GATE EC 2021: Full Syllabus Rapid Mock-2 (App update required to attempt this test) for ESE & GATE EC Exams

Question 1

The area bounded by the curves y = x+1, y=cos (x) and the x-axis is

Question 2

And

For the given state space model, linear system, this system will be uncontrollable and unobservable when

Question 3

An article is sold at a certain price. If it is sold at

of this price, there is a loss of

. What is the percentage profit when it is sold at 60% of the original selling price?

Question 4

If a n-channel MOSFET is operating under saturation region with

and

then intrinsic gain of MOSFET will be ________.

Question 5

Considering a transistor that is operating in common emitter configuration. It has a reverse leakage current of 20 µA. Now if this transistor is again connected in CB configuration, it is observed that its leakage current gets reduced to 1.2 µA. Determine α_dc of the transistor.

Question 6

A linear hamming code is used to map 4 bit message to 7 bit code word . the encoder mapping is linear. the message 0001 is mapped to the code word 0000111 and the message 1001 is mapped to the 0010001.then 1000 message is mapped to which codeword?

Question 7

The integral

is evaluated along the semi-circular arc |z| = 1 above real axis. If I = A + Bi, Then the value of B is______

Question 8

For a feedback control system of type-2, the steady state error for a ramp input is:

Question 9

If the diameter of the base of a cone is 42 cm and its curved surface area is 2310cm², then what will be its volume (in cm³)?

Question 10

In a DRAM,

Question 11

If

and the angle between

is

then

is equal to ________.

Question 12

For N type material as doping concentration __________Fermi level moves closer & toward conduction band & as temperature __________ Fermi level moves closer to for bidden bond. Fill in the blanks

Question 13

A train travelling at the speed of x km/h crossed a 200m long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x?

Question 14

The figure given below, shows the transfer characteristic of the which circuit

Question 15

The matrix

satisfies the following polynomials:

A⁵ – 4A⁴ – 7A³ + 11A² – 2A + KI = 0

The value of k is ______

Question 16

The loop transfer function of negative feedback system is given as

. The gain margin of the system for gain k = 6 is ______ dB

Question 17

If the given counter uses synchronous clock then it is a modulus ________ counter.

Question 18

When 12, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 4 and also x is divisible by 7. What is the digit at the thousands place in x?

Question 19

If at 112 MHz frequency the earth to be considered as good dielectric with σ = 5 × 10^–3 S/m, ϵ_r = 8 and µ_r = 1. The attenuation constant will be equal to

Question 20

The transfer function, H(s) =

and input of the system, X(s) =

. Determine the stability of the system.

Question 21

If 1 and 3 are the eigen values of 2 × 2 square matrix A, then A³ can be written as (I₂ denotes identity matrix of second order)

Question 22

A Binary Asymmetric Channel is shown as below denoting the crossover probabilities. If bit 0 is received at the receiver, determine the conditional probability that 1 was transmitted.

(Given p(0) = 0.3 and p(1) = 0.7 at the transmitter)

Question 23

A function F (A, B, C) = A

C +

+ AB

. Find out the Dual form of the function.

Question 24

A system has three stage cascaded amplifier each stage having a power gain of 10dB and noise figure of 6 dB, find overall noise figure.

Question 25

A parallel polarized wave propagates from air to a dielectric at Brewster angle of 55°. Find ε_r2.

Question 26

The CMOS equivalent of the following NMOS gate (figure) is

Question 27

A shopkeeper allows 28% discount on the marked price of an article and still makes a profit of 20%. If he gains Rs 30.80 on the sale of one article, then what will be the cost price of the article?

Question 28

A function f(x) is defined as f(x) = 3x⁴ – 2x³ – 6x² + 6x + 1, 0 ≤ x ≤ 2. The value of f(x) at the point of minimum is__________.

Question 29

In the following circuit, the expression of Y is

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Question 30

It is _______ to read this year’s textbook _____ the last year’s.