Permutation and Combination JEE Questions PDF with Solution, Practice Now

Permutation and Combination JEE Questions: Permutation and Combination is an essential Mathematics chapter for JEE Mains & JEE Advanced preparation. This chapter teaches students how to arrange objects or select them in various ways. Permutation and Combination lay the foundation for advanced chapters such as Probability and Algebra. Every year in JEE, there are Permutation and Combination JEE questions. Some 1–2 JEE Advanced PnC questions are also asked in the JEE exam. This chapter has 2–3% weightage in the JEE, on average.

Solving PYQs on permutations and combinations provides a realistic exam experience for students. It also helps in enhancing speed, logical, and problem-solving skills. These skills are extremely crucial for bagging high marks.

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Permutation and Combination JEE Questions Overview

In JEE exams, this chapter is a scoring chapter once the basic formulas and concepts are clear to you. Questions like in how many ways we can arrange objects, in how many ways we can select objects with some conditions, some advanced PnC problems with connection to probability, etc., are asked. Important PYQs of permutation and combination have revealed the fact that the examiners are more in favor of conceptual and application based questions rather than those sums which can be directly found from the formulas. 

Questions of this topic in JEE Mains are usually direct, but your speed to solve calculations comes into play, whereas in JEE Advanced, the questions are more tricky and multi-step solutions are required. With some good revision, all the questions of this topic can be attempted in very less time during the exam.

Practice Permutation and Combination JEE Questions

Here are some permutation and combination JEE questions:

1. If a, b, c and d are odd natural numbers such that a + b + c + d = 20, the number of values of the ordered quadruplet (a, b, c, d) is

A. 165
B. 455
C. 310
D. None of these

2. If l = LCM of 8!, 10! and 12! and h = HCF of 8!, 10! and 12!, then l/h is equal to

A. 132
B. 11800
C. 11880
D. None of these

3. The number of positive integers satisfying the inequality n+1Cn-2 + n+1Cn-1 ≤ 100 is

A. 9
B. 8
C. 5
D. None of these

4. The number of ways in which a score of 11 can be made by three persons, each throwing a single die once, is

A. 45
B. 18
C. 27
D. 68

5. In a plane there are 37 straight lines, of which 13 pass through one point A and 11 pass through one point B. Besides, no three lines pass through one point, no line passes through both points A and B and no two are parallel, the number of intersection points the lines have, is

A. 535
B. 601
C. 728
D. 96

6. If a denotes the number of permutations of x + 2 things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x–11 things taken all at a time such that a = 182 bc, the value of x is

A. 15
B. 12
C. 14
D. None of these

7. On a railway route there are 19 stations between station A and station B. The number of different tickets required in order that it may be possible to travel from any station to any other station, in direction from A to B, is

A. 210
B. 225
C. 196
D. 105

8. A set contains n elements. A subset P of A is chosen. The set A is reconstructed by replacing the element of P. A subset Q of A is again chosen the number of ways of choosing P and Q, so that P ∩ Q = ϕ, is

A. 22n – 2nCn
B. 2n
C. 2n – 1
D. 3n

9. The straight lines l₁, l₂, l₃ are parallel and lie in the same plane. A total number of m points on l₁; n points on l₂; k points on l₃, the maximum number of triangles formed with vertices at these points is

A. m+n+kC₃
B. m+n+kC₃ – mC₃ – nC₃ – kC₃
C. mC₃ + nC₃ + kC₃
D. mnk

10. The number of three-digit numbers of the form xyz such that x < y, z ≤ y and x ≠ 0, is

A. 240
B. 244
C. 276
D. 285

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Permutation and Combination JEE Questions PDF with Solution

Students can practice Physics Wallah's detailed Permutation and Combination JEE Questions PDF with answers, which contains step-by-step procedures and full explanations to boost their understanding. It also covers some important points of the theory, which makes it easy to learn. The PDF also contains some quick tips and shortcuts that help the students to solve questions easily in less time during the exam.