A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
Options:
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 150 sec
(D) 164 sec
(E) 2 mins 44 sec

D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 se So the answer is: (C).

10 books are placed at random in a shelf. The probability that a pair of books will always be together is -
Options:
(A) 1/5
(B) 1/3
(C) 1/4
(D) 118/2
(E) 21/4

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 ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan’s age was thrice as that of Rahul’s,find their present ages
Options:
(A) 14 years, 30 years
(B) 12 years, 28 years
(C) 16 years, 34 years
(D) 18 years, 38 years
(E) none of these

Let Rahul’s age = x years
So, Madhan’s age = ( x + 16 )years
Also, 3(x - 6) = x + 16 - 6 or, x = 14
Rahul’s age = 14 years
And, Madhan’s age 14 + 16 = 30 years So the answer is: (A).

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?
Options:
(A)  1/8
(B)  1/2
(C)  3/4
(D)  7/8
(E)  15/16

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8. So the answer is: (D).