1.The accuracy of Simpson’s rule quadrature for a step size h is
(a) O(h^{2})
(b) O(h^{3})
(c) O(h^{4})
(d) O(h^{5})
(1 Mark, 2003)

Ans: c
2.The values of a function f(x) are tabulated below:
Using Newton’s forward difference formula, the cubic polynomial that can be fitted to the above data, is
(a) 2x^{3} + 7x^{2} – 6x + 2
(b) 2x^{3} + 7x^{2} – 6x + 2 ^{ }
(c) x^{3} – 7x^{2} – 6x + 1
(d) 2x^{3} – 7x^{2} + 6x + 1
(2 Mark, 2004)

Ans: d
Explanation:
3. Starting from x_{0} = 1, one step of Newton – Raphson method in solving the equation x^{3} + 3x − 7 = 0 gives the next value (x_{1}) as
(a) x_{1} = 0.5
(b) x_{1} = 1.406
(c) x_{1} = 1.5
(d) x_{1} = 2 ^{ }
(2 Mark, 2005)

Ans: c
Explanation:
4. Match the items in columns I and II.
(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
(1 Mark, 2006)

Ans: d
5. Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE ?
(a) E (XY) = E (X) E (Y)
(b) Cov (X, Y) = 0
(c) Var (X + Y) = Var (X) + Var (Y)
(d) E (X^{2 }Y^{2}) = (E(X))^{2 }(E(Y))^{2}
(2 Mark, 2007)

Ans: b
6. A calculator has accuracy up to 8 digits after decimal place. The value of when evaluated using the calculator by trapezoidal method with 8 equal intervals, to 5 significant digits is
(a) 0.00000
(b) 1.0000
(c) 0.00500
(d) 0.00025
(2 Mark, 2007)

Ans: a
Explanation:
7. Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson’s rule is
(a) 542
(b) 993
(c) 1444
(d) 1986
(2 Mark, 2010)

Ans: b
Explanation:
8. The integral \int _{ 1 }^{ 3 }{ \frac { 1 }{ x } } dx, when evaluated by using Simpson’s 1/3 rule on two equal subintervals each of length 1, equals
(a) 1.000
(b) 1.098
(c) 1.111
(d) 1.120
(2 Mark, 2011)

Ans: c
Explanation:
9. Match the CORRECT pairs.
(a) P2, Q1, R3
(b) P3, Q2, R1
(c) P1, Q2, R3
(d) P3, Q1, R2
(1 Mark, 2013)

Ans: d
10. Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral \int _{ 1 }^{ +1 }{ x } dx is _____.
(2 Mark, 2014[1])

Ans: 1.11
Explanation:
11.The value \int _{ 2.5 }^{ 4 }{ ln(x) } dx of calculated using the Trapezoidal rule with five subintervals is _______.
(2 Mark, 2014[2])

Ans: 1.75
Explanation:
12. The definite integral \int _{ 1 }^{ 3 }{ \frac { 1 }{ x } dx } is evaluated using Trapezoidal rule with a step size of 1. The correct answer is _______.
(1 Mark, 2014[3])

Ans: 1.165
Explanation:
13. Consider an ordinary differential equation \frac { dx }{ dt } =4t+4. If x = x_{0} at t = 0, the increment in x calculated using Runge – Kutta fourth order multistep method with a step size of Δt = 0.2 is
(a) 0.22
(b) 0.44
(c) 0.66
(d) 0.88
(2 Mark, 2014[4])

Ans: d
Explanation:
14. Simpson’s 1/3^{rd} rule is used to integrate the function (x) = \frac { 3 }{ 5 } x^{2} + \frac { 9 }{ 5 } between x = 0 and x = 1 using the least number of equal subintervals. The value of the integral is _____.
(1 Mark, 2015[1])

Ans: 2
Explanation:
16. Using unit step size, the value of integral \int _{ 1 }^{ 2 }{ xlnxdx } by Trapezoidal rule is __.
(1 Mark, 2015[3])

Ans: 0.693
Explanation:
17. Solve the equation x = 10 cos(x) using the NewtonRaphson method. The initial guess is x = π/4. The value of the predicted root after the first iteration, up to second decimal, is ____.
(1 Mark, 2016[1])

Ans: 1.56
Explanation:
18. Gauss – Seidel method is used to solve the following equations (as per the given order):
x_{1} + 2x_{2} + 3x_{3} = 5,
2x_{1} + 3x_{2} + x_{3} = 1,
3x_{1} + 2x_{2} + x_{3} = 3,
Assuming initial guess as x_{1} = x_{2} = x_{3} = 0,the value of x_{3} after the first iteration is _____.
(2 Mark, 2016[1])

Ans: 6
Explanation:
19. Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
(a) Linear
(b) Parabolic
(c) Logarithmic
(d) Hyperbolic
(1 Mark, 2016[2])

Ans: a
Explanation:
20. The error in numerically computing the integral \int _{ 0 }^{ \pi }{ (sinx+cosx)dx } using the trapezoidal rule with three intervals of equal length between 0 and \pi is ___.
(2 Mark, 2016[2])

Ans: 0.186
Explanation:
21. The root of the function f(x) = x^{3 }+ x – 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x_{0} = 1 is
(a) 0.682
(b) 0.686
(c) 0.750
(d) 1.000
(1 Mark, 2016[3])

Ans: c
Explanation:
22. Evaluation of \int _{ 2 }^{ 4 }{ { x }^{ 3 }dx } dx using a 2equalsegment trapezoidal rule gives a value of _____.
(1 Mark, 2019[1])

Ans: 63
Explanation: