Allied & ICAR Exam Bank • ALLIED_0038 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Taylor and MacLaurin series

Question Statement:

The first three non-zero terms in the Maclaurin expansion of $e^{2x}$ are $1 + 2x + k x^2$. The value of $k$ is:

Answer Key:

2

Step-by-Step Solution & Explanation

$e^{2x} = 1 + (2x) + \frac{(2x)^2}{2!} + \dots = 1 + 2x + 2x^2 + \dots \implies k = 2$.
← Previous (ALLIED_0037) Next (ALLIED_0039) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test