Free Printable CAT II: MCQ:Numerical Methods

1.

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)

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

2.

$\Delta\nabla$

a)

$\nabla-\Delta$

b)

$\Delta-\nabla$

c)

$\Delta+\nabla$

d)

none

3.

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

a)

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

b)

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

c)

E(x)

d)

none

4.

$If\ h=1\ then\ \Delta\left(x^2\right)=$

a)

$\left(x+1\right)^2$

b)

2x-1

c)

2x+1

d)

1

5.

$\delta=$

a)

$E^{\frac{1}{2}}-E^{-\frac{1}{2}}$

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)

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

6.

$E^{-2}f\left(x\right)=$

a)

$f\left(x-2h\right)$

b)

$f\left(x-2h\right)-f\left(x\right)$

c)

$f\left(x+2h\right)$

d)

$f^{-2}\left(x\right)$

7.

$If\ f\left(x\right)=a_0x^n+a_1x^{n-1}+...+a_{n-1}x+a_n,\ \ a_0\ne0,\ then\ \Delta^nf\left(x\right)=$

a)

$a_0h^n$

b)

$n!h^n$

c)

$a_0n!h^n$

d)

$n!$

8.

1. Given a set of n points, interpolating polynomials is of degree

a)

2

b)

$\ge n$

c)

$\le n$

d)

$<n$

9.

1. Find p if x₀ = 0.75825, x = 0.759 and h = 0.00005.

a)

1.5

b)

2.5

c)

15

d)

25

10.

The Newton’s divided difference second order polynomial for the given data is

a)

option a

b)

option b

c)

option c

d)

option d

CAT II: MCQ:Numerical Methods

Total questions: 10

Worksheet time: 30mins

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