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# JEE Main Math Previous Year Papers Permutations and Combinations Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Math Previous Year Paper Permutations and Combinations Questions Answer Keys Solutions.

### JEE Mains Mathematics Permutations and Combinations Questions Bank

JEE Permutations and Combinations Questions No:1

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are

[2002]

Option A: 312

Option B: 3125

Option C: 120

Option D: 216

Option D: 216

JEE Main Permutations and Combinations Questions No: 2

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are

[2002]

Option A: 216

Option B: 375

Option C: 400

Option D: 720

Option D: 720

JEE Mathematics Permutations and Combinations Questions No: 3

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

[2002]

Option A: 3000

Option B: 3050

Option C: 3600

Option D: 3250

Option B: 3050

JEE Main Math Permutations and Combinations Questions No:4

If nCr denotes the number of combination of n things taken r at a time, then the expression nCr+1 + nCr-1 + 2 × nCr equals

[2003]

Option A:  n+1Cr+1

Option B: n+2Cr

Option C: n+2Cr+1

Option D: n+1Cr

Option C: n+2Cr+1

Permutations and Combinations JEE Questions No: 5

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

[2003]

Option A: 346

Option B: 140

Option C: 196

Option D: 280

Option C: 196

Permutations and Combinations JEE Main Questions No: 6

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

[2004]

Option A: 8C3

Option B: 21

Option C: 38

Option D: 5

Option B: 21

Permutations and Combinations Questions for JEE Mains Questions No: 7

The range of the function f (x) = 7-xPx-3  is

[2004]

Option A: {1, 2, 3, 4, 5}

Option B: {1, 2, 3, 4, 5, 6}

Option C: {1, 2, 3, 4}

Option D: {1, 2, 3,}

Option D: {1, 2, 3}

Permutations and Combinations Questions and Answers No: 8

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

[2004]

Option A: 480

Option B: 240

Option C: 360

Option D: 120

Option C: 360

Permutations and Combinations Questions with Solutions No: 9

The value of 50C4 +

56-rC3 is

[2005]

Option A: 55C4

Option B: 55C3

Option C: 56C3

Option D: 56C4

Option D: 56C4

JEE Mains Permutations and Combinations Questions No: 10

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is

[2006]

Option A: 5040

Option B: 6210

Option C: 385

Option D: 1110

Option C: 385

JEE Mains Math Permutations and Combinations Questions No: 11

The set S = {1, 2, 3,….12) is to be partitioned into three sets A, B, C of equal size. Thus A ∪ B ∪ C = S, A ⋂ B = B ⋂ C = A ⋂ C = ⌽. The number of ways to partition S is

[2007]

Option A: 12! / (4!)3

Option B: 12! / (4!)4

Option C: 12! / 3! (4!)3

Option D: 12! / 3! (4!)4

Option A: 12! / (4!)3

Permutations and Combinations Questions for JEE Questions No: 12

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

[2008]

Option A: 8. 6C. 7C4

Option B: 6. 7. 8C

Option C: 6. 8. 7C

Option D: 7. 6C. 8C4

Option D: 7. 6C4 . 8C4

Permutations and Combinations Problems for Class 11 Questions No: 13

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

Statement I: The number of different ways the child can buy the six ice-creams is 10C5.

Statement II: 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.

[2008]

Option A: Statement I is True; Statement II is true, Statement Il is not a correct explanation for Statement I.

Option B: Statement I is True; Statement II is False

Option C: Statement I is False; Statement II is True.

Option D: Statement I is True: Statement Il is True; Statement II is a correct explanation for Statement I

Option C: A Statement I is False; Statement II is True.

