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General Aptitude

10 Questions
GATE→2022→General Aptitude→Verbal Ability
Q1
MCQ[1 Mark]
Inhaling the smoke from a burning _____ could _____ you quickly.
GATE→2022→General Aptitude→Quantitative Aptitude
Q2
MCQ[1 Mark]
A sphere of radius r cm is packed in a box of cubical shape. What should be the minimum volume (in cm3\text{cm}^{3}) of the box that can enclose the sphere?
GATE→2022→General Aptitude→Quantitative Aptitude
Q3
MCQ[1 Mark]
Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute... what is the capacity of the storage tank (in litres)?
GATE→2022→General Aptitude→Quantitative Aptitude
Q4
MCQ[1 Mark]
Six persons P, Q, R, S, T and U are sitting around a circular table facing the center... Based on the above statements, Q is a neighbor of
GATE→2022→General Aptitude→Quantitative Aptitude
Q5
MCQ[1 Mark]
A building has several rooms and doors as shown in the top view of the building given below... What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?
Figure for Question 5
GATE→2022→General Aptitude→Verbal Ability
Q6
MCQ[2 Marks]
Rice, a versatile and inexpensive source of carbohydrate... Which one of the following is the CORRECT logical inference based on the information given in the above passage?
GATE→2022→General Aptitude→Quantitative Aptitude
Q7
MCQ[2 Marks]
A game consists of spinning an arrow around a stationary disk... What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
Figure for Question 7
GATE→2022→General Aptitude→Quantitative Aptitude
Q8
MCQ[2 Marks]
Consider the following inequalities. 3p−q<43p - q < 4, 3q−p<123q - p < 12. Which one of the following expressions below satisfies the above two inequalities?
GATE→2022→General Aptitude→Verbal Ability
Q9
MCQ[2 Marks]
Given below are three statements and four conclusions drawn based on the statements... Which one of the following options can be logically inferred?
GATE→2022→General Aptitude→Quantitative Aptitude
Q10
MCQ[2 Marks]
Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.
Figure for Question 10

Engineering Mathematics

9 Questions
GATE→2022→Engineering Mathematics→Calculus
Q11
MCQ[1 Mark]
A periodic function f(x)f(x), with period 2, is defined as... The Fourier series of this function contains
GATE→2022→Engineering Mathematics→Linear Algebra
Q12
MSQ[1 Mark]
Given M=[2376474614]M = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix}, which of the following statement(s) is/are correct?
GATE→2022→Engineering Mathematics→Calculus
Q13
NAT[1 Mark]
The global minimum of x3e−∣x∣x^{3}e^{-|x|} for x∈(−∞,∞)x \in (-\infty, \infty) occurs at x=x = (round off to one decimal place).
GATE→2022→Engineering Mathematics→Probability and Statistics
Q14
NAT[1 Mark]
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is (round off to two decimal places).
GATE→2022→Engineering Mathematics→Numerical Methods
Q15
NAT[1 Mark]
The Newton-Raphson method is applied to determine the solution of f(x)=0f(x) = 0 where f(x)=x−cos⁡(x)f(x) = x - \cos(x). If the initial guess of the solution is x0=0x_{0} = 0, the value of the next approximation x1x_{1} is (round off to two decimal places).
GATE→2022→Engineering Mathematics→Differential Equations
Q16
MCQ[2 Marks]
Consider the differential equation dydx+yln⁡(y)=0\frac{dy}{dx} + y \ln(y) = 0. If y(0)=ey(0) = e then y(1)y(1) is
GATE→2022→Engineering Mathematics→Linear Algebra
Q17
MSQ[2 Marks]
The matrix A=[439−2]A = \begin{bmatrix} 4 & 3 \\ 9 & -2 \end{bmatrix} has eigenvalues -5 and 7. The eigenvector(s) is/are
GATE→2022→Engineering Mathematics→Analysis of Complex Variables
Q18
MSQ[2 Marks]
For the complex number z=a+jba−jbz = \frac{a+jb}{a-jb}, where a>0a > 0 and b>0b > 0. Which of the following statement(s) is/are true?
GATE→2022→Engineering Mathematics→Analysis of Complex Variables
Q19
NAT[2 Marks]
Consider the function f(z)=1(z+1)(z+2)(z+3)f(z) = \frac{1}{(z+1)(z+2)(z+3)}. The residue of f(z)f(z) at z=−1z = -1, is

Electricity and Magnetism

2 Questions
GATE→2022→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q20
NAT[2 Marks]
A conducting semi-circular loop of radius R=0.1R = 0.1 m... the peak-to-peak current (in milliamperes) in the loop is (round off to one decimal place).
Figure for Question 20
GATE→2022→Electricity and Magnetism→Electric and Magnetic Fields & Laws
Q21
NAT[2 Marks]
A capacitor is constructed using two concentric spheres and air as the dielectric medium... The capacitance (in picofarads) is (round off to 2 decimal places).

