Free Printable MCQ:ICS

1.

f(x)-f(x-h)=

a)

$\Delta f\left(x\right)$

b)

undefined

c)

E(x)

d)

none

2.

In Simpson’s one third rule, the number of ordinates must be ..................

a)

odd

b)

even

c)

multiple of 3

d)

no condition required

3.

∆2^x=…………….

a)

2^(x+h)-2^x

b)

2^(x+h)

c)

2^(x-h)-2^x

d)

2^(x-h)

4.

In numerical integration the width of the sub intervals is given by

a)

$h=\frac{x_n-x_0}{n}$

b)

$h=\frac{x_n+x_0}{n}$

c)

$h=\frac{x_0-x_n}{n}$

d)

none of thesse

5.

Simpson’s 1/3 rule is applicable for five ordinates.

a)

True

b)

False

6.

Given $\frac{\text{d}y}{\text{d}x}=1-y,\ y\left(0\right)=0$ using a step size of h=0.1 , the value of y(0.2) using Euler’s method is most nearly

a)

0.1

b)

0.119

c)

0.19

d)

0.01

7.

Order of convergence of Regula falsi method is

a)

1.618

b)

1.168

c)

1.681

d)

1.816

8.

Error in trapezoidal rule is of order

a)

h

b)

h²

c)

h³

d)

h⁴

9.

Newton-Raphson method is also called as

a)

Method of chords

b)

Method of tangents

c)

halving method

d)

succesive approximation method

10.

Backward difference operator pronounced as

a)

delta

b)

lamda

c)

nabla

d)

alpha

11.

$\Delta^2y_0=$

a)

$\Delta y_1-\Delta y_0$

b)

$\Delta y_0-\Delta y_1$

c)

$\Delta^2y_1-\Delta^2y_0$

d)

$\Delta y_1+\Delta y_0$

12.

The (n+1)^th and higher differences of a polynomial of degree n are -----

a)

zeros

b)

variables

c)

constant

d)

unique

13.

$E\nabla\ =$

a)

E

b)

$\nabla$

c)

$\Delta$

d)

1

14.

The central difference operator is denoted by ----

a)

$\Delta$

b)

$\nabla$

c)

$\delta$

d)

$\mu$

15.

$\delta=$

a)

$\frac{1}{2}\left(E^{\frac{1}{2}}-E^{-\frac{1}{2}}\right)$

b)

$\frac{1}{2}\left(E^{\frac{1}{2}}+E^{-\frac{1}{2}}\right)$

c)

$\frac{1}{2}\left(E^{-\frac{1}{2}}-E^{\frac{1}{2}}\right)$

d)

$\frac{h}{2}\left(E^{-\frac{1}{2}}-E^{\frac{1}{2}}\right)$

16.

Which of the following formula is a particular case of Runge – Kutta formula of the second order?.

a)

Taylor's

b)

Modified Eulers

c)

Eulers

d)

Picards

17.

Which of the following are single step techniques?

a)

Taylor's

b)

Euler's

c)

RK Mehod

d)

Milne's

18.

Given the two points $\left(a,f\left(a\right)\right),\left(b,f\left(b\right)\right)$ , the linear Lagrange polynomial $f1\left(x\right)$ that passes through these two points is given by

a)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{a-b}f\left(b\right)$

b)

$f1\left(x\right)=\frac{x}{b-a}f\left(a\right)+\frac{x}{b-a}f\left(b\right)$

c)

$f1\left(x\right)=f\left(a\right)+\frac{f\left(b\right)-f\left(a\right)}{b-a}\left(b-a\right)$

d)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{b-a}f\left(b\right)$

19.

h=0.25

a)

0.388

b)

0.188

c)

0.288

d)

0.488

20.

In numerical solutions, if all the n conditions are specified at the initial point only then it is called an ...................

a)

Initial value problem

b)

boundary value problem

c)

no such exists

d)

arbitrary constants

MCQ:ICS

Total questions: 20

Worksheet time: 30mins

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