Ques: In how many different ways can the letters of the word "BICYCLE" be rearrangement?
Options:
(A) 5040
(B) 5045
(C) 5140
(D) 5010
(E) 5020
Ans: (A)
CoT: Option 'A'
The total number of arrangements is
7P7 = 7! = 5040

Ques: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 6 hours. Harvesting machine K harvested how many acres of wheat per hour?
Options:
(A) 4
(B) 8
(C) 12
(D) 13
(E) 15
Ans: (A)
CoT: Rate of H = 6 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/6 = 10 acres/hr
Rate of K = 10 - 6 = 4

Ques: Find the probability that the number drawn is a factor of 50.
Options:
(A) 1/25
(B) 1/50
(C) 3/25
(D) 3/50
(E) 7/50
Ans: (D)
CoT: The factors of 50 are 1, 2, 5, 10, 25, 50
Therefore, required probability = 6/100 = 3/50.

Ques: The average of first 15 natural numbers is?
Options:
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Ans: (B)
CoT: Sum of 15 natural no. = 240/2 = 120
Average = 120/15 = 8