Allied & ICAR Exam Bank • ALLIED_0102 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

Using the Newton-Raphson method to find the root of $x^2 - 5 = 0$ with initial guess $x_0 = 2$, the first iteration $x_1$ is:

Answer Key:

2.25

Step-by-Step Solution & Explanation

$f(x) = x^2 - 5, f'(x) = 2x$. $x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2 - \frac{2^2 - 5}{2(2)} = 2 - \frac{-1}{4} = 2 + 0.25 = 2.25$.
← Previous (ALLIED_0101) Next (ALLIED_0103) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test