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

A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
(A) 350 m
(B) 250 m
(C) 300 m
(D) 148 m
(E) 150 m
Answer and stream of consciousness: (E)
Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m

The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
Options:
(A) 1/56
(B) 1/42
(C) 1/40
(D) 1/41
(E) 1/47
Answer and stream of consciousness: (B)
Stream of consciousness: 2/3 * 6/7 * 1/3 * 1/8 = 1/42

Two trains are moving at 85 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 5 25/31 sec
(B) 7 1/17 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/9 sec
Answer and stream of consciousness:
(A)
Stream of consciousness: 70 + 85 = 155 * 5/18 = 775/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/775 = 180/31 = 5 25/31 sec