JEE Mathematics Permutation and Combination MCQs Set 03

Question: If 1/9! + 1/10 ! = x/11! then the value of x is -

• a) 121
• b) 123
• c) None of these
• d) 125

Answer: 121

Question: The number of different words (meaningful or meaningless) can be formed by taking four different letters from English alphabets is-

• a) 358800
• b) 15600
• c) (26)⁴
• d) (25)⁴

Answer: 358800

Question: In how many ways can a committee of 6 persons be made out of 10 persons ?

• a) 210
• b) 151200
• c) 300
• d) None of these

Answer: 210

Question: In how many ways a committee of 5 members can be selected from 6 men and 5 women, consisting of 3 men and 2 women?

• a) 200
• b) 300
• c) 100
• d) None of these

Answer: 200

Question: Out of 5 men and 2 women, a committee of 3 is to be formed. In how many ways can it be formed if atleast one woman is to be included?

• a) 25
• b) 20
• c) 30
• d) None of these

Answer: 25

Question: In how many ways 11 players can be selected out of 15 players when (a) one particular player is always to be selected.(b) one particular player is never to be selected.

• a) 1001,364
• b) 3003,1001
• c) 364,1365
• d) 3003, 364

Answer: 1001,364

Question: In how many ways can I purchase one or more shirts if 6 different shirts are available ?

• a) 63
• b) 64
• c) 62
• d) 126

Answer: 63

Question: A bag contains 3 one rupee coins, 4 fifty paise coins and 5 ten paise coins. How many selections of money can be formed by taking atleast one coin from the bag ?

• a) 119
• b) 120
• c) 60
• d) 59

Answer: 119

Question: The value of ⁸P₃ is -

• a) 336
• b) 56
• c) 386
• d) None of these

Answer: 336

Question: The number of numbers which can be formed with the digits 2, 3, 4, 5, 6 by taking 4 digits at a time are-

• a) 120
• b) None of these
• c) 135
• d) 150

Answer: 120

Question: In how many ways can three persons sit on 6 chairs?

• a) 120
• b) 150
• c) 140
• d) 110

Answer: 120

Question: How many different signals can be made by 5 flags from 8 flags of different colours?

• a) 6720
• b) 4720
• c) 5720
• d) None of these

Answer: 6720

Question: How many numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6 if the repetition of digits is not allowed?

• a) 120
• b) None of these
• c) 30
• d) 50

Answer: 120

Question: How many four digit numbers are there with distinct digits?

• a) 4536
• b) 4516
• c) 4526
• d) None of these

Answer: 4536

More Questions....................................

Question: How many different words can be formed with the letters of the word “ALLAHABAD” ?

• a) 7560
• b) 8640
• c) 10080
• d) 15120

Answer: 7560

Question: How many numbers can be formed with the digits 2,3,3,4,2,3 taken all at a time.

• a) 60
• b) None of these
• c) 460
• d) 260

Answer: 60

Question: There are 6 pockets in the coat of a person. In how many ways he can put 4 pens in these pockets ?

• a) 1296
• b) None of these
• c) 360
• d) 4096

Answer: 1296

Question: The number of three digit numbers can be formed without using the digits 0,2,3,4, 5 and 6 is (if repetition of digit is allowed)–

• a) 64
• b) None of these
• c) 54
• d) 44

Answer: 64

Question: The number of numbers lies in between 100 and 1000 in which all the digits are distinct is –

• a) 648
• b) 548
• c) 448
• d) None of these

Answer: 648

Question: The number of three digit numbers greater than 600 can be formed by using the digits 2,3,4, 6,7 if repetition of digits is allowed, is

• a) 50
• b) 30
• c) 20
• d) None of these

Answer: 50

Question: In how many ways 3 prizes can be distributed among 5 students, when- (i) no student receives more than one prize. (ii) a student can receive any number of prizes. (iii) a student does not get all prizes.

• a) 60,125,120
• b) 125,120,60
• c) 125,60,120
• d) None of these

Answer: 60,125,120

Question: The number of ways in which 10 candidates A₁, A₂,…, A₁₀ can be ranked, so that A₁ is always above A₂ is

(1) 10!/2

(2) 8! × ¹⁰C₂

(3) ¹⁰P₂

(4) ¹⁰C₂

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question: Ten persons, amongst whom any three persons A, B and C speak in a function. The number of ways in which it can be done if A wants to speak before B, and B wants to speak before C is

(1) 21870 (2) 10!/6
(3) 10!/3  (4) ¹⁰P₇

• a) 2 and 4 are correct
• b) 1, 2 and 3 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 2 and 4 are correct

Question:

Statement 1 : The value of expression n! × (20 – n)! is minimum, when n = 10.
Statement 2 : ^2mC_r is maximum when r = m.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is True, Statement-2 is False
• d) Statement -1 is False, Statement-2 is True.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement 1 : Number of permutations of “n” dissimilar things taken all at a time is ⁿP_n.
Statement 2 : n(a) = n(b) = n, then the total number of functions from A to B are n!

