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

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**Option B: 3050**

**JEE Main Math Permutations and Combinations Questions No:4**

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

**[2003]**

**Option A**: ^{n+1}C_{r+1}

**Option B**: ^{n+2}C_{r}

**Option C**: ^{n+2}C_{r+1}

**Option D**: ^{n+1}C_{r}

**Show/Hide Answer Key**

**Option C: ^{n+2}C_{r+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

**Show/Hide Answer Key**

**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**: ^{8}C_{3}

**Option B**: 21

**Option C**: 3^{8}

**Option D**: 5

**Show/Hide Answer Key**

**Option B: 21**

**Permutations and Combinations Questions for JEE Mains Questions No: 7**

The range of the function f (x) = ^{7-x}P_{x-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,}

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**Option C: 360**

**Permutations and Combinations Questions with Solutions No: 9**

The value of ^{50}C_{4} +

^{56-r}C

_{3}is

**[2005]**

**Option A**: ^{55}C_{4}

**Option B**: ^{55}C_{3}

**Option C**: ^{56}C_{3}

**Option D**: ^{56}C_{4}

**Show/Hide Answer Key**

**Option D: ^{ 56}C_{4}**

**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

**Show/Hide Answer Key**

**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}

**Show/Hide Answer Key**

**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. ^{6}C_{4 }. ^{7}C_{4}

**Option B**: 6. 7. ^{8}C_{4 }

**Option C**: 6. 8. ^{7}C_{4 }

**Option D**: 7. ^{6}C_{4 }. ^{8}C_{4}

**Show/Hide Answer Key**

**Option D: 7. ^{6}C_{4 . }^{8}C_{4}**

**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 ^{10}C_{5}.

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

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**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 ^{9}C_{2}.

Statement 2 : The number of ways of choosing any 3 places from 9 different places is ^{9}C_{3}

**[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

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**Option A: N≤100**

**JEE Main Permutations and Combinations Questions No: 18**

If the number of 5-element subsets of the set A= {a_{1}, a_{2},….. a_{20}) of 20 distinct elements is k times the number of 5-element subsets containing a_{4}, then k is

**[2012]**

**Option A**: 5

**Option B**: 20 / 7

**Option C**: 4

**Option D**: 10 / 3

**Show/Hide Answer Key**

**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 q^{p}.

Statement 2: The total number of selections of p different objects out of q objects is ^{q}C_{p}.

**[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

**Show/Hide Answer Key**

**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 = ^{m}C_{2}, then the value of ^{n}C_{2} is given by

**[2012]**

**Option A**: 3(^{m + 1}C_{4})

**Option B**: ^{m – 1}C_{4}

**Option C**: ^{m + 1}C_{4}

**Option D**: 2(^{m + 2}C_{4})

**Show/Hide Answer Key**

**Option A: 3 ( ^{m+1}C_{4} )**

**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

**Show/Hide Answer Key**

**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!

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**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**: 2^{5}

**Option B**: 5^{3}

**Option C**: 5^{2}

**Option D**: 3^{5}

**Show/Hide Answer Key**

**Option D: 3 ^{5}**

**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

**Show/Hide Answer Key**

**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**: ^{30}C_{7}

**Option B**: ^{21}C_{8}

**Option C**: ^{21}C_{7}

**Option D**: ^{30}C_{8}

**Show/Hide Answer Key**

**Option C: ^{21}C_{7}**

**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

**Show/Hide Answer Key**

**Option B: 205**

**Permutations and Combinations Questions for JEE Questions No: 28**

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

**[2013]**

**Option A**: 7

**Option B**: 5

**Option C**: 10

**Option D**: 9

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**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

**Show/Hide Answer Key**

**Option B: 108**

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 | |