# Electrical Engineering - GATE 2013 Paper Solution

Question No. 1

In the circuit shown below what is the output voltage (Vout) in Volts if a silicon transistor Q and an ideal op-amp are used?

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Question No. 2

The transfer function $\frac{{V}_{2}\left(s\right)}{{V}_{1}\left(s\right)}$ of the circuit shown below is

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Question No. 3

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is

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Question No. 4

The impulse response of a system is h(t) = t u(t) . For an input u(t -1) , the output is

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Question No. 5

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

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Question No. 6

Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

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Question No. 7

A source ${\nu }_{s}\left(t\right)=V\mathrm{cos}100\pi t$ has an internal impedance of $\left(4+j3\right)\mathrm{\Omega }$.If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\mathrm{\Omega }$ should be

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Question No. 8

A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is $10\angle -150°$ A and if the voltage at the load terminals is $100\angle 60°$ V, then the

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Question No. 9

A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at

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Question No. 10

The flux density at a point in space is given by $\mathbf{B}\mathbf{=}4x{\mathbf{a}}_{\mathrm{x}}+2ky{\mathbf{a}}_{\mathbf{y}}+8{\mathbf{a}}_{\mathbf{z}}$ Wb/m2. The value of constant k must be equal to

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Question No. 11

A continuous random variable X has a probability density function $f\left(x\right)={e}^{-x},0.Then $P\left\{X>1\right\}$ is

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Question No. 12

The curl of the gradient of the scalar field defined by $V=2{x}^{2}y+3{y}^{2}z+4{z}^{2}x$ is

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Question No. 13

In the feedback network shown below, if the feedback factor k is increased, then the

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Question No. 14

The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is

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Question No. 15

The Bode plot of a transfer function G(s) is shown in the figure below.

The gain $\left(20log\left|G\left(s\right)\right|\right)$ is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G(s) is

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Question No. 16

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

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Question No. 17

For a periodic signal $v\left(t\right)=30sin100t+10cos300t+6sin\left(500t+\mathrm{\pi }/4\right)$, the fundamental frequency in rad/s is

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Question No. 18

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is

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Question No. 19

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

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Question No. 20

The angle δ in the swing equation of a synchronous generator is the