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 Math Previous Year Paper Permutations and Combinations Questions Answer Keys Solutions*.

### JEE Mains Mathematics Permutations and Combinations Questions Bank

**Permutations and Combinations Problems for Class 11 Questions No: 61**

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word ‘EXAMINATION’ is

**[2020]**

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**Correct Ans: 2454**

**Permutations and Combinations Problems for Class 12 Questions No: 62**

If a, b and c are the greatest values of ^{19}C_{p}, ^{20}C_{q}, and ^{21}C_{r}, respectively, then:

**[2020]**

**Option A**: (a / 11) = (b / 22) = (c / 21)

**Option B**: (a / 10) = (b / 11) = (c / 21)

**Option C**: (a / 11) = (b / 22) = (c / 42)

**Option D**: (a / 10) = (b / 11) = (c / 42)

**Show/Hide Answer Key**

**Option C: (a / 11) = (b / 22) = (c / 42)**

**Permutations and Combinations Problems for Class 11 JEE Questions No: 63**

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is

**[2020]**

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**Correct Ans : 490**

**Permutations and Combinations Problems for Class 12 JEE Questions No: 64**

If C_{r }= ^{25}C_{r} and C_{0} + 5·C_{1} + 9·C_{2 }+…+ (101)·C_{25} = 2^{25}·k, then k is equal to

**[2020]**

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**Correct Ans : 51**

**JEE Permutations and Combinations Questions No: 65**

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is

**[2020]**

**Option A**: 201

**Option B**: 200

**Option C**: 101

**Option D**: 199

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**Option A: 201**

**JEE Main Permutations and Combinations Questions No: 66**

The total number of 3-digit numbers, whose sum of digits is 10 is

**[2020]**

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**Correct Ans : 54**

**JEE Mathematics Permutations and Combinations Questions No: 67**

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

**[2020]**

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**Correct Ans : 135**

**JEE Main Math Permutations and Combinations Questions No: 68**

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:

**[2020]**

**Option A**: 3000

**Option B**: 1500

**Option C**: 2255

**Option D**: 2250

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**Option D: 2250**

**Permutations and Combinations JEE Questions No: 69**

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ‘SYLLABUS’ such that two letters are distinct and two letters are alike, is

**[2020]**

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**Correct Ans: 240**

**Permutations and Combinations JEE Main Questions No: 70**

The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is

**[2020]**

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**Correct Ans: 120**

**Permutations and Combinations Questions for JEE Mains Questions No: 71**

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is

**[2020]**

**Option A**: 1 / 2 (5!)

**Option B**: 6!

**Option C**: 5^{6}

**Option D**: 5 / 2 (6!)

**Show/Hide Answer Key**

**Option D: 5 / 2 (6!)**

**Permutations and Combinations Questions and Answers No: 72**

If the number of five digit numbers with distinct digits and 2 at the 10^{th} place is 336 k, then k is equal to:

**[2020]**

**Option A**: 4

**Option B**: 6

**Option C**: 7

**Option D**: 8

**Show/Hide Answer Key**

**Option D: 8**

**Permutations and Combinations Questions with Solutions No: 73**

If the letters of the word ‘MOTHER’ be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ‘MOTHER’ is

**[2020]**

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**Correct Ans : 309**

**JEE Mains Permutations and Combinations Questions No: 74**

The value of (2.^{1}P_{0 }– 3. ^{2}P_{1 }+ 4. ^{3}P_{2 }– … up to 51th term) + (1! – 2! + 3! – … up to 51^{th} term) is equal to :

**[2020]**

**Option A**: 1 – 51 (51!)

**Option B**: 1 + (51!)

**Option C**: 1 + (52!)

**Option D**: 1

**Show/Hide Answer Key**

**Option C: 1 + (52!)**

**JEE Mains Math Permutations and Combinations Questions No: 75**

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

**[2020]**

**Option A**: 2! 3! 4!

**Option B**: (3!)^{3} (4!)

**Option C**: (3!)^{2} (4!)

**Option D**: 3! (4!)^{3}

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**Option B: (3!) ^{3 }(4!)**

**Permutations and Combinations Questions for JEE Questions No: 76**

The students S_{1}, S_{2},…… S_{10} are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is

**[2021]**

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**Correct Ans : 31650**

**Permutations and Combinations Problems for Class 11 Questions No: 77**

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is

**[2021]**

**Option A**: 1625

**Option B**: 575

**Option C**: 560

**Option D**: 1050

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**Option A: 1625**

**Permutations and Combinations Problems for Class 12 Questions No: 78**

If the sides AB, BC and CA of triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to:

**[2021]**

**Option A**: 240

**Option B**: 364

**Option C**: 360

**Option D**: 333

**Show/Hide Answer Key**

**Option D: 333**

**Permutations and Combinations Problems for Class 11 JEE Questions No: 79**

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is

**[2021]**

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**Correct Ans : 777**

**Permutations and Combinations Problems for Class 12 JEE Questions No: 80**

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100 k, then k is equal to

**[2021]**

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**Correct Ans : 238**

**JEE Permutations and Combinations Questions No: 81**

The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit “1” and they all are multiple of 11, is

**[2021]**

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**Correct Ans : 7744**

**JEE Main Permutations and Combinations Questions No: 82**

If ^{1}P_{1} + ^{2}P_{2} + ^{3}P_{3 }+…..+ 15. ^{15}P_{15} = ^{q}P_{r }– s, 0 ≤ s ≤ 1, then ^{q+s}P_{r-s } is equal to

**[2021]**

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**Correct Ans : 136**

**JEE Mathematics Permutations and Combinations Questions No: 83**

The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is

**[2021]**

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**Correct Ans : 5143**

**JEE Main Math Permutations and Combinations Questions No: 84**

The total number of numbers, lying between 100 and 1000 than can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is

**[2021]**

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**Correct Ans : 32**

**Permutations and Combinations JEE Questions No: 85**

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is

**[2021]**

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**Correct Ans : 1000**

**Permutations and Combinations JEE Main Questions No: 86**

Team ‘A’ consists of 7 boys and n girls and Team ‘B’ has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to

**[2021]**

**Option A**: 5

**Option B**: 6

**Option C**: 2

**Option D**: 4

**Show/Hide Answer Key**

**Option D: 4**

**Permutations and Combinations Questions for JEE Mains Questions No: 87**

The missing value in the following figure is

**[2021]**

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**Correct Ans :4**

**Permutations and Combinations Questions and Answers No: 88**

The number of times the digit 3 will be written when listing the integers from 1 to 1000

**[2021]**

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**Correct Ans : 300**

**Permutations and Combinations Questions with Solutions No: 89**

If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to

**[2021]**

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**Correct Ans : 96**

**JEE Mains Permutations and Combinations Questions No: 90**

Let n be a non-negative integer. Then the number of divisors of the form “4n+ 1” of the number (10)^{10} . (11)^{11}. (13)^{13} is equal to

**[2021]**

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**Correct Ans : 924**

**JEE Mains Math Permutations and Combinations Questions No: 91**

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is

**[2021]**

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**Correct Ans : 52**

**Permutations and Combinations Questions for JEE Questions No: 92**

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is

**[2021]**

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**Correct Ans : 100**

**Permutations and Combinations Problems for Class 11 Questions No: 93**

The number of six letter words (with or without meaning), formed using all the letters of the word ‘VOWELS’, so that all the consonants never come together, is

**[2021]**

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**Correct Ans : 576**

**Permutations and Combinations Problems for Class 12 Questions No: 94**

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 77**

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 | |