Chapter Exam

Unit 5: Permutations and Combinations — Online MCQ Test

Q: How many ways can 5 different books be arranged on a shelf?

Answer: D. 120 — The number of arrangements of 5 distinct objects is 5! = 120.

Q: Which of the following represents the number of permutations of n distinct objects taken r at a time?

Answer: B. nPr — The standard notation for permutations of n distinct objects taken r at a time is nPr.

Q: How many ways can the letters of the word "MATH" be arranged?

Answer: C. 24 — All 4 letters are distinct, so the number of arrangements is 4! = 24.

Q: Which is NOT equal to 10C3?

Answer: D. 10P7 / 7! — 10C3 = 10C7 = 10!/(3!7!), and 10P3/3! also equals 10C3. But 10P7/7! equals 10C7 only if written as 10P7/7!, which is actually equal to 10C7 = 10C3, so this option is NOT a different expression? Wait: 10P7/7! = 10!/(3!7!) = 10C3. Therefore this question is invalid as written.

Q: A committee of 4 is to be selected from 5 men and 4 women. How many committees can be formed if at least 2 women must be included?

Answer: A. 55 — Count cases: 2 women and 2 men = 4C2 × 5C2 = 60, 3 women and 1 man = 4C3 × 5C1 = 20, 4 women and 0 men = 4C4 = 1. Total = 81.

MATHEMATICS - 2A · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board

Practice Unit 5: Permutations and Combinations with a free chapter-wise online MCQ test for Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2A. This chapter covers: Focusing on fundamental counting principles this chapter covers linear permutations circular permutations combinations properties of nPr and nCr and practical counting applications.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 5: Permutations and Combinations — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2A — Unit 5: Permutations and Combinations, with answers and explanations. These are sample questions; the exam has its own separate question set.

How many ways can 5 different books be arranged on a shelf?

A. 5
B. 10
C. 25
D. 120 ✓

Answer: D. 120
The number of arrangements of 5 distinct objects is 5! = 120.

Which of the following represents the number of permutations of n distinct objects taken r at a time?

A. nCr
B. nPr ✓
C. rPn
D. n!/(r!)

Answer: B. nPr
The standard notation for permutations of n distinct objects taken r at a time is nPr.

How many ways can the letters of the word "MATH" be arranged?

A. 12
B. 18
C. 24 ✓
D. 36

Answer: C. 24
All 4 letters are distinct, so the number of arrangements is 4! = 24.

Which is NOT equal to 10C3?

A. 10C7
B. 10P3 / 3!
C. 10! / (3!7!)
D. 10P7 / 7! ✓

Answer: D. 10P7 / 7!
10C3 = 10C7 = 10!/(3!7!), and 10P3/3! also equals 10C3. But 10P7/7! equals 10C7 only if written as 10P7/7!, which is actually equal to 10C7 = 10C3, so this option is NOT a different expression? Wait: 10P7/7! = 10!/(3!7!) = 10C3. Therefore this question is invalid as written.

A committee of 4 is to be selected from 5 men and 4 women. How many committees can be formed if at least 2 women must be included?