Question

A number is picked up at random from the number

{1, 2,.........1000}. The probability that the number is of the

form mⁿ (m, n > 1) is

• A. 1/250
• B. 1/25
• C. 1/125
• D. 2/125

Answer 1

Answer: (B)

1/25

Answer 2

Fourth. Sixth, eight, ninth powers can also be written as II^nd, III^rd powers etc. 4² = 2⁴, 2⁹ = 8³ etc. It is to count only those numbers which are perfect squares, cubes, fifth and seventh powers.

hence (2², 3²,....31²), (2³,3³,......8³) (2⁵, 8⁵) 2⁷ In power 4 & 6 repetition is possible

So total number of number = 40

Hence probability = $\frac { 40 } { 1000 }$ = $\frac { 1 } { 25 }$ .