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# JEE Main Mathematics Previous Paper Permutations and Combinations Questions Answer

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 Mathematics Previous Paper Permutations and Combinations Questions Answer.

### JEE Mains Mathematics Permutations and Combinations Questions Bank

Permutations and Combinations Problems for Class 11 JEE Questions No: 31

An eight digit number divisible by 9 is to be formed digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is:



Option A: 72 (7!)

Option B: 18 (7!)

Option C: 40 (7!)

Option D: 36 (7!)

Option D: 36 (7!)

Permutations and Combinations Problems for Class 12 JEE Questions No: 32

8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places, is



Option A: 160

Option B: 120

Option C: 60

Option D: 48

Option B: 120

JEE Permutations and Combinations Questions No: 33

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:



Option A: [8, 9]

Option B: [10, 12)

Option C: (11, 13]

Option D: (14, 17)

Option B:  [10, 12)

JEE Main Permutations and Combinations Questions No: 34

If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is



Option A: 12

Option B: 6

Option C: 10

Option D: 9

Option A: 12

JEE Mathematics Permutations and Combinations Questions No: 35

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is



Option A: 275

Option B: 510

Option C: 219

Option D: 256

Option C: 219

JEE Main Math Permutations and Combinations Questions No: 36

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is



Option A: 1120

Option B: 1880

Option C: 1950

Option D: 1240

Option D: 1240

Permutations and Combinations JEE Questions No: 37

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is



Option A: 120

Option B: 72

Option C: 216

Option D: 192

Option D: 192

Permutations and Combinations JEE Main Questions No: 38

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is:



Option A: 820

Option B: 780

Option C: 901

Option D: 861

Option B: 780

Permutations and Combinations Questions for JEE Mains Questions No: 39

The value of r2 (15Cr / 15Cr-1) is equal to:



Option A: 1240

Option B: 560

Option C: 1085

Option D: 680

Option D: 680

Permutations and Combinations Questions and Answers No: 40

If n+2C6 / n-2P6 = 11, then n satisfies the equation



Option A: n2 + n – 110 = 0

Option B: n2 + 2n – 80 = 0

Option C: n2 + 3n – 108 = 0

Option D: n2 + 5n – 84 = 0

Option C:  n+ 3n – 108 = 0

Permutations and Combinations Questions with Solutions No: 41

If the four letter words (need not be meaningful) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such



Option A: 110

Option B: 59

Option C: 11! / (2!)3

Option D: 56

Option B:  59

JEE Mains Permutations and Combinations Questions No: 42

The sum (r2+1) × (r!) is equal to



Option A: 11 × (11!)

Option B: 10 × (11!)

Option C: (11!)

Option D: 101 × (10!)

Option B: 10 × (11!)

JEE Mains Math Permutations and Combinations Questions No: 43

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is



Option A: 59th

Option B: 52th

Option C: 58th

Option D: 46th

Option C:  58th

Permutations and Combinations Questions for JEE Questions No: 44

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:



Option A: 484

Option B: 485

Option C: 468

Option D: 469

Option B: 485

Permutations and Combinations Problems for Class 11 Questions No: 45

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B, and a particular girl G1 never sit adjacent to each other, is



Option A: 5 × 6!

Option B: 6 × 6!

Option C: 7!

Option D: 5 ×7!

Option A: 5 × 6!

Permutations and Combinations Problems for Class 12 Questions No: 46

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. The number of such arrangements is



Option A: Less than 500

Option B: At least 500 but less than 750

Option C: At least 750 but less than 1000

Option D: At least 1000

Option D: At least 1000

Permutations and Combinations Problems for Class 11 JEE Questions No: 47

n- digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is



Option A: 6

Option B: 8

Option C: 9

Option D: 7

Option D: 7

Permutations and Combinations Problems for Class 12 JEE Questions No: 48

The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?



Option A: 30

Option B: 48

Option C: 24

Option D: 36

Option A: 30

JEE Permutations and Combinations Questions No: 49

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:



Option A: 500

Option B: 200

Option C: 300

Option D: 350

Option C: 300

JEE Main Permutations and Combinations Questions No: 50

If 20Ci-1 / + 20Ci + 20Ci-1)3 = (k / 21) then k equals:



Option A: 400

Option B: A50

Option C: 200

Option D: 100

Option D: 100

JEE Mathematics Permutations and Combinations Questions No: 51

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:



Option A: 180

Option B: 175

Option C: 160

Option D: 162

Option A: 180

JEE Main Math Permutations and Combinations Questions No: 52

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:



Option A: m + n = 68

Option B: m = n = 78

Option C: n = m – 8

Option D:  n = m – 8

Option B: m = n = 78

Permutations and Combinations JEE Questions No: 53

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is :



Option A: 170

Option B: 180

Option C: 210

Option D: 190

Option A: 170

Permutations and Combinations JEE Main Questions No: 54

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to



Option A: 28

Option B: 27

Option C: 25

Option D: 24

Option C: 25

Permutations and Combinations Questions for JEE Mains Questions No: 55

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct is



Option A: 220 – 1

Option B: 221

Option C: 220

Option D: 221 + 1

Option C: 220

Permutations and Combinations Questions and Answers No: 56

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is



Option A: 9

Option B: 18

Option C: 36

Option D: 32

Option C: 36

Permutations and Combinations Questions with Solutions No: 57

Consider three boxes, each containing 10 balls labelled 1,2,…, 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1 <n2 <n3 is:



Option A: 120

Option B: 82

Option C: 240

Option D: 164

Option A: 120

JEE Mains Permutations and Combinations Questions No: 58

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is:



Option A: 288

Option B: 360

Option C: 306

Option D: 310

Option D: 310

JEE Mains Math Permutations and Combinations Questions No: 59

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is:



Option A: 72

Option B: 60

Option C: 48

Option D: 36

Option B: 60

Permutations and Combinations Questions for JEE Questions No: 60

The number of ordered pairs (r, k) for which 6.35Cr = (k2 – 3).36Cr+1  where k is an integer, is:



Option A: 3

Option B: 2

Option C: 6

Option D: 4