# Numerical methods 1 marks

GATE 2016 Set-1

1. Solve the equation x=10 cos(x) using the Newton-Raphson method. The initial guess is $$\large x=\pi/4$$. The value of the predicted root after the first iteration, up to second decimal, is ________

GATE 2016 Set-2

1. Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

(A) linear

(B) parabolic

(C) logarithmic

(D) hyperbolic

GATE 2015 Set-1

1. Simpson’s 1/3rd rule is used to integrate the function $$\large f(x)=\frac{3}{5}x^2+\frac{9}{5}$$ between x = 0 and x = 1 using the least number of equal sub-intervals. The value of the integral is ____

GATE 2015 Set-3

1. Using a unit step size, the value of integral $$\large \int_{1}^{2}x\ln x dx$$ by trapezoidal rule is ______

GATE 2014 Set-3

1. The definite integral $$\large \int_{1}^{3}\frac{1}{x}dx$$ is evaluated using Trapezoidal rule with a step size of 1. The correct answer is ____

GATE 2013

1. Match the following

Numerical Integration   Scheme Order of Fitting Polynomial

P. Simpson’s 3/8 Rule        1. First

Q. Trapezoidal Rule            2. Second

R. Simpson’s 1/3 Rule        3. Third

(A) P-2, Q-1, R-3    (B) P-3, Q-2, R-1

(C) P-1, Q-2, R-3    (D) P-3, Q-1, R-2

GATE 2006

1. Match the items in columns I and II.

Column I

(P) Gauss-Seidel method
(Q) Forward Newton-Gauss method
(R) Runge-Kutta method
(S) Trapezoidal Rule

Column II

(1) Interpolation
(2) Non-linear differential equations
(3) Numerical integration
(4) Linear algebraic equations

(A) P – 1 Q – 4 R – 3 S – 2

(B) P – 1 Q – 4 R – 2 S – 3

(C) P – 1 Q – 3 R – 2 S – 4

(D) P – 4 Q – 1 R – 2 S – 3