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:

**[2014]**

**Option A**: 72 (7!)

**Option B**: 18 (7!)

**Option C**: 40 (7!)

**Option D**: 36 (7!)

**Show/Hide Answer Key**

**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

**[2014]**

**Option A**: 160

**Option B**: 120

**Option C**: 60

**Option D**: 48

**Show/Hide Answer Key**

**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:

**[2014]**

**Option A**: [8, 9]

**Option B**: [10, 12)

**Option C**: (11, 13]

**Option D**: (14, 17)

**Show/Hide Answer Key**

**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

**[2015]**

**Option A**: 12

**Option B**: 6

**Option C**: 10

**Option D**: 9

**Show/Hide Answer Key**

**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

**[2015]**

**Option A**: 275

**Option B**: 510

**Option C**: 219

**Option D**: 256

**Show/Hide Answer Key**

**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

**[2015]**

**Option A**: 1120

**Option B**: 1880

**Option C**: 1950

**Option D**: 1240

**Show/Hide Answer Key**

**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

**[2015]**

**Option A**: 120

**Option B**: 72

**Option C**: 216

**Option D**: 192

**Show/Hide Answer Key**

**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:

**[2015]**

**Option A**: 820

**Option B**: 780

**Option C**: 901

**Option D**: 861

**Show/Hide Answer Key**

**Option B: 780**

**Permutations and Combinations Questions for JEE Mains Questions No: 39**

The value of r^{2} (^{15}C_{r }/ ^{15}C_{r-1}) is equal to:

**[2016]**

**Option A**: 1240

**Option B**: 560

**Option C**: 1085

**Option D**: 680

**Show/Hide Answer Key**

**Option D: 680**

**Permutations and Combinations Questions and Answers No: 40**

If ^{n+2}C_{6} / ^{n-2}P_{6} = 11, then n satisfies the equation

**[2016]**

**Option A**: n^{2 }+ n – 110 = 0

**Option B**: n^{2 }+ 2n – 80 = 0

**Option C**: n^{2 }+ 3n – 108 = 0

**Option D**: n^{2 }+ 5n – 84 = 0

**Show/Hide Answer Key**

**Option C: n ^{2 }+ 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

**[2016]**

**Option A**: 110

**Option B**: 59

**Option C**: 11! / (2!)^{3}

**Option D**: 56

**Show/Hide Answer Key**

**Option B: 59**

**JEE Mains Permutations and Combinations Questions No: 42**

The sum (r^{2}+1) × (r!) is equal to

**[2016]**

**Option A**: 11 × (11!)

**Option B**: 10 × (11!)

**Option C**: (11!)

**Option D**: 101 × (10!)

**Show/Hide Answer Key**

**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

**[2016]**

**Option A**: 59^{th}

**Option B**: 52^{th}

**Option C**: 58^{th}

**Option D**: 46^{th}

**Show/Hide Answer Key**

**Option C: 58 ^{th}**

**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:

**[2017]**

**Option A**: 484

**Option B**: 485

**Option C**: 468

**Option D**: 469

**Show/Hide Answer Key**

**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 G_{1} never sit adjacent to each other, is

**[2017]**

**Option A**: 5 × 6!

**Option B**: 6 × 6!

**Option C**: 7!

**Option D**: 5 ×7!

**Show/Hide Answer Key**

**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

**[2018]**

**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

**Show/Hide Answer Key**

**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

**[2018]**

**Option A**: 6

**Option B**: 8

**Option C**: 9

**Option D**: 7

**Show/Hide Answer Key**

**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?

**[2018]**

**Option A**: 30

**Option B**: 48

**Option C**: 24

**Option D**: 36

**Show/Hide Answer Key**

**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:

**[2019]**

**Option A**: 500

**Option B**: 200

**Option C**: 300

**Option D**: 350

**Show/Hide Answer Key**

**Option C: 300**

**JEE Main Permutations and Combinations Questions No: 50**

If ^{20}C_{i-1} / + ^{20}C_{i }+ ^{20}C_{i-1})^{3} = (k / 21) then k equals:

**[2019]**

**Option A**: 400

**Option B**: A50

**Option C**: 200

**Option D**: 100

**Show/Hide Answer Key**

**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:

**[2019]**

**Option A**: 180

**Option B**: 175

**Option C**: 160

**Option D**: 162

**Show/Hide Answer Key**

**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:

**[2019]**

**Option A**: m + n = 68

**Option B**: m = n = 78

**Option C**: n = m – 8

**Option D**: n = m – 8

**Show/Hide Answer Key**

**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 :

**[2019]**

**Option A**: 170

**Option B**: 180

**Option C**: 210

**Option D**: 190

**Show/Hide Answer Key**

**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

**[2019]**

**Option A**: 28

**Option B**: 27

**Option C**: 25

**Option D**: 24

**Show/Hide Answer Key**

**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

**[2019]**

**Option A**: 2^{20} – 1

**Option B**: 2^{21}

**Option C**: 2^{20}

**Option D**: 2^{21} + 1

**Show/Hide Answer Key**

**Option C: 2 ^{20}**

**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

**[2019]**

**Option A**: 9

**Option B**: 18

**Option C**: 36

**Option D**: 32

**Show/Hide Answer Key**

**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 n_{i}, the label of the ball drawn from the i^{th} box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n_{1} <n_{2} <n_{3} is:

**[2019]**

**Option A**: 120

**Option B**: 82

**Option C**: 240

**Option D**: 164

**Show/Hide Answer Key**

**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:

**[2019]**

**Option A**: 288

**Option B**: 360

**Option C**: 306

**Option D**: 310

**Show/Hide Answer Key**

**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:

**[2019]**

**Option A**: 72

**Option B**: 60

**Option C**: 48

**Option D**: 36

**Show/Hide Answer Key**

**Option B: 60**

**Permutations and Combinations Questions for JEE Questions No: 60**

The number of ordered pairs (r, k) for which 6.^{35}C_{r} = (k^{2 }– 3).^{36}C_{r+1 } where k is an integer, is:

**[2020]**

**Option A**: 3

**Option B**: 2

**Option C**: 6

**Option D**: 4

**Show/Hide Answer Key**

**Option A: 3**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |