Numerical Methods - Study Mode

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[#21] In numerical integration using Simpson's rule, the approximating function in interval is a

(A) constant

(B) straight line

(C) cubic B-spline

(D) parabola

Correct Answer

(D) parabola

[#22] Using Simpson's 1/3 rule for numerical integration, the consecutive points are joined by a

(A) line

(B) parabola

(C) polynomial with power 3

(D) polynomial with power 1/3

Correct Answer

(B) parabola

[#23] The differential equation $$frac{{{ ext{dx}}}}{{{ ext{dt}}}} = frac{{4 - { ext{x}}}}{ au },$$ xa0 with x(0) = 0 and the constant $$ au $$ > 0, is to be numerically integrated using the forward Euler method with a constant integration time step T. The maximum value of T such that the numerical solution of x converges is

(A) $$frac{ au }{4}$$

(B) $$frac{ au }{2}$$

(C) $$ au $$

(D) $$2 au $$

Correct Answer

(D) $$2 au $$

[#24] Match the following: List-I List-II P. 2 nd order differential equation 1. Runge-Kutta Method Q. Non-linear algebraic equation 2. Newton-Raphson Method R. Linear algebraic equation 3. Gauss Elimination S. Numerical integration 4. Simpson's rule

(A) P-3, Q-2, R-4, S-1

(B) P-2, Q-4, R-3, S-1

(C) P-1, Q-2, R-3, S-4

(D) P-1, Q-3, R-2, S-4

Correct Answer

(C) P-1, Q-2, R-3, S-4

[#25] Match the application to appropriate numerical method. Application Numerical Method P1: Numerical integration M1: Newton-Raphson Method P2: Solution to a transcendental equation M2: Runge-Kutta Method P3: Solution to a system of linear equations M3: Simpson's 1/3-rule P4: Solution to a differential equation M4: Gauss Elimination Method

(A) P1-M3, P2-M2, P3-M4, P4-M1

(B) P1-M3, P2-M1, P3-M4, P4-M2

(C) P1-M4, P2-M1, P3-M3, P4-M2

(D) P1-M2, P2-M1, P3-M3, P4-M4

Correct Answer

(B) P1-M3, P2-M1, P3-M4, P4-M2