−a a |x| < a ⟺ −a < x < a Flip sign when ÷ by negative! ax > b → x < b/a (if a<0)
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Chapter 6  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Permutations & Combinations

Count Every Possibility — The Art of Smart Enumeration

📋 50 MCQs ⭐ 18 PYQs ⏱ 92 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
12Easy
22Medium
15Hard
18PYQs
92 secAvg Time/Q
11Topics
Easy 24% Medium 44% Hard 30%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSATKVPY

P&C is consistently one of the highest-scoring JEE topics — 4 to 5 questions per JEE Main paper, 2 to 4 in JEE Advanced. Combined with Probability, it forms 14–16% of the paper. BITSAT always includes tricky circular and restricted arrangement problems. KVPY favours elegant combinatorial reasoning.

Topic-wise MCQ Breakdown

Fundamental Counting3 Q
Factorial2 Q
Permutation ⁿPᵣ12 Q
Permutation with Repeats9 Q
Circular Permutations3 Q
Combination ⁿCᵣ8 Q
Properties of nCr6 Q
Restricted Selection5 Q
Distribution0 Q
Rank of Word1 Q
Derangements0 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$ⁿPᵣ = n!/(n−r)!$
$ⁿCᵣ = n!/[r!(n−r)!]$
$Circular = (n−1)!$
$ⁿCᵣ+ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ$
$Σ ⁿCᵣ = 2ⁿ$

MCQ Solving Strategy

The first question to ask every P&C MCQ: "Does order matter?" — Yes → Permutation, No → Combination. For circular arrangements, fix one element and arrange the rest. For "at least one" type problems, use complementary counting: Total − None. Rank of word MCQs: count letters alphabetically smaller than the first letter.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Basic ⁿPᵣ and ⁿCᵣ calculations, FCP applications

② Medium

Circular arrangements, identical objects, restricted positions

③ Hard

Rank of word, derangements, distribution into groups

★ PYQ

JEE Advanced — multi-step combinatorics; BITSAT — speed problems

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Binomial Theorem MCQs
🎯 Knowledge Check

