Vidaara.orgClass 11 · Mathematics
CodeVID-M11-06-PER-01
Permutations — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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.
$ {}^{n}P_{r}=$
- A.$\dfrac{n!}{r!(n-r)!}$
- B.$\dfrac{n!}{(n-r)!}$
- C.$n!\,r!$
- D.$\dfrac{n!}{r!}$
2.
$ {}^{5}P_{3}=$
- A.$10$
- B.$60$
- C.$20$
- D.$120$
3.
$ {}^{n}P_{0}=$
- A.$0$
- B.$1$
- C.$n$
- D.$n!$
4.
The number of arrangements of "CAT" is:
- A.$3$
- B.$6$
- C.$9$
- D.$1$
5.
$ {}^{n}P_{n}=$
- A.$1$
- B.$n$
- C.$n!$
- D.$2n$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $ {}^{7}P_{2}$.
7.
Evaluate $ {}^{6}P_{3}$.
8.
How many arrangements of the letters of "BOOK" are there?
9.
Find $r$ if $ {}^{5}P_{r}=20$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
How many words can be formed from the letters of "DELHI" (all distinct)?
11.
How many arrangements of the letters of "MISSISSIPPI" are there?
12.
In how many ways can $5$ books be arranged on a shelf?
13.
How many $4$-letter words (no repetition) can be formed from the $8$ letters of "EQUATION"?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
In how many ways can the letters of the word "ARRANGE" be arranged?
15.
In how many ways can $6$ people be seated in a row if two particular persons must sit together?
Answer Key
Section A — Multiple Choice Questions
- (B) $\dfrac{n!}{(n-r)!}$
- (B) $60$
- (B) $1$
- (B) $6$
- (C) $n!$
Section B — Short Answer (2 marks)
- $42$.
- $120$.
- $12$.
- $r=2$.
Section C — Short Answer (3 marks)
- $120$.
- $34650$.
- $120$.
- $1680$.
Section D — Long Answer (5 marks)
- $1260$.
- $240$.
Generated by Vidaara.org · Assignment VID-M11-06-PER-01 · vidaara.org