Allied & ICAR Exam Bank • ALLIED_1032 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Taylor series

Question Statement:

The coefficient of $(x - 1)^2$ in the Taylor series expansion of $f(x) = x^4$ about $x = 1$ is:

Options:

  • (A) 4
  • (B) 6
  • (C) 12
  • (D) 24

Answer Key:

B

Step-by-Step Solution & Explanation

In Taylor series about $a=1$, coefficient of $(x-1)^2$ is $\frac{f''(1)}{2!}$. $f'(x) = 4x^3 \implies f''(x) = 12x^2 \implies f''(1) = 12$. Coefficient $= \frac{12}{2} = 6$.
← Previous (ALLIED_1031) Next (ALLIED_1033) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test