IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 24

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Binomial Theorem, with the answer and a step-by-step solution.

Binomial TheoremAlgebraMultiple choiceMedium
The term independent of x in the expansion of {\left({x}^{2}- \frac{2}{x}\right)}^{6}, x \ne 0, is:
  1. A
    160
  2. B
    −240
  3. C
    60
  4. D
    240
Pick an option, then check.
Answer & solution

Answer: Option D

The general term is C(6, k) (x²)^(6−k) (−2/x)^k.

Collecting the powers of x: x^(12 − 2k) × x^(−k) = x^(12 − 3k).

For the term independent of x we need 12 − 3k = 0, so k = 4.

That term is C(6, 4) × (−2)⁴ = 15 × 16.

The term independent of x is 240.

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