GATE 2021: Toppers Mini Mock Quiz 2 (App update required to attempt this test) for ESE & GATE EC Exams

Question 1

An FM signal with a deviation δ is passed through a mixer and has its frequency reduced fivefold. The deviation in the output of the mixer is

Question 2

The transfer function of a PID controller is given by G(s) = 10[1+

+2s] as ω tends to zero

Question 3

The matrix

has det A = 100 and trace A=14
The value of

is?

Question 4

In the given below circuit, if cut in voltage of each diode is 0.7V, then plot transfer characteristics V_D1 vs V_s.

Question 5

An analog signal with a bandwidth of 4.2 MHz is to be converted into binary PCM and transmitted over a channel. The peak signal quantizing noise ratio must be at least 55 dB.

If there is no bit error and no inter symbol interference, what will be the number of quantizing steps needed?

Question 6

An analog signal with a bandwidth of 4.2 MHz is to be converted into binary PCM and transmitted over a channel. The peak signal quantizing noise ratio must be at least 55 dB.

What will be the channel bandwidth required if rectangular pulse shapes are used?

Question 7

For the polynomial P(s) = s⁵ + s⁴ + 2s³ + 2s² + 3s + 15, the number of roots which lie in the right half of the s-plane is

Question 8

A silicon n⁺ P junction solar cell has a surface area of 1 cm² and acceptor concentration N_a = 10¹⁵ cm^–3 in the base region. Assume diffusion coefficient of electrons D_n = 35 cm² sec^–1, carrier lifetime of electrons, t_n = 2.57 μsec, and electron–hole pair generation rate (G_L= 2.7 × 10¹⁹ cm^–3 sec^–1). Then the open circuit voltage (V_OC) of the solar cell is ________ V.

(Assume V_T = 26 mV, n_i = 1.5 × 10¹⁰ cm^–3 neglect the contribution of n⁺ region and depletion region).

Question 9

A bipolar transistor has I_CBO = 0.5 mA, common base current gain

= 0.98 and emitter current I_E = 2mA . Then the trans conductance of the transistor is _______ m

.

(Assume V_T = 26 mV and ղ= 1)

Question 10

A two port network is characterized by the following equations:
3V₁ - I₁ + 4I₂ = 0
4I₁ + 2I₂ - 6V₁ = 5V₂The y - parameter y₂₁ will be ___________

.

Question 11

Two AC sources feed a common variable resistive load as shown in figure below

The maximum power that can be transferred to a variable load R_L is _______ W.

Question 12

If the number of bits in a PCM system is increased from n to n+ 1, the signal-to-quantization noise ratio will increase by a factor.

Question 13

Find the average conversion time(in μs) required for the counter – type

ADC (5 – bit) and frequency of clock = 5 MHz

Question 14

Determine the frequency of given circuit (in Hz)

Question 15

Consider the causal discrete time system shown below, minimum magnitude of K for which system become unstable is

Question 16

If the diode in the circuit shown below is ideal, the current I_D will be

Question 17

A narrow band FM signal approximately defined by

If the maximum and minimum value of its envelope is given by 9.5 and 4.2 respectively then the value of

is __________.

Question 18

Direction: A communication channel of bandwidth 100 kHz is to be used for transmission of an analog source m(t), where | m(t)| < 1. The bandwidth of message signal is W = 4 kHz and power content of the message signal is 0.1 W.

The ratio of the output SNR of an FM system that utilizes the whole bandwidth, to the output SNR of an conventional AM system with a modulation index of 0.85 is

Question 19

Direction: A communication channel of bandwidth 100 kHz is to be used for transmission of an analog source m(t), where | m(t)| < 1. The bandwidth of message signal is W = 4 kHz and power content of the message signal is 0.1 W.

If an FM system and PM system are employed and these system have the same output signal to noise ratio, then the ratio of bandwidth of PM signal to that of the FM signal would be

Question 20

Given a vector field

If the vector field is solenoidal, then the value of k²+5 will be

Question 21

The electric field intensity in free space is given by

The amount of work necessary by the field to move a 2.5 μC charge from (2, 1, 1) to (5, 1, 2) is ______.(Choosing path (2, 1, –1) to (5, 1, –1) to (5, 1, 2)

Question 22

Given,

. Find the value of ‘n’ such that the given fields satisfy the Maxwell equations.

Question 23

Consider the following network.

The value of magnitude of current I is

Question 24

In figure, the value of R is

Question 25

In the circuit below, the value of current I_x is ……………………

Question 26

The contour integral

is evaluated around

in the anti-clockwise direction is:

Question 27

Let μ=10^-5H/m, ϵ = 4 ×10^-9F/m, σ =0 and ρ_V = 0. Find K so that D = 6a_x – 2a_y + 2za_z nC/m² and H = kxa_x – 10ya_y - 25 za_z A/m satisfies Maxwell’s equations.

Question 28

Which of the following equation is the integral form of the given Maxwell equation?

Question 29

A system is described by following equation

A steady state error due to step input is:

Question 30

Consider the system given below.

Find the steady state error due to unit step input is ______?

Question 31

The figure shows part of a signal x(t) and its odd part x₀(t), for

only, that is x(t) and x₀(t) are not given for t < 0

The complete odd part x₀(t) of the signal will be

Question 32

The figure shows part of a signal x(t) and its odd part x₀(t), for

only, that is x(t) and x₀(t) are not given for t < 0

The complete even part x_e(t) of the signal x(t) is.

Question 33

A and B throw alternatively a pair of dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A starts the game, then the probability that B wins the game is

Question 34

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

Question 35

“Even though there is a vast scope for its __________, tourism has remained a/an __________ area.”
The words that best fill the blanks in the above sentence are