IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 4

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

LimitsCalculusMultiple choiceEasy
Evaluate: \lim_{x \to 2}{\frac{{x}^{2}- 4}{x - 2}}.
  1. A
    4
  2. B
    The limit does not exist.
  3. C
    2
  4. D
    0
Pick an option, then check.
Answer & solution

Answer: Option A

Substituting x = 2 directly gives 0/0, so factorise first.

x² − 4 = (x − 2)(x + 2).

So the expression becomes (x − 2)(x + 2) ÷ (x − 2) = x + 2 for every x ≠ 2.

The limit as x approaches 2 is therefore 2 + 2 = 4.

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