GATE 2021: Toppers Mini Mock Quiz 1 (App update required to attempt this test) for ESE & GATE EC Exams

Question 1

In the following question, some statements followed by some conclusions are given. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows the given statements.

Statement:
Parents must understand that their child cannot attain excellence on his own. He needs their support. They must thus be open to help him at various steps rather than merely setting high expectations.

Conclusion:
I. Ideal students are not born ideal or perfect. They are nurtured to become ideal by their educators. The environment at home has a great impact on the way a student performs in school.

II. The life of an ideal student may seem tough from a distance. However, it is actually much more sorted as compared to those who procrastinate and do not give complete attention to their studies.

Question 2

Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.

A man deposited Rs. ‘x’ in bank which gives simple interest at the rate of 8% p.a. Find the value of ‘x’.

Statement I: After 3 years, amount received by him is Rs. (x + 672).

Statement II: Interest earned by him after 3 years is 24% of the amount deposited by him.

Question 3

The Fourier series coefficient for the periodic signal below is

Question 4

In the circuit shown in figure below, what is the value of R_L such that maximum power is transferred to the load?

Question 5

In a silicon p–n junction, the variation of the hole concentration in the space charge region is shown in the figure below, where the hole concentration changes from P_PO to P_no aver the space charge layer width

The hole diffusion constant in the space charge region is 6.5 cm²/sec. Then the hole diffusion current density J_P is _______ kA/cm².
(Note: Depletion width in the p–side, x_p = 1 and in the n–side, x_n = 2 )

Question 6

Considered two signals,

,

also Y(n) = X(n) * h(n).

Then the value of ?

Question 7

An analog signal of bandwidth 20kHz is sampled at a rate of 40kHz, and quantized into 16 levels. The resultant digital signal is transmitted using M-ary PSK with raised cosine pulse(with α = 0.3). A channel with a 110 kHz bandwidth is available to transmit the data. Then find the smallest acceptable value of number of phase angles.

Question 8

A unity-feedback servo-driven instrument has an open loop transfer function given as

. It is given that the peak overshoot of the system on step input is 35.1 %. Find the steady state error to an input (1 + 4t)u(t).

Question 9

Find the Laplace transform of the function f(t) given as

Question 10

An LTI system has the impulse response shown below.

If the system is excited by an input x(t) = δ (t – 1) + δ (t – 3), then output y(t) will be

Question 11

Calculate the time constant, τ (in sec) of the circuit shown below?

Question 12

Find the output voltage of the following circuit assume the ideal op-amp behavior.

______ V.

Question 13

The value of integral

, where C is the square with vertices at ±i, 2 ±i is ………………….

Question 14

An enhancement type NMOS transistor has threshold voltage of 0.8 V, process transconductance parameter

and channel length modulation parameter λ= O, V_G = 2.8 V, drain Voltage (V_D) = 5 V, Source Voltage V_S = 1V and drain current I_D = 0.24 m. Then the ratio (W/L) is

Question 15

The magnetic field intensity in a region is

, the current density in A/m² at a point (1, 2, 3) is

Question 16

The given pie chart shows the breakup of total number of the employees of a company working in different offices (A, B, C, D and E).

Total no. of employees = 2400

What is the number of offices in which the number of employees of the company is between 350 and 650?

Question 17

Find the numbers a, b, c between 2 and 18 such that

I. their sum is 25,

II. the numbers 2, a, b are consecutive terms of an A.P. and

III. The numbers b, c, 18 are consecutive terms of a G.P.

Question 18

Statements:

All lions are ducks.

No duck is a horse.

All horses are fruits.

Conclusions:

I. No lion is a horse.

II. Some fruits are horses.

III. Some ducks are lions.

IV. Some lions are horses.

Question 19

The loop transfer function of the system

. The root locus plot of the system has

Question 20

Consider the NMOS transistor as shown in figure. The MOSFET has parameters

, V_T = 2V and λ = 0. The transistor is used to amplify the small signal V_in as shown in the figure. If the value of signal V_in = 3sin(wt) mV, then the value of output signal V₀(t) is equal to :-

Question 21

The given integral

for some

. Then the value of k is:

Question 22

A binary PAM communication system employs rectangular pulse of duration T_b and amplitudes +A to transmit digital transmission information at a rate R_b = 10⁵ bps. If power-spectral density of AWGN is N_o/2 where N_o = 10^–2 W/Hz, determine the value of A that is required to achieve a probability of error P_e = 10^–6

Assume Q(4.5) ≈ 10^–6

Question 23

The cut off wavelength of wave guide is given as 80 mm. find the length (in km) of waveguide to ensure signal of 5 GHz emerging out of waveguide is delayed by 10μ sec with respect to the signal that is propogating in free space outside the waveguide is _________ km.

Question 24

A memory is mapped to 8085 microprocessor. The memory map is B00F to FCDE H. The number of bytes stored in memory are (____________)₁₀.

Question 25

The normalized radiation intensity of an antenna in spherical coordinates is given by
U = sinθ sinφ, 0≤ θ ≤ π , 0≤ φ ≤ π

The directivity of antenna is given by _______.

Question 26

In a lightly depend p–type semiconductor, the corresponding acceptor dopping concentration to get minimum conducting is ____

10¹⁰ cm^–3.

(Assume intrinsic carries concentration is n_i = 2.5 x 10¹⁰/cm³ & _p = 0.4 _n)

Question 27

The Nyquist plot for a stable open loop system is shown below:

For , how many closed loop poles of a unity feedback system are in the right half of s-plane

Question 28

The switch S in the circuit of figure has been closed for a long time and is opened at t = 0. The current i(t) for t > 0 is

Question 29

The solution curve of the differential equation

passes through the point (1,0). Then among the points given below, the curve also passes through:

Question 30

Consider the channel

P(Y/X) =

P(X₁) =1/8 P(X₂) =1/8 P(X₃) =6/8

Calculate information carried by the channel.

Question 31

The characteristic equation of the system is

C.E = = 0

The number of symmetric poles located in right half of s-plane is

Question 32

All queens and kings are removed from a deck of playing cards. Ace will be considered as 1 and jack will be considered as 0. You took out 4 cards. The probability that all cards will be in order (order is - 1234,0123,2345,6789….) from the same deck is M. What is (M x 10⁵ )?