Maths — PERMUTATIONS AND COMBINATIONS

50 Questions Class 11 MCQs
1
The number of ways of arranging 3 different objects taken all at a time is
(Basic Concept – Counting)
2
The value of \(5!\) is
(Basic Factorial)
3
The number of permutations of 4 objects taken 2 at a time is
(Formula Application)
4
The value of \(^{6}P_{6}\) is
(Basic Permutations)
5
The number of combinations of 5 objects taken 2 at a time is
(Basic Combination)
6
If \(^{n}C_{1} = 15\), then \(n\) is
(Simple Combination Property)
7
The number of ways of arranging the letters of the word “CAT” is
(Simple Word Problem)
8
The number of ways of selecting 3 students from 7 students is
(Basic Selection)
9
The value of \(^{n}P_{1}\) is
(Permutation Property)
10
The number of ways of arranging 4 different books on a shelf is
(Simple Arrangement)
11
The number of permutations of the letters of the word “BOOK” is
(Repetition of Letters)
12
The value of \(^{8}C_{0}\) is
(Combination Property)
13
The number of ways of choosing a president and a vice-president from 6 people is
(Permutation in Selection)
14
The number of combinations of 6 objects taken 4 at a time is
(Combination Formula)
15
The number of ways of arranging the letters of “LEVEL” is
(Repetition-Based Arrangement)
16
If \(^{n}C_{2} = 45\), then \(n\) is
(Algebraic Combination)
17
The number of ways of selecting 5 cards from a deck of 52 cards is
(Standard Combination)
18
The number of permutations of 5 objects taken 3 at a time is
(Intermediate Permutation)
19
The number of ways of forming a committee of 3 members from 8 members is
(Committee Formation)
20
The value of \(^{n}C_{n}\) is
(Combination Identity)
21
The number of ways of arranging 6 people in a row is
(Linear Arrangement)
22
The number of combinations of 10 objects taken 1 at a time is
(Simple Combination)
23
The number of ways of arranging the letters of “MATH” is
(Simple Word Arrangement)
24
If \(^{n}P_{2} = 56\), then \(n\) is
(Intermediate Algebraic Permutation)
25
The number of ways of selecting at least one object from 3 distinct objects is
(Conceptual Counting)
26
The number of permutations of the letters of the word “MISS” is
(Repetition with Multiple Letters)
27
The number of ways of choosing 2 boys and 1 girl from 4 boys and 3 girls is
(Mixed Selection)
28
The value of \(^{9}C_{7}\) is
(Combination Symmetry)
29
The number of ways of arranging 5 people around a round table is
(Circular Permutation)
30
The number of combinations of 7 objects taken 3 at a time is
(Intermediate Combination)
31
The number of ways of arranging 7 different books if 2 particular books are always together is
(Constraint-Based Arrangement)
32
The number of ways of selecting a team of 4 from 6 men and 5 women consisting of 2 men and 2 women is
(Mixed Combination)
33
The value of \(^{10}P_{0}\) is
(Permutation Property)
34
The number of ways of arranging the letters of “INDIA” is
(Repetition and Distinct Letters)
35
The number of subsets of a set containing 5 elements is
(Power Set Concept)
36
If \(^{n}C_{3} = 35\), then \(n\) is
(Advanced Combination)
37
The number of ways of arranging 4 boys and 3 girls in a row such that all boys are together is
(Advanced Arrangement)
38
The number of ways of choosing at most 2 objects from 5 distinct objects is
(Conceptual Combination)
39
The number of permutations of the digits 1, 2, 3, 4 taken all at a time is
(Digit Arrangement)
40
The number of ways of forming a 3-digit number from the digits 1, 2, 3, 4 without repetition is
(Permutation of Digits)
41
The number of combinations of 8 objects taken 5 at a time is
(Intermediate Combination)
42
The number of ways of arranging the letters of “BANANA” is
(Advanced Repetition)
43
The number of ways of choosing 4 balls from a box containing 6 red and 5 blue balls is
(Color-Based Selection)
44
The number of ways of selecting exactly 3 red balls from 6 red and 5 blue balls is
(Restricted Combination)
45
The number of permutations of 10 objects taken all at a time is
(High-Level Permutation)
46
The number of ways of choosing a chairman, vice-chairman, and secretary from 7 persons is
(Advanced Permutation)
47
The number of ways of arranging 5 men and 5 women alternately in a row is
(Advanced Arrangement)
48
The number of combinations of 12 objects taken 10 at a time is
(Combination Symmetry)
49
The number of ways of arranging the letters of “STATISTICS” is
(High-Level Repetition)
50
The number of ways of selecting a committee of 5 from 10 people if 2 particular people are always included is
(Advanced Selection Constraint)
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Can You Solve All 50? Permutations & Combinations MCQ Challenge
Can You Solve All 50? Permutations & Combinations MCQ Challenge — Complete Notes & Solutions · academia-aeternum.com
Permutations and Combinations form the backbone of counting techniques in Class XI Mathematics and serve as a gateway to higher topics such as probability, discrete mathematics, and advanced combinatorics. Mastery of this chapter is essential not only for school examinations but also for competitive exams where logical counting, arrangement, and selection problems frequently appear. The following set of 50 Multiple Choice Questions has been carefully structured with a gradual increase in…
🎓 Class 11 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Frequently Asked Questions

A permutation is an arrangement of objects in a definite order. If the order of selection changes, the permutation changes.

A combination is a selection of objects where order is not important. Different orders of the same objects represent the same combination.

In permutation, order matters; in combination, order does not matter.

The number of permutations is \(^{n}P_{r} = \dfrac{n!}{(n-r)!}\).

The number of combinations is \(^{n}C_{r} = \dfrac{n!}{r!(n-r)!}\).

The factorial of \(n\), written as \(n!\), means the product \(n \times (n-1) \times (n-2) \times \cdots \times 1\).

By definition, \(0! = 1\).

This definition ensures the validity of formulas such as \(^{n}P_{n} = n!\) and \(^{n}C_{0} = 1\).

The value of \(^{n}P_{n}\) is \(n!\), which represents all possible arrangements of \(n\) objects.

Both \(^{n}C_{0}\) and \(^{n}C_{n}\) are equal to 1.

For all integers \(n\) and \(r\), \(^{n}C_{r} = {}^{n}C_{n-r}\).

They are related by \(^{n}P_{r} = {}^{n}C_{r} \times r!\).

A linear permutation is an arrangement of objects in a straight line.

A circular permutation is an arrangement of objects around a circle, where relative positions matter.

The number of circular permutations is \((n-1)!\).

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