Numerical Methods MCQs Question and Answer in Engineering Maths

31

A calculator has accuracy up to 8 digits after decimal place. The value of $$\int\limits_0^{2\pi } {\sin {\text{x dx}}} $$ when evaluated using this 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

Discuss

Answer & Solution

Answer: Option A

No explanation is given for this question. Let's Discuss on Board

32

The following table lists an n^th order polynomial f(x) = a_n xⁿ + a_{n - 1} x^{n - 1} + , .... a₁x + a₀ and the forward difference evaluated at equally spaced values of x. The order of the polynomial is

x	f(x)	Δf	Δ²f	Δ³f
-0.4	1.7648	-0.2965	0.089	-0.03
-0.3	1.4683	-0.2075	0.059	-0.0228
-0,2	1.2608	-0.1485	0.0362	-0.0156
-0.1	1.1123	-0.1123	0.0206	-0.0084
0	1	-0.0917	0.0122	-0.0012
0.1	0.9083	-0.0795	0.011	0.006
0.2	0.8288	-0.0685	0.017	0.0132

A) 1 B) 2 C) 3 D) 4

Discuss

Answer & Solution

Answer: Option D

No explanation is given for this question. Let's Discuss on Board

33

P(0, 3), Q(0.5, 4) and R(1, 5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits x = 0 and x = 1 for the curve. The difference between the two results will be

A) 0 B) 0.25 C) 0.5 D) 1

Discuss

Answer & Solution

Answer: Option A

No explanation is given for this question. Let's Discuss on Board

34

The recursion relation to solve x = e^-x using Newton-Raphson method is

A) $${{\text{x}}_{{\text{n}} + 1}} = {{\text{e}}^{ - {{\text{x}}_{\text{n}}}}}$$ B) $${{\text{x}}_{{\text{n}} + 1}} = {{\text{x}}_{\text{n}}} - {{\text{e}}^{ - {{\text{x}}_{\text{n}}}}}$$ C) $${{\text{x}}_{{\text{n}} + 1}} = \left( {1 + {{\text{x}}_{\text{n}}}} \right)\frac{{{{\text{e}}^{ - {{\text{x}}_{\text{n}}}}}}}{{1 + {{\text{e}}^{ - {{\text{x}}_{\text{n}}}}}}}$$ D) $${{\text{x}}_{{\text{n}} + 1}} = \frac{{{\text{x}}_{\text{n}}^2 - {{\text{e}}^{ - {{\text{x}}_{\text{n}}}}}\left( {1 + {{\text{x}}_{\text{n}}}} \right) - 1}}{{{{\text{x}}_{\text{n}}} - {{\text{e}}^{ - {{\text{x}}_{\text{n}}}}}}}$$

Discuss

Answer & Solution

Answer: Option C

No explanation is given for this question. Let's Discuss on Board

35

Given that one root of the equation x³ - 10x² + 31x - 30 = 0 is 5, the other two roots are

A) 2 and 3 B) 2 and 4 C) 3 and 4 D) -2 and -3

Discuss

Answer & Solution

Answer: Option A

No explanation is given for this question. Let's Discuss on Board

36

The bisection method is applied to compute a zero of the function f(x) = x⁴ - x³ - x² - 4 in the interval [1, 9]. The method converges to a solution after . . . . . . . . iterations.

A) 1 B) 3 C) 5 D) 7

Discuss

Answer & Solution

Answer: Option B

No explanation is given for this question. Let's Discuss on Board

37

The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x² - N = 0. If i denotes the iteration index, the correct iterative scheme will be

A) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$ B) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{\text{x}}_{\text{i}}^2 + \frac{{\text{N}}}{{{\text{x}}_{\text{i}}^2}}} \right)$$ C) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{{{\text{N}}^2}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$ D) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} - \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

Discuss

Answer & Solution

Answer: Option A

No explanation is given for this question. Let's Discuss on Board

38

During the numerical solution of a first order differential equation using Euler method with step size h, the local truncation error is of order of

A) h² B) h³ C) h⁴ D) h⁵

Discuss

Answer & Solution

Answer: Option A

No explanation is given for this question. Let's Discuss on Board

39

With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$ where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.

A) I only B) II only C) Both I and II D) Neither I nor II

Discuss

Answer & Solution

Answer: Option C

No explanation is given for this question. Let's Discuss on Board

40

The following equation needs to be numerically solved using the Newton-Raphson method. x³ + 4x - 9 = 0. The iterative equation for this purpose is (k indicates the iteration level)

A) $${{\text{x}}_{{\text{k}} + 1}} = \frac{{2{\text{x}}_{\text{k}}^3 + 9}}{{3{\text{x}}_{\text{k}}^2 + 4}}$$ B) $${{\text{x}}_{{\text{k}} + 1}} = \frac{{3{\text{x}}_{\text{k}}^2 + 4}}{{2{\text{x}}_{\text{k}}^2 + 9}}$$ C) $${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - 3{\text{x}}_{\text{k}}^2 + 4$$ D) $${{\text{x}}_{{\text{k}} + 1}} = \frac{{4{\text{x}}_{\text{k}}^2 + 3}}{{9{\text{x}}_{\text{k}}^2 + 2}}$$

Discuss

Answer & Solution

Answer: Option A

No explanation is given for this question. Let's Discuss on Board