# Numerical Methods and Optimization 1

Mechanical Engineering MCQ Question Papers: DRDO, ISRO, Interview

Subject: Numerical Methods and Optimization 1

Part 1: List for questions and answers of Numerical Methods and Optimization

Q1.Operations Research (OR), which is a very powerful tool for ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
a) Research
b) Decision – Making
c) Operations
d) None of the above

Q2.Who coined the term Operations Research?
a) J.F. mccloskey
b) F.N. Trefethen
d) Both A and B

Q3.The term Operations Research was coined in the year ‐‐‐‐‐‐‐‐‐‐‐‐‐‐
a) 1950
b) 1940
c) 1978
d) 1960

Q4.Operations Research was known as an ability to win a war without really going in to a ‐‐‐‐‐‐‐‐‐‐‐‐‐
a) Battle field
b) Fighting
c) War
d) Both A and B

Q5.Operations Research has the characteristics done by a team of ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
a) Scientists
b) Mathematicians
d) All of the above

Q6.The convergence of which of the following method is sensitive to starting value?
a) False position
b) Gauss seidal method
c) Newton‐Raphson method
d) All of these

Q7.Which of the following statements applies to the bisection method used for finding roots of functions?
a) Converges within a few iterations
b) Guaranteed to work for all continuous functions
c) Is faster than the Newton‐Raphson method
d) Requires that there be no error in determining the sign of the function

Q8. We wish to solve: x^2 ‐ 2 = 0. By Newton Raphson technique. If initial guess is x0 = 1.0, subsequent estimate of x (i.e. X1) will be
a) 1.414
b) 1.5
c) 2.0
d) None of these

Q9.Using Newton‐Raphson method, find a root correct to three decimal places of the equation: x^3 ‐ 3x ‐ 5 = 0
a) 2.275
b) 2.279
c) 2.222
d) None of these

Q10.In the Gauss elimination method for solving a system of linear algebraic equations, triangularzation leads to
a) Diagonal matrix
b) Lower triangular matrix
c) Upper triangular matrix
d) Singular matrix

Q11. If Δf(x) = f(x+h) ‐ f(x), then a constant k, Δk equals
a) 1
b) 0
c) F(k)‐ f(0)
d) (x + k) ‐ f(x)

Q12.Double (Repeated) root of 4x^3‐ 8x^2‐ 3x + 9 = 0. By Newton‐rap son method is
a) 1.4
b) 1.5
c) 1.6
d) 1.55

Q13.Using Bisection method, negative root of x^3 ‐ 4x + 9 = 0 correct to three decimal places is
a) 2.506
b) 2.706
c) 2.406
d) None of these

Q14.The root of x^3 ‐ 2x ‐ 5 = 0 correct to three decimal places by using Newton‐Raphson method is
a) 2.0946
b) 1.0404
c) 1.7321
d) 0.7011

Q15.Newton‐Raphson method of solution of numerical equation is not preferred when
a) Graph of A(B) is vertical
b) Graph of x(y) is not parallel
c) The graph of f(x) is nearly horizontal‐where it crosses the x‐axis
d) None of these

Q16.Following are the values of a function y(x): y(‐1) = 5, y (0), y(1) = 8
dy/dx at x = 0 as per Newton’s central difference scheme is
a) 0
b) 1.5
c) 2.0
d) 3.0

Q17.A root of the equation x^3 ‐ x ‐ 11 = 0 correct to four decimals using bisection method is
a) 2.3737
b) 2.3838
c) 2.3736
d) None of these

Q18.Newton‐Raphson method is applicable to the solution of
a) Both algebraic and transcendental Equations
b) Both algebraic and transcendental and also used when the roots are complex
c) Algebraic equations only
d) Transcendental equations only

Q19.The order of error s the Simpson’s rule for numercal integration with a step size h is
a) H
b) H2
c) H3
d) H4

Q20.In which of the following methods proper choice of initial value is very important?
a) Bisection method
b) False position
c) Newton‐Raphson
d) Bairsto method

Part 1: List for questions and answers of Numerical Methods and Optimization