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8th Grade > Mathematics

EXPONENTS AND POWERS MCQs

Total Questions : 58 | Page 4 of 6 pages
Question 31.


Find the multiplicative inverse of 105.


  1.     - 50
  2.     0.00001
  3.     - 100000
  4.     100000
 Discuss Question
Answer: Option D. -> 100000
:
D

105
= 1105
= 1100000
When a number is multiplied with its multiplicative inverse, the result is 1. To make the given number, which is 1100000, equal to 1, we need to multiply it with 100000, which is the reciprocal of 1100000.
Therefore, 100000, or 105 is the multiplicative inverse of 105.


Question 32.


(4×103+3×1+1×101+6×100)=


___
 Discuss Question
Answer: Option D. -> 100000
:

4×103+3×1+1×101+6×100=(4×1000)+(3×1)+110+(6×1)=4000+3+0.1+6=4009.1


Question 33.


Express  4.95×105 in usual form.


  1.     49500
  2.     4950
  3.     495000
  4.     4950000
 Discuss Question
Answer: Option C. -> 495000
:
C

4.95×105=4.95×100000=495000


Question 34.


The value of 1000 is 1000.


  1.     True
  2.     False
  3.     2.16×105   
  4.     216×1000000
 Discuss Question
Answer: Option B. -> False
:
B

Note that a0=1 for any a0
Thus, the value of 1000 is 1.


Question 35.


Find the value of ‘m‘ if (2)2×(5)3=50m


  1.     -10
  2.     10
  3.     50
  4.     -50
 Discuss Question
Answer: Option A. -> -10
:
A

(2)2×(5)3=50m
4×(125)=50m
500=50m
m=10


Question 36.


If 4x = 64, then 


  1.     22x=64
  2.     2x = 6
  3.     x = 3
  4.     10x=10000
 Discuss Question
Answer: Option A. -> 22x=64
:
A, B, and C

 4x=64
 4x=43            (as 64 is 43 )
 x=3   (am = an if and only if m=n for a0,1,1)
 Since x=3,  22x = 64 ,  and 2x =6


Question 37.


(9×102)+(9×103) in usual form is given by 


  1.     9000.09
  2.     900.9
  3.     9000.9
  4.     900.09
 Discuss Question
Answer: Option A. -> 9000.09
:
A

The usual forms of the expressions 9×102 and 9×103 are given by 0.09 and 9000.
Thus, 9000 + 0.09 = 9000.09.


Question 38.


Evaluate the exponential expression x5 × x4, for x = 2.


  1.     32
  2.     128
  3.     256
  4.     512
 Discuss Question
Answer: Option D. -> 512
:
D

x5 × x4, for x = 2
Substituting 2 in place of x
= 25× 24
= 29   (am×an=am+n) = 512


Question 39.


Find the value of 73.


  1.     343
  2.     1343
  3.     121
  4.     149
 Discuss Question
Answer: Option B. -> 1343
:
B

We know that am=1am for any non-zero integer a and integer m.
73=173
                 =17×7×7=1343


Question 40.


Find the multiplicative inverse of 107.


  1.     102
  2.     102
  3.     107
  4.     106
 Discuss Question
Answer: Option C. -> 107
:
C

Multiplicative inverse of a non-zero x is 1x; so that when these two are multiplied, the product value is 1. Therefore, the multiplicative inverse of 107should be a number which when multiplied with 107 gives 1.
Let the multiplicative inverse of 107 be x.
Then, 107×x=1.
                 x=1107=107
(an=1an1an=11an=an)
Thus, the multiplicative inverse of 107 is 107.


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