a2zinterviews

6.	In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
	A.  63
	B.  90
	C.  126
	D.  45

Solution

Required number of ways = (7C2 ×3C2) = (7C2 ×3C1) = ( 7 ×6 / 2 ×1 ×3) ‹=›63.

7.	How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
	A.  5
	B.  10
	C.  15
	D.  20

Solution

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. Tens place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any one of the remaining 4 digits. So there are 4 ways of filling it. Required number of numbers(1x5x4) = 20.

8.	How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using all the letters of the word 'DELHI' using each letter exactly once?
	A.  10
	B.  25
	C.  60
	D.  120

Solution

The word 'DELHI' contains 5 different letters. Required numbers of words = Number of arrangements of 5 letters, taken all at a time = 5P5 = 5! = (5 x 4 x 3 x 2 x 1) = 120.

9.	In how many different ways can the letters of the word 'RUMOUR' be arranged?
	A.  180
	B.  90
	C.  30
	D.  720

Solution

The word 'RUMOUR' contains 6 letters, namely 2R, 2U, 1M and 1U. Required number of ways = 6 ! / (2!) (2!) (1!) (1 !) ‹=›180..

10.	The value of 75P2 is
	A.  2775
	B.  150
	C.  5550
	D.  None of these

Solution

75P2 = 75 ! / 73 ! ‹=› 75 x 74 x (73!) / 73! ‹=› (75 x 74). ‹=› 5550.