Test: Engineering Mathematics & General Aptitude- 1

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This mock test of Test: Engineering Mathematics & General Aptitude- 1 for GATE helps you for every GATE entrance exam. This contains 15 Multiple Choice Questions for GATE Test: Engineering Mathematics & General Aptitude- 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Engineering Mathematics & General Aptitude- 1 quiz give you a good mix of easy questions and tough questions. GATE students definitely take this Test: Engineering Mathematics & General Aptitude- 1 exercise for a better result in the exam. You can find other Test: Engineering Mathematics & General Aptitude- 1 extra questions, long questions & short questions for GATE on EduRev as well by searching above.

QUESTION: 1

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

A.
ML^-1T²
B.
ML^-3T^-2
C.
ML^-2T^-2
D.
M^-1L^-1T^-2

Solution:

Pressure gradient= Pressure per unit length
Pressure= Force/ Area= (Mass x Acceleration)/Area =

QUESTION: 2

The following Newton-Raphson iteration formula finds

A.
B.
C.
a²
D.

Solution:

QUESTION: 3

Find the 2^nd approximation to the root of the equation t⁴ -4t-9 = 0 between 2 and 2.5 using Bisection method.

A.
2.625
B.
2.25
C.
2.75
D.
2.125

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?

A.
Both P & Q are linearly dependent
B.
Both P & Q are linearly independent
C.
P is dependent, Q is independent
D.
P is independent, Q is dependent

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

A.
6,10
B.
6,16
C.
0,10
D.
0,16

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?

A.
(A v B) → A
B.
A v (B → A)
C.
A v (A → B)
D.
A → (A → B)

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?

A.
Only G1 has a Hamiltonian circuit
B.
Only G2 has a Hamiltonian circuit
C.
Both the graphs have Hamiltonian circuits
D.
None of the above 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

A.
(A → B) → C
B.
C → (A → B)
C.
~ (A→ B) v C
D.
None of these

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.

A.
λ = 9, μ = 5
B.
λ = 7, μ = 5
C.
λ = 5, μ = 7
D.
λ = 5, μ = 9

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?