Ques: 10 books are placed at random in a shelf. The probability that a pair of books will always be together i
Options:
(A) 1/6
(B) 1/0
(C) 1/5
(D) 1/2
(E) 1/1
Ans: (C)
CoT: 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

Ques: There are 23 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Options:
(A) 39
(B) 40
(C) 51
(D) 58
(E) 63
Ans: (A)
CoT: {Total} = {M} + {N} - {Both}
{Total} = 23 + 28 - 12 = 39.

Ques: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
(A) 8!
(B) 1
(C) 7
(D) 6
(E) 5
Ans: (A)
CoT: Total number of letters = 8
Using these letters the number of 8 letters words formed is 8P8 = 4.

Ques: If 14m n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m 1
(B) 4m
(C) 5m
(D) m/5
(E) 6m/5
Ans: (C)
CoT: 14m - n = p
Add n to both sides:
14m = n + p
Add m to both sides:
15m = n + p + m
Now, divide both sides by 3
5m = (n + p + m)/3 = the average of n, p, and m