2nd Year Mathematics Chapter 10 Test10: Numerical Methods

Q1. Multiple choice questions (Attempt all · 8 × 1 = 8)

1. What does the Bisection method do?
   1. Finds the maximum of a function
   2. Estimates the area under the curve
   3. Finds the root of the function
   4. Differentiates a function
2. Numerical techniques more commonly involve:
   1. Elimination
   2. Reduction
   3. Iterative method
   4. Direct methods
3. Which method splits the half to find the root?
   1. Newton’s method
   2. Regula Falsi method
   3. Bisection method
   4. Trapezoidal rule
4. Using Bisection method, one root of x⁴− x − 1 = 0 lies between 1 and 2. After $2^{nd}$ iteration the root may lie in the interval:
   1. (1.25, 1.5)
   2. (1, 1.25)
   3. (1, 1.5)
   4. None of these
5. Which of the following method requires the calculation of derivative of the function?
   1. Trapezoidal rule
   2. Bisection method
   3. Regula Falsi method
   4. Newton’s method
6. The Trapezoidal rule is used to:
   1. Find roots of equations
   2. Integrate functions
   3. Differentiate functions
   4. Solve system of equations
7. Which of the following is a root-finding method?
   1. Trapezoidal rule
   2. Simpson’s rule
   3. Bisection method
   4. Both (a) and (c)
8. Which of the methods requires two initial guesses?
   1. Bisection method
   2. Regula Falsi method
   3. Newton’s method
   4. Both (a) and (c)