GATE 2020: Toppers Mini Mock Quiz 1 (App update required to attempt this test) for ESE & GATE EC Exams

Question 1

A regulated power supply, shown in figure below has an unregulated input (UR) of 15 Volts and generates a regulated output V_out. Use the component values shown in the figure.

In the figure above, the ground has been shown by the symbol.

The power dissipation across the transistor Q1 shown in the figure is:

Question 2

In the circuit shown below the op-amps are ideal. Then V_out in volts is

Question 3

A small signal source

is applied to a transistor amplifier as shown below. The transistor has

and

. Which expression best approximates v₀(t)?

Question 4

For the BJT circuit shown, assume that the β of the transistor is very large and V_BE = 0.7 V. The mode of operation of the BJT is:

Question 5

The cut off frequency of a second order high pass filter, as shown in figure for R₁ = 1.1 kΩ, R₂ = 2.1 kΩ, C₁ = 0.1 μF, C₂ = 0.05 μF and R_G = 10 kΩ, R_F = 50 kΩ is

Question 6

A signal of duration 10s is sampled at the rate of 8 kHz and then encoded. Calculate the storage capacity (in kbits) needed to

accommodate. This digitized speech signal if required signal-to-(quantization) noise ratio is 40 dB

Question 7

Consider a curve described by f(x) = 2x³ – 3x² – 36x + 10. Minimum of slope for the given curve occurs at what value of x.

Question 8

The feedback system is shown below

The value of k = 5, then identify how many closed loop poles will have real part greater than s= -1

Question 9

A sinusoidal message signal of amplitude Am and frequency f_m is passed through a delta modulator whose step size in 0.628 V and sampling rate is given by 40K sample/ sec then which of the following delta modulator will be slope overloaded.

Question 10

Continuous time Fourier transform of a signal

given below is

, then the value of

at

is given by ____.

Question 11

Let x (t) = a s (t) + s (–t) with s (t) = βe^–4t u (t), where u (t) is unit step function. If the bilateral Laplace transform of x (t) is
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Then the value of β is _________

Question 12

A communication channel having AWGN characteristics is operating in such a way that SNR >> 1. The bandwidth of signal being transmitted is B and capacity C₁. Determine the capacity of channel if a signal with half the bandwidth is transmitted through the same channel with same quality.

Question 13

Which of the following represents the characteristics of a PID controller?

Question 14

If R₁ = R₂ = R₄=R and R₃ = 1.1R in the bridge circuit shown in figure, then the reading in the ideal voltmeter connected between a and b is
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Question 15

The z-parameter matrix

for the two-port network shown in

Question 16

The impedance parameters

of the two–port network in figure as

Question 17

The transfer function of a compensation network is of the form ( 1+αTs)/(1+Ts). If this is phase –lag network,the value of α should be

Question 18

What is the mod number of counter circuit shown below ? Assume initially rest.

Question 19

A low pass network for which |H(0)| = 4 is true, has a white noise of bandwidth 3 MHz applied at input. The applied white noise has a power density of N₀. The obtained average output power in a 1 Ohm resistor is 0.1 W, the value of N₀ (in nW/Hz) is_______.

Question 20

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?

Question 21

Consider the following charge density distribution of step junction of a PN diode under thermal equilibrium condition

If W_P = 1mm and W_N = 1.5 mm, then the relation between the doping concentration N_A and N_D is _______

Question 22

The periodic signal f(t) with period 2π and defined for one period as, f(t) = t – t² from t = –π to t = π

Then find the value of

Question 23

What are the roots of denominator of the Laplace transform of the state transition matrix of a system?

Question 24

Find the value of A if

Where * represents convolution,

Question 25

What is the value of

Question 26

For a given wide sense stationary process PSD is

. If it is derived from a LTI system by zero mean white noise with PSD=1 then system which can perform desired result is?

Question 27

A cab was involved in a hit and run accident at night.
You are given the following data about the cabs in the city and the accident.
i. 85% of cabs in the city are green and the remaining cabs are blue.
ii. A witness identified the cab involved in the accident as blue.
iii. It is known that a witness can correctly identify the cab colour only 80% of the time.
Which of the following options is closest to the probability that the accident was caused by a blue cab?

Question 28

Suppose we are given the following five facts about a particular. LTI system S with impulse response h(n) and z transform H(z)

1) h(n) is real

2) h(n) is right sided

3)

4) H(z) has two zeroes

5) H(z) has one of its poles at a non – real location on the circle defined by |z| = ¾

The system S is

Question 29

A digital measuring instrument uses a sampling rate of 200 samples/second. The samples input x(n) is averaged having transfer function H(z) = 1 + z^-1 + z^-3 + 2z^-5
y[n] = x[n] + x[n-1] + x[n-3] + 2x[n-5]. For a step input, the maximum time taken for output to reach the final value after input transition is

Question 30

Consider a CT signal x(t) whose F.T is X(

)=U(

)-U(

-2), then signal

is______

Question 31

Consider the state-variable model of the system given by

The transfer function of the system is given by

Question 32

If the probability of a bad reaction from a certain injection is 0.001, and then the probability that out of 2000 individuals more than two will get a bad reaction will be

Question 33

Suppose we have a Random Wide sense stationary process (WSS), whose auto-covariance is C_XX(Ƭ)=5δ(Ƭ), and mean is -3. Determine the DC Power of X(t).

Question 34

Let

where z is a complex number not equal to zero. Then z is solution of

Question 35

If a system has a gain margin which is close to unity then the system is