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QUESTION: 1

The dimension of a pressure gradient in a fluid flow are :

Solution:

Pressure gradient= Pressure per unit length

Pressure= Force/ Area= (Mass x Acceleration)/Area =

QUESTION: 2

The following Newton-Raphson iteration formula finds

Solution:

QUESTION: 3

Find the 2^{nd} approximation to the root of the equation t^{4} -4t-9 = 0 between 2 and 2.5 using Bisection method.

Solution:

QUESTION: 4

Consider two sets of vectors P and Q as

P = {(2,-1,3,2), (1,3,4,2), (3,-5,2,2)}

Q = {(.1,2,-1,0), (1,3,1,2), (4,2,1,0), (6,1,0,1)}

Which of the following is true?

Solution:

QUESTION: 5

Let G1 and G2 be two edge disjoint and vertex disjoint graphs. G1 has 4 vertices and 6 edges, G2 has 6 vertices and 10 edges. Then number of edges in (G1 intersection G2) and (G1 union G2) are respectively

Solution:

Edge disjoint means no edge is common and vertex disjoint means no vertex is common.

As there is no edge is common between G1 and G2, hence number of edges in (G1 intersection G2) = 0 and number of edges in (G1 union G2) = number of edges in G1 + number of edges in G2 = 6+10 = 16

QUESTION: 6

Which of the following propositions is a tautology?

Solution:

*Answer can only contain numeric values

QUESTION: 7

The minimum number of connected components of a simple graph with 20 vertices and 12 edges is

Solution:

e: number of edges = 12, n: number of vertices = 20

k: number of connected components, e __>__ n - k , Or, 12 __>__ 20-K ⇒ K = 8

QUESTION: 8

Which of the following graphs has a Hamiltonian circuit?

Solution:

G1 has a Hamiltonian circuit: 1-2-8-6-4-3-5-7-1

G2 has a bridge (an edge which, if removed, disconnects the graph), namely the middle edge of the thcee horizontal edges at the bottom of the given .drawing of G2. Whichever side of the bridge you start, you cannot, having crossed the bridge, re-cross it without visiting vertices twice. Hence you cannot complete a Hamiltonian circuit.

QUESTION: 9

The proposition logically equivalent to

Solution:

QUESTION: 10

Investigate the values of λ and μ so that the equations

2x+3y+5z = 9, 7x+3y-2z = 8, 2x+3y+λ z = μ

have an infinite number of solutions.

Solution:

QUESTION: 11

A complex (P+ iQ, P,Q : real numbers) n x n matrix A is said to be unitary if AA° = I_{n}, where If A be a unitary matrix, then which of the following is true?

Solution:

*Answer can only contain numeric values

QUESTION: 12

Consider the function

At how many points, f(x) Is discontinuous?

Solution:

QUESTION: 13

Evaluate the integral

Solution:

QUESTION: 14

Consider the following matrix:

Determine the eigen values of the given matrix.

Solution:

QUESTION: 15

Consider the function f (x) = 2x^{3} - 9x^{2} + 12x -12

The function attains minima at x =

Solution:

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