Electrical Circuits and Machines

5 Questions
GATE→2022→Electrical Circuits and Machines→Electrical Machines
Q22
NAT[1 Mark]
A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is (round off to one decimal place).
GATE→2022→Electrical Circuits and Machines→Electrical Circuits
Q23
NAT[1 Mark]
In the bandpass filter circuit shown, R0=50R_{0} = 50 \Omega, L0=1L_{0} = 1 mH, C0=10C_{0} = 10 nF. The Q factor of the filter is (round off to two decimal places).
Figure for Question 23
GATE→2022→Electrical Circuits and Machines→Electrical Circuits
Q24
NAT[2 Marks]
In the circuit shown, the load is driven by a sinusoidal ac voltage source... the power factor is (round off to one decimal place).
Figure for Question 24
GATE→2022→Electrical Circuits and Machines→Electrical Circuits
Q25
NAT[2 Marks]
Given Circuit A with currents I1I_{1} and I2I_{2} as shown, the current I3I_{3} in Circuit B (in amperes), is (round off to one decimal place).
Figure for Question 25
GATE→2022→Electrical Circuits and Machines→Electrical Circuits
Q26
NAT[2 Marks]
In the circuit shown, the capacitance C0=10C_{0} = 10 \mu\text{F} and inductance L0=1L_{0} = 1 mH and the diode is ideal... the voltage Vc(t)V_{c}(t) (in volts) across the capacitor at t=0.5t = 0.5 s is (round off to one decimal place).
Figure for Question 26

Signals and Systems

5 Questions
GATE→2022→Signals and Systems→Signals and Systems
Q27
MCQ[1 Mark]
The input x(t)x(t) to a system is related to its output y(t)y(t) as dy(t)dt+y(t)=3x(t−3)u(t−3)\frac{dy(t)}{dt} + y(t) = 3x(t-3)u(t-3)... The transfer function of this system is
GATE→2022→Signals and Systems→Signals and Systems
Q28
MCQ[1 Mark]
The output of a system y(t)y(t) is related to its input x(t)x(t) according to the relation y(t)=x(t)sin⁡(2πt)y(t) = x(t)\sin(2\pi t). This system is
GATE→2022→Signals and Systems→Signals and Systems
Q29
MCQ[1 Mark]
A signal x(t)x(t) is band-limited between 100 Hz and 200 Hz. A signal y(t)y(t) is related to x(t)x(t) as follows: y(t)=x(2t−5)y(t) = x(2t-5). The statement that is always true is
GATE→2022→Signals and Systems→Signals and Systems
Q30
MCQ[2 Marks]
Consider the transfer function Hc(s)=1(s+1)(s+3)H_{c}(s) = \frac{1}{(s+1)(s+3)}. Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function Hd(z)H_{d}(z). Then Hd(z)H_{d}(z) is
GATE→2022→Signals and Systems→Signals and Systems
Q31
MCQ[2 Marks]
The signal x(t)=(t−1)2u(t−1)x(t) = (t-1)^{2}u(t-1), where u(t)u(t) is the unit-step function, has the Laplace transform X(s)X(s). The value of X(1)X(1) is

Control Systems

6 Questions
GATE→2022→Control Systems→Control Systems and Actuators
Q32
MCQ[1 Mark]
A unity-gain negative-feedback control system has a loop-gain L(s)L(s) given by L(s)=6s(s−5)L(s) = \frac{6}{s(s-5)}. The closed-loop system is
GATE→2022→Control Systems→Control Systems and Actuators
Q33
NAT[1 Mark]
The transfer function of a system is... In the state-space representation of the system, the minimum number of state variables (in integer) necessary is
GATE→2022→Control Systems→Control Systems and Actuators
Q34
MCQ[2 Marks]
The signal flow graph of a system is shown. The expression for Y(s)/X(s)Y(s)/X(s) is
Figure for Question 34
GATE→2022→Control Systems→Control Systems and Actuators
Q35
MCQ[2 Marks]
A proportional-integral-derivative (PID) controller is employed to stably control a plant... the steady-state error in tracking a ramp reference signal
GATE→2022→Control Systems→Control Systems and Actuators
Q36
MCQ[2 Marks]
The Nyquist plot of a stable open-loop system G(jω)G(j\omega) is plotted... The phase margin (PM) and the gain margin (GM) of the system are
Figure for Question 36
GATE→2022→Control Systems→Control Systems and Actuators
Q37
NAT[2 Marks]
In a unity-gain feedback control system, the plant... The slope (in dB/decade) of the asymptotic Bode magnitude plot of the loop gain at ω=3\omega = 3 rad/s is (in integer).