Permutations and Combinations Problems for Class 12 Questions No: 14

From 6 different novels and 3 different dictionaries,4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is

[2009]

Option A: At least 500 but less than 750

Option B: At least 750 but less than 1000

Option C: At least 1000

Option D: Less than 500

Option C: At least 1000

Permutations and Combinations Problems for Class 11 JEE Questions No: 15

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

[2010]

Option A: 36

Option B: 66

Option C: 108

Option D: 3

Option C: 108

Permutations and Combinations Problems for Class 12 JEE Questions No: 16

Statement 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C2.

Statement 2 : The number of ways of choosing any 3 places from 9 different places is 9C3

[2011]

Option A: Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

Option B: Statement 1 is true, Statement 2 is false.

Option C: Statement 1 is false, Statement 2 is true

Option D: Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1

Option A: Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

JEE Permutations and Combinations Questions No:17

There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points. Then

[2011]

Option A: N ≤ 100

Option B: 100 < N 140

Option C: 140 < N 190

Option D: N > 190

Option A: N≤100

JEE Main Permutations and Combinations Questions No: 18

If the number of 5-element subsets of the set A= {a1, a2,….. a20) of 20 distinct elements is k times the number of 5-element subsets containing a4, then k is

[2012]

Option A: 5

Option B: 20 / 7

Option C: 4

Option D: 10 / 3

Option C: 4

JEE Mathematics Permutations and Combinations Questions No: 19

Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is qp.

Statement 2: The total number of selections of p different objects out of q objects is qCp.

[2012]

Option A: Statement 1 is true, Statement 2 is false.

Option B: A Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1

Option C: Statement 1 is false, Statement 2 is true

Option D: Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1

Option B: A Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1

JEE Main Math Permutations and Combinations Questions No: 20

If n = mC2, then the value of nC2 is given by

[2012]

Option A: 3(m + 1C4)

Option B: m – 1C4

Option C: m + 1C4

Option D: 2(m + 2C4)

Option A: 3 (m+1C4 )

Permutations and Combinations JEE Questions No: 21

The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is

[2012]

Option A: 96

Option B: 128

Option C: 24

Option D: 72

Option A: 96

Permutations and Combinations JEE Main Questions No: 22

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is

[2012]

Option A: 6! 7!

Option B: (6!)2

Option C: (7!)2

Option D: N7!

Option A: 6! 7!

Permutations and Combinations Questions for JEE Mains Questions No: 23

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:

[2012]

Option A: 880

Option B: 629

Option C: 630

Option D: 879

Option D: 879

Permutations and Combinations Questions and Answers No: 24

Let X= (1, 2, 3, 4, 5). The number of different ordered pairs (Y, Z) that can be formed such ordered pairs (Y,Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

[2012]

Option A: 25

Option B: 53

Option C: 52

Option D: 35

Option D:  35

Permutations and Combinations Questions with Solutions No: 25

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is

[2013]

Option A: 40

Option B: 41

Option C: 16

Option D: 32

Option B: 41

JEE Mains Permutations and Combinations Questions No: 26

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is

[2013]

Option A: 30C7

Option B: 21C8

Option C: 21C7

Option D: 30C8

Option C: 21C7

JEE Mains Math Permutations and Combinations Questions No: 27

On the sides AB, BC, CA of a △ABC, 3, 4, 5 distinct points (excluding vertices A, B, C) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are

[2013]

Option A: 210

Option B: 205

Option C: 215

Option D: 220

Option B: 205

Permutations and Combinations Questions for JEE Questions No: 28

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 -Tn 10, then the value of n is

[2013]

Option A: 7

Option B: 5

Option C: 10

Option D: 9

Option B: 5

Permutations and Combinations Problems for Class 11 Questions No: 29

5-digit numbers are to be formed using 2, 3, 5, 7, 9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000, then p : q is:

[2013]

Option A: 6 : 5

Option B: 3 : 2

Option C: 4 : 3

Option D: 5 : 3

Option D: 5 : 3

Permutations and Combinations Problems for Class 12 Questions No: 30

The sum of the digits in the unit’s place of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition, is:

[2014]

Option A: 432

Option B: 108

Option C: 36

Option D: 18