive nor a negative rational number. So
Statement I is true .

Statement II: Ravi’s final distance from point A.

Statement II is false.

15. State ‘T’ for true and ‘F’ for False.

(i). Every rational number can not be expressed with a positive numerator.

(ii). Rational numbers are arranged in ascending order.

(iii).

(iv).

(i)

(ii)

(iii)

(iv)

A.

F

F

F

T

B.

F

T

T

T

C.

F

T

T

F

D.

F

F

T

T

Ans. 15. C

Solution :

(i) False; Every rational number can be expressed with a positive numerator.
(ii) True;

(ii) True;

(iii) False;