Class 11 • Maths • Chapter 6
PERMUTATIONS AND COMBINATIONS
True & False Quiz
Order matters. Or does it?
✓True
✗False
25
Questions
|
Ch.6
Chapter
|
XI
Class
Why True & False for PERMUTATIONS AND COMBINATIONS?
How this format sharpens your conceptual clarity
🔵 P&C is the mathematics of counting and arrangement — underlying probability, cryptography, and algorithms.
✅ The T/F distinction — order matters (permutation) vs order does not (combination) — is tested every year.
🎯 Key trap: 0! = 1 (TRUE, not 0). Also ⁿCᵣ = ⁿCⁿ−ᵣ (symmetry) tested frequently.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The factorial of a natural number \(n\) is defined only for \(n \ge 1\).
Q 2
The value of \(1!\) is equal to \(1\).
Q 3
The number of permutations of \(n\) distinct objects taken all at a time is \(n!\).
Q 4
The number of permutations of \(n\) objects taken \(r\) at a time is denoted by \(^nP_r\).
Q 5
\(^nP_r = \dfrac{n!}{(n-r)!}\).
Q 6
The value of \(^nP_0\) is zero.
Q 7
The number of combinations of \(n\) distinct objects taken all at a time is \(1\).
Q 8
The number of combinations of \(n\) objects taken \(r\) at a time is denoted by \(^nC_r\).
Q 9
\(^nC_r = \dfrac{n!}{r!(n-r)!}\).
Q 10
\(^nC_r = ^nC_{n-r}\).
Q 11
The number of combinations is always less than or equal to the corresponding number of permutations.
Q 12
If all objects are identical, the number of distinct permutations is \(1\).
Q 13
The number of permutations of the letters of the word “LEVEL” is \(\dfrac{5!}{2!2!}\).
Q 14
The number of ways of arranging \(n\) objects in a circle is \((n-1)!\).
Q 15
The number of ways of arranging \(n\) distinct objects around a round table is \(n!\).
Q 16
The number of permutations of \(n\) distinct objects taken \(r\) at a time increases as \(r\) increases.
Q 17
The number of combinations of \(n\) objects taken \(r\) at a time is maximum when \(r = \dfrac{n}{2}\) (for even \(n\)).
Q 18
The sum \(^nC_0 + ^nC_1 + \cdots + ^nC_n = 2^n\).
Q 19
The number of solutions of \(x+y+z=5\) in non-negative integers is \(^7C_2\).
Q 20
The number of ways of selecting at least one object from \(n\) distinct objects is \(2^n-1\).
Q 21
If repetitions are allowed, the number of combinations of \(n\) objects taken \(r\) at a time is \(^ {n+r-1}C_r\).
Q 22
The number of ways of arranging the letters of the word “ENGINEERING” is \(\dfrac{11!}{3!3!2!}\).
Q 23
The number of ways of choosing a committee of \(r\) people from \(n\) people is affected by the order of selection.
Q 24
The number of onto functions from a set with \(m\) elements to a set with \(n\) elements \((m \ge n)\) can be evaluated using permutations and combinations.
Q 25
The number of ways of distributing \(r\) identical objects among \(n\) distinct persons with no restriction is \(^ {n+r-1}C_{n-1}\).
Key Takeaways — PERMUTATIONS AND COMBINATIONS
Core facts for CBSE Boards & JEE
1
0! = 1 by definition — TRUE and frequently tested in objective questions.
2
ⁿPᵣ = n!/(n−r)! counts ordered arrangements; ⁿCᵣ = n!/(r!(n−r)!) counts selections.
3
ⁿCᵣ = ⁿCⁿ−ᵣ — choosing r is same as rejecting n−r (symmetry property).
4
ⁿCᵣ + ⁿCᵣ−₁ = ⁿ⁺¹Cᵣ — Pascal's Identity (used in Binomial Theorem).
5
Circular permutations of n objects = (n−1)! — NOT n!
6
ⁿPⁿ = n! and ⁿP₀ = 1.