Vidaara.orgClass 11 · Mathematics
CodeVID-M11-06-CT
Permutations and Combinations — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$4!=$
- A.$12$
- B.$24$
- C.$16$
- D.$8$
2.
$ {}^{n}P_{r}=$
- A.$\dfrac{n!}{r!(n-r)!}$
- B.$\dfrac{n!}{(n-r)!}$
- C.$n!\,r!$
- D.$\dfrac{n!}{r!}$
3.
$ {}^{n}C_{r}=$
- A.$\dfrac{n!}{(n-r)!}$
- B.$\dfrac{n!}{r!(n-r)!}$
- C.$n!\,r!$
- D.$\dfrac{n!}{r!}$
4.
$0!=$
- A.$0$
- B.$1$
- C.$\infty$
- D.undefined
5.
$ {}^{5}P_{3}=$
- A.$10$
- B.$60$
- C.$20$
- D.$120$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $5!$.
7.
Evaluate $ {}^{7}P_{2}$.
8.
Evaluate $ {}^{8}C_{3}$.
9.
Evaluate $\dfrac{6!}{4!\,2!}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
How many $3$-digit numbers can be formed from the digits $1$–$5$ without repetition?
11.
How many words can be formed from the letters of "DELHI" (all distinct)?
12.
From $8$ players, in how many ways can $5$ be chosen?
13.
Find $n$ if $n!=720$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
How many numbers between $100$ and $1000$ have all distinct digits?
15.
In how many ways can the letters of the word "ARRANGE" be arranged?
Answer Key
Section A — Multiple Choice Questions
- (B) $24$
- (B) $\dfrac{n!}{(n-r)!}$
- (B) $\dfrac{n!}{r!(n-r)!}$
- (B) $1$
- (B) $60$
Section B — Short Answer (2 marks)
- $120$.
- $42$.
- $56$.
- $15$.
Section C — Short Answer (3 marks)
- $60$.
- $120$.
- $56$.
- $n=6$.
Section D — Long Answer (5 marks)
- $648$.
- $1260$.
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