10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
Options:
(A) 1/7
(B) 1/9
(C) 1/5
(D) 1/8
(E) 1/2

10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5 So the answer is: (C).

The average age of A, B and C is 27 years. If the average age of A and C is 29 years, what is the age of B in years ?
Options:
(A) 19
(B) 35
(C) 20
(D) 32
(E) 23

Age of B = Age of (A + B + C) Age of (A + C) = 27 3 29 2 = 81 58 = 23 years So the answer is: (E).

X can finish a work in 30 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 3
(B) 10
(C) 6
(D) 8
(E) 9

Work done by X in 1 day = 1/30
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/30) = 10 So the answer is: (B).

The edge of a cube is 7a cm. Find its surface?
Options:
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 294a2
6a2 = 6 * 7a * 7a = 294a2 So the answer is: (E).