Question: In wardrobe Karan has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens his wardrobein the dark and pick out one shirttrouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options:
(A) 1/2
(B) 2/3
(C) 4/5
(D) 6/11
(E) 4/5
Answer: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
Required probability = 2/3 x 3/4 = 1/2
The answer is (A).

Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
(A) 5/9
(B) 5/12
(C) 1/36
(D) 7/12
(E) 4/9
Answer: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
The answer is (B).

Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 5 strokes ?
Options:
(A) 31/32
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
Answer: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16
Left After 5th stroke = 1/2 * 1/16 = 1/32
So removed = 1- 1/32 = 31/32
The answer is (A).

Question: A owes B Rs.50. He agrees to pay B over a number of consecutive days on a Monday, paying single note or Rs.10 or Rs.20 on each day. In how many different ways can A repay B.
Options:
(A) 2
(B) 8
(C) 9
(D) 6
(E) 5
Answer:
He can pay by all 10 rupee notes = 1 way
3 Ten rupee + 1 twenty rupee = 4!3!1!4!3!1! = 4 ways
1 Ten rupee + 2 twenty rupee notes = 3!2!1!3!2!1! = 3 ways
Total ways = 1 + 4 + 3 = 8
The answer is (B).