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Binomial Theorem — 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

How many terms occur in the expansion of (a + b)ⁿ for a positive integer n?
  1. n + 1 ✓
  2. n
  3. 2n
  4. n − 1
Answer: A. The general terms correspond to r = 0, 1, …, n, giving n + 1 terms in total.
Why not B: This equates the number of terms with the exponent, overlooking that the powers run from 0 through n inclusive.
Why not C: Doubling the exponent does not count the successive choices r = 0, 1, …, n.
Why not D: Subtracting one omits both the correct inclusive count and the two endpoint terms aⁿ and bⁿ.
What is the 5th term in the expansion of (a + b)⁷?
  1. 21a⁵b²
  2. 35a⁴b³
  3. 35a³b⁴ ✓
  4. 21a²b⁵
Answer: C. For the 5th term r = 4, so T₅ = ⁷C₄a³b⁴ = 35a³b⁴.
Why not A: This is the 3rd term, found by using r = 2 instead of r = 4 for the 5th position.
Why not B: This is the 4th term; it results from treating the 5th term as though r itself were the term number minus two.
Why not D: This is the 6th term, produced by using r = 5 rather than r = 4.
What is the term independent of x in (x² + 3/x)⁶?
  1. 1215 ✓
  2. 405
  3. 729
  4. 2430
Answer: A. The net exponent is 12 − 3r, so r = 4. The constant is ⁶C₄3⁴ = 15 × 81 = 1215.
Why not B: This uses ⁶C₄ × 3³, one power of 3 short for the r = 4 constant term.
Why not C: This keeps 3⁶ from the final term, but that term contains x⁻⁶ and is not constant.
Why not D: This doubles the correct coefficient as though the constant term appeared in a symmetric pair.

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Read the chapter first

Every NCERT question in this chapter is solved, free: NCERT solutions — Binomial Theorem →

Other NEET Maths chapters

SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsLinear InequalitiesPermutations and Combinations

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Questions

How many NEET questions are there on Binomial Theorem?

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.