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.

Question: There are 3 letters and 3 envelopes. Number of ways in which all letters are put in the wrong envelopes, is

• a) 2
• b) 6
• c) 4
• d) None of these

Answer: 2

Question: There are 4 balls of different colour and 4 boxes of colours same as those of the balls. Then the number of ways to place two balls in the boxes with respect to their colour is

• a) 6
• b) 2
• c) 4
• d) None of these

Answer: 6

Question: In how many way can 52 playing cards be distributed into 3 groups of 17 cards each and one group of one card.

• a) 52!/(17!) 3!
• b) 52!/(17!) 3! 2!
• c) None of these
• d) Both

Answer:    52!/(17!) 3!

Question: 3 copies each of 4 different books are available. The number of ways in which these can be arranged on the shelf is-

• a) 369,600
• b) 12!
• c) 369,000
• d) None of these

Answer: 369,600

Question: Number of words that can be formed containing 4 consonants and 3 vowels out of 6 consonants and 5 vowels is

• a) ⁶C₄ × ⁵C₃× 7!
• b) ⁶C₄ × ⁵C₃
• c) ⁶C₄ × ⁵P₃× 7!
• d) None of these

Answer: ⁶C₄ × ⁵C₃× 7!

Question: In how many ways can 7 persons be seated round two circular tables when 4 persons can sit on the first table and 3 can sit on the other ?

• a) 420
• b) 210
• c) 35
• d) 2520

Answer: 420

Question: The number of words by taking 4 letters out of the letters of the word ‘COURTESY’, when T and S are always included are-

• a) 360
• b) 120
• c) 720
• d) None of these

Answer: 360

Question: The number of ways in which 5 out of 7 persons be seated at 5 places round a table are-

• a) 504
• b) None of these
• c) 252
• d) 2520

Answer: 504

Question: In how many ways can 5 beads out of 7 different beads be strung into a ring ?

• a) 252
• b) 504
• c) 2520
• d) None of these

Answer: 252

Question: Number of ways that can 6 persons be seated round a circular table when two particular persons sit together is

• a) 48
• b) 120
• c) 240
• d) 24

Answer: 48

Question: The number of ways in which 16 identical toys are to be distributed among 3 children such that each child does not receive less than 3 toys is

• a) 36
• b) 72
• c) 18
• d) 54

Answer: 36

Question:  Find the number of non-negative integral solutions of x₁+ x₂+ x₃ + 4x₄ = 20.

• a) 536
• b) 436
• c) 418
• d) 318

Answer: 536

Question: In how many ways can 10 identical toys be distributed among 3 children such that the first receives a maximum of 6 toys, the second receives a maximum of 7 toys and the third receives a maximum of 8 toys ?

• a) 47
• b) 37
• c) 51
• d) 27

Answer: 47

Question: In how many ways 5 identical balls can be distributed into 3 different boxes so that no box remains empty?

• a) 6
• b) 36
• c) 18
• d) 12

Answer: 6

Question: Find the number of permutation of 4 letters taken from the word EXAMINATION.

• a) 2454
• b) 2520
• c) 1504
• d) 2552

Answer: 2454

Question: The sum of all numbers which can be formed with digits 1,2 and 3 is-

• a) 1332
• b) None of these
• c) 716
• d) 2148

Answer: 1332

Question: The number of ways in which 7 girls can be stand in a circle so that they do not have the same neighbour in any two arrangements is

• a) 360
• b) 720
• c) 380
• d) None of these

Answer: 360

Question: The number of ways in which 7 men and 7 women can sit arround a circular table so that no two women sit together is

• a) 7! . 6!
• b) 7!
• c) 7! . 7!
• d) (6!)2

Answer: 7! . 6!

Question: There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which one ball each box could be placed such that a ball does not go to box of its own colour is-

• a) 9
• b) 8
• c) 7
• d) None of these

Answer: 9

Question:  In a shop there are five types of ice-creams available. A child buys six ice-creams

Statement-1 : The number of different ways the child can buy the six ice-creams is ¹⁰C₅.
Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1..
• d) None of these

Answer: Statement -1 is False, Statement-2 is True.