# NTA NET Electrical Engineering GATE 2018 Higher Questions and Answers Part 1

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**(Topic: Electric Circuits)**

**(Subtopic: Network Graph)**

**(Sub-Subtopic: Calculation of nodes, branches, and loops)**

The graph of a network has 8 nodes and 5 independent loops. The number of branches of

the graph is

(A) 11

(B) 12

(C) 13

(D) 14

**(Topic: Electric Circuits)**

**(Subtopic: Power and power factor in AC circuits)**

**(Sub-Subtopic: Power calculation)**

In the figure, the voltages are 𝑣_{1}(𝑡) = 100cos(𝜔𝑡), 𝑣_{2}(𝑡) = 100cos(𝜔𝑡 + 𝜋/18) and

𝑣_{3}(𝑡) = 100cos(𝜔𝑡 + 𝜋/36). The circuit is in sinusoidal steady state, and 𝑅 << 𝜔𝐿. 𝑃_{1} ,

𝑃_{2} and 𝑃_{3} are the average power outputs. Which one of the following statements is true?

(A) 𝑃_{1} = 𝑃_{2} = 𝑃_{3} = 0

(B) 𝑃_{1} < 0, 𝑃_{2} > 0, 𝑃_{3} > 0

(C) 𝑃_{1} < 0, 𝑃_{2} > 0, 𝑃_{3} < 0

(D) 𝑃_{1} > 0, 𝑃_{2} < 0, 𝑃_{3} > 0

**(Topic: Control Systems)**

**(Subtopic:** **Transient and Steady‐state analysis of linear time invariant systems)**

**(Sub-Subtopic:** **Time response of 2nd order system)**

Match the transfer functions of the second order systems with the nature of systems given below.

(A) P-I, Q-II, R-III

(B) P-II, Q-I, R-III

(C) P-III, Q-II, R-I

(D) P-III, Q-I, R-II

**(Topic: Electromagnetic Fields)**

**(Subtopic: Electric Field Intensity)**

**(Sub-Subtopic: Image concept )**

A positive charge of 1nC is placed at (0,0,0.2) where all dimensions are in metres. Consider the x-y plane to be a conducting ground plane. Take . The z component of the E field at (0,0,0.1) is closest to

(A) 899.18 V/m

(B) -899.18 V/m

(C) 999.09 V/m

(D) -999.09 V/m

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Calculus)**

**(Sub-Subtopic:** **Continuity and Differentiability)**

Let be a real valued function of a real variable defined as , and . Which one of the following statements is true?

(A). is discontinuous at .

(B). is continuous but not differentiable at .

(C). is differentiable but its first derivative is not continuous at .

(D). is differentiable but its first derivative is not differentiable at .

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Calculus)**

**(Sub-Subtopic:** **Directional directive)**

The value of the directional derivative of the function at the point (2,-1,1) in the direction of the vector is

(A). 1

(B). 0.95

(C). 0.93

(D). 0.9

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Complex Variables)**

**(Sub-Subtopic:** **Cauchy’s residue theorem)**

The value of the integral in counter clockwise direction around a circle C of radius 1 with center at the point is

(A).

(B).

(C).

(D).

**(Topic: Analog and Digital Electronics)**

**(Subtopic:** **Combinational and Sequential logic circuits)**

**(Sub-Subtopic:** **Logic gates)**

In the logic circuit shown in the figure, Y is given by

(A).

(B).

(C).

(D).