GATE CH Numerical Methods PYQs & Answers — Page 2

Questions 11–16 of 16. Imported answers require independent review unless marked reviewed.

Topic practice 16 questionsPage 2 of 2

Given

, and

, the value of

is ________ (round off to nearest integer).

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Consider the following dataset:

	1	3	5	15	25
	6	8	10	12	5

The value of the integral

using Simpson’s 1/3rd rule is ________ (round off to 1 decimal place).

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The Newton-Raphson method is used to determine the root of the equation

. If the initial guess for the root is 0, the estimate of the root after two iterations is ________ (rounded off to three decimal places).

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The fourth order Runge-Kutta (RK4) method to solve an ordinary differential equation

is given as

For a special case when the function

depends solely on x, the above RK4 method reduces to

Your answerChoose one option.

Euler’s explicit method

Trapezoidal rule

Euler’s implicit method

Simpson’s 1/3 rule

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The volume of liquid filled in a spherical storage tank of radius R is computed from height of liquid, h, in the outside tube (neglecting the volume of liquid in the outside tube) as

Diagram for Chemical Engineering question 49

The estimate of liquid height (in m) to store V = 30 m³ of water in R = 3 m tank, after performing ONE iteration of Secant method, using 1 m and 3 m as two initial guesses of liquid height is ____________ (rounded off to second decimal place).

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Match the problem type in Group-1 with the numerical method in Group-2.

Group-1 P) System of linear algebraic equations Q) Non-linear algebraic equations R) Ordinary differential equation S) Numerical integration

Group-2 I) Newton-Raphson II) Gauss-Seidel III) Simpson’s rule IV) Runge-Kutta

Choose the correct set of combinations.

Your answerChoose one option.

P-II, Q-I, R-III, S-IV

P-I, Q-II, R-IV, S-III

P-IV, Q-III, R-II, S-I

P-II, Q-I, R-IV, S-III

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GATE CH Numerical Methods PYQs

Question 54

Question 55

Question 36

Question 2

Question 49

Question 28