4 Solved Factorial Problems To Prepare For Bank of Baroda PO Exam

Dear Reader,
Below are four problems on basic calculations of factorials.

Note:
1) (n+1)! = (n+1)n!
2) (n+5)! = n!(n+1)(n+2)(n+3)(n+4)(n+5)

Question 1

Evaluate 29!/27!

a) 784 b) 812 c) 996 c) 128

Answer : b)812

Solution :

Given 29!/27!
By using the note (2), we can rewrite
29! = 27!(28)(29)
Then, 29!/27! = 27!(28)(29) / 27!
= 28 x 29
= 812
Hence the answer is 812.

Question 2

Evaluate (15! - 14!)/ 13!

a) 144 b) 169 c) 196 c) 125

Answer : c)196

Solution :

Given that, (15! - 14!)/ 13!
(15)14! - 14! / 13!
14!(15 - 1)/13!
14!(14)/13!
13!(14)(14)/13!
14 x 14
196
Hence the required answer is 196.

Question 3

Evaluate 13!/9!6!

a) 143/6 b) 155 c) 155/3 d) 187/7

Answer : a)143/6

Solution :

13! = 9! x 10 x 11 x 12 x 13
Then the given expression 13!/9!6! = 9! x 10 x 11 x 12 x 13 / 9!6!
13!/9!6! = 9! x 10 x 11 x 12 x 13 / 9!6!
= 10 x 11 x 12 x 13 / 6!
= 10 x 11 x 12 x 13 / 1 x 2 x 3 x 4 x 5 x 6
= 11 x 12 x 13 / 3 x 4 x 6
= 11 x 13 / 6
= 143/6

Question 4

Evaluate 1/12! + 1/13! - 1/14!

a) 522/16! b) 224/13! c) 195/14! d) 185/11!

Answer : c)195/14!

Solution :

Given that, 1/12! + 1/13! - 1/14!
1/12! = 14 x 13 / 14 x 13 x 12! = 14 x 13 / 14!
1/13! = 14 / 14 x 13! = 14/14!
1/14! = 1/14!
Then given expression = 14 x 13/14! + 14/14! - 1/14!
= (182 + 14 - 1)/14!
= 195/14!
Hence the answer is option c.


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