Allied & ICAR Exam Bank • ALLIED_1024 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Bisection method

Question Statement:

To reduce the initial bracket interval containing a root to at most $1/1000$ of its initial length, the minimum number of iterations required in the Bisection method is:

Options:

  • (A) 8
  • (B) 9
  • (C) 10
  • (D) 12

Answer Key:

C

Step-by-Step Solution & Explanation

After $n$ iterations, the interval length is $\frac{L_0}{2^n}$. We need $\frac{1}{2^n} \le \frac{1}{1000} \implies 2^n \ge 1000$. Since $2^9 = 512$ and $2^{10} = 1024$, the minimum integer is $n = 10$.
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