1
Q:

5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?

A) 2880 B) 1440
C) 720 D) 2020

Answer:   A) 2880

Explanation:

There are total 9 places out of which 4 are even and rest 5 places are odd.

4 women can be arranged at 4 even places in 4! ways.

and 5 men can be placed in remaining 5 places in  ways.

Hence, the required number of permutations  = 4! x  = 24 x 120 = 2880

Q:

A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group ?

A) 600 B) 610
C) 609 D) 599
 
Answer & Explanation Answer: A) 600

Explanation:

Two men, three women and one child can be selected in ⁴C₂ x ⁶C₃ x ⁵C₁ ways

=

= 600 ways.

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1 3
Q:

The number of sequences in which 4 players can sing a song, so that the youngest player may not be the last is ?

A) 2580 B) 3687
C) 4320 D) 5460
 
Answer & Explanation Answer: C) 4320

Explanation:

Let 'Y' be the youngest player.

The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.

The required number of ways = 3(3!) = 4320.

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3 63
Q:

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most  ?

A) 215 B) 268
C) 254 D) 216
 
Answer & Explanation Answer: A) 215

Explanation:

Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.

Maximum number of unsuccessful attempts = 216 - 1 = 215.

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1 28
Q:

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is  ?

A) 2(6!) B) 6! x 7
C) 6! x ⁷P₆ D) None
 
Answer & Explanation Answer: C) 6! x ⁷P₆

Explanation:

We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.

Hence required number of ways = 6! x ⁷P₆

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1 49
Q:

The number of permutations of the letters of the word 'MESMERISE' is  ?

A) 9!/(2!)^{2}x3! B) 9! x 2! x 3!
C) 0 D) None
 
Answer & Explanation Answer: A) 9!/(2!)^{2}x3!

Explanation:

n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements =

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0 98