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Permutations and Combinations — NEET Maths MCQs

30 questions written by hand against the NCERT chapter. Every wrong option is explained, not just the right one.

30questions
10/14/6easy / medium / hard
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Sample questions from this chapter

What is the value of 5!?
  1. 120 ✓
  2. 20
  3. 25
  4. 60
Answer: A. 5! = 5 × 4 × 3 × 2 × 1 = 120. The factorial multiplies every integer from n down to 1.
Why not B: Multiplies only the first two factors, 5 × 4, and stops.
Why not C: Computes 5² instead of the product of all the integers down to 1.
Why not D: Stops at 5 × 4 × 3 and never reaches the 2.
In how many ways can the letters of the word LEVEL be arranged?
  1. 30 ✓
  2. 120
  3. 60
  4. 15
Answer: A. LEVEL has 5 letters with L twice and E twice: 5!/(2! × 2!) = 120/4 = 30.
Why not B: 120 is 5!, which treats the two L's as different letters and the two E's likewise. Swapping the two L's gives the same word.
Why not C: Divides by 2! once, correcting for only ONE of the two repeated letters.
Why not D: Divides by 2! three times, correcting for a third repeat that does not exist.
In how many ways can 5 boys and 3 girls sit in a row so that no two girls sit together?
  1. 14400 ✓
  2. 40320
  3. 4320
  4. 2400
Answer: A. Seat the 5 boys first: 5! = 120 ways. They create 6 gaps; choose 3 and arrange the girls in them: ⁶P₃ = 120. Total 120 × 120 = 14400.
Why not B: 40320 is 8!, every seating with no restriction at all.
Why not C: 4320 = 6! × 3! counts the seatings where the three girls sit TOGETHER as one block — the opposite of what was asked.
Why not D: 2400 = 5! × ⁶C₃ picks the three gaps but forgets to ARRANGE the girls among them, missing a factor of 3!.

These are 3 of the 30 questions in the test. Take the full chapter test →

Read the chapter first

Every NCERT question in this chapter is solved, free: NCERT solutions — Permutations and Combinations →

Other NEET Maths chapters

SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsLinear InequalitiesBinomial Theorem

All 27 chapters →

Questions

How many NEET questions are there on Permutations and Combinations?

This chapter test has 30 questions — 10 easy, 14 medium and 6 hard — all written against the NCERT Class 11 chapter.

Is this NEET Maths chapter test free?

Yes. Every chapter test is free with no login, and you get your all-India rank on every one. Nothing on the site is on sale right now.

Do the questions explain the wrong options?

Yes — every distractor carries its own explanation naming the specific misconception that makes a student pick it. That is the part most question banks skip, and it is the part that changes your next attempt.