Analog Electronics

9 Questions
GATE→2022→Analog Electronics→Analog Electronics
Q38
NAT[1 Mark]
A Zener diode is used as a 4 V voltage regulator in the circuit shown... the maximum current (in milliamperes) permitted to flow through the load RLR_{L} is (round off to one decimal place).
Figure for Question 38
GATE→2022→Analog Electronics→Analog Electronics
Q39
NAT[1 Mark]
An OPAMP has a gain of 10410^{4}, an input impedance of 10 M\Omega and an output impedance of 100 \Omega... The closed-loop output impedance of the OPAMP (in milliohms) in the circuit is (round off to one decimal place).
GATE→2022→Analog Electronics→Analog Electronics
Q40
MCQ[2 Marks]
A signal Vin(t)V_{in}(t) shown is applied from t=0t=0 ms to t=6t=6 ms to the circuit shown... the open circuit voltage Vout(t)V_{out}(t) at t=5t=5 ms is
Figure for Question 40
GATE→2022→Analog Electronics→Analog Electronics
Q41
MCQ[2 Marks]
A resistor ladder digital-to-analog converter (DAC) receives a digital input... the Thevenin voltage, VthV_{th}, and Thevenin resistance, RthR_{th} as seen at the output node are
Figure for Question 41
GATE→2022→Analog Electronics→Analog Electronics
Q42
MCQ[2 Marks]
In the small signal circuit shown, the enhancement mode n-channel MOSFET is biased in saturation... the small signal impedance looking into the node P is given by
Figure for Question 42
GATE→2022→Analog Electronics→Analog Electronics
Q43
MCQ[2 Marks]
In the small signal circuit shown, the enhancement mode n-channel MOSFET... the small signal gain vo/vdv_{o}/v_{d} is given by
Figure for Question 43
GATE→2022→Analog Electronics→Analog Electronics
Q44
NAT[2 Marks]
The circuit shown is driven by a sinusoidal input voltage... The frequency (in kilohertz) at which the voltage gain is 0 dB is (round off to two decimal places).
Figure for Question 44
GATE→2022→Analog Electronics→Analog Electronics
Q45
NAT[2 Marks]
In the circuit shown, R1=100R_{1} = 100 \Omega and R2=1R_{2} = 1 \Omega... the β\beta (current gain) of the BJT is (round off to two decimal places).
Figure for Question 45
GATE→2022→Analog Electronics→Analog Electronics
Q46
NAT[2 Marks]
In the circuit shown, the switch is initially closed. It is opened at t=0t = 0 s... The time (in milliseconds) at which the output voltage VoutV_{out} becomes LOW is (round off to three decimal places).
Figure for Question 46

Digital Electronics

5 Questions
GATE→2022→Digital Electronics→Digital Electronics and Embedded Systems
Q47
MCQ[1 Mark]
The logic block shown has an output F given by
Figure for Question 47
GATE→2022→Digital Electronics→Digital Electronics and Embedded Systems
Q48
MSQ[1 Mark]
The output F of the digital circuit shown can be written in the form(s)
Figure for Question 48
GATE→2022→Digital Electronics→Digital Electronics and Embedded Systems
Q49
NAT[1 Mark]
An analog-to-digital converter with resolution 0.01 V converts analog signals between 0 V to +10 V to an unsigned binary output. The minimum number of bits (in integer) in the output is
GATE→2022→Digital Electronics→Digital Electronics and Embedded Systems
Q50
MCQ[2 Marks]
The digital circuit shown
Figure for Question 50
GATE→2022→Digital Electronics→Digital Electronics and Embedded Systems
Q51
MCQ[2 Marks]
A=a1a0A = a_{1}a_{0} and B=b1b0B = b_{1}b_{0} are two 2-bit unsigned binary numbers... then F can be minimized to the form

Measurements

6 Questions
GATE→2022→Measurements→Measurements and Instruments
Q52
MCQ[1 Mark]
The resistance of a pure copper wire of length 10 cm and diameter 1 mm is to be measured. The most suitable method from amongst the choices given below is
GATE→2022→Measurements→Measurements and Instruments
Q53
MSQ[1 Mark]
In which of the following bridge(s) is the balancing condition frequency-independent?
GATE→2022→Measurements→Measurements and Instruments
Q54
NAT[2 Marks]
In the balanced three-phase circuit shown, C0=8.2C_{0} = 8.2 \mu\text{F}... The reading on the wattmeter (in watts) is (round off to two decimal places).
Figure for Question 54
GATE→2022→Measurements→Measurements and Instruments
Q55
NAT[2 Marks]
A 1 kHz sine-wave generator having an internal resistance of 50 \Omega generates an open