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 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
Show/Hide Answer Key
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
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: 8C3
Option B: 21
Option C: 38
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-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,}
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 50C4 + 
56-rC3 is
[2005]
Option A: 55C4
Option B: 55C3
Option C: 56C3
Option D: 56C4
Show/Hide Answer Key
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
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. 6C4 . 7C4
Option B: 6. 7. 8C4
Option C: 6. 8. 7C4
Option D: 7. 6C4 . 8C4
Show/Hide Answer Key
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
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 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
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= {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
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 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
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 = 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)
Show/Hide Answer Key
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
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: 25
Option B: 53
Option C: 52
Option D: 35
Show/Hide Answer Key
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
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: 30C7
Option B: 21C8
Option C: 21C7
Option D: 30C8
Show/Hide Answer Key
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
Show/Hide Answer Key
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
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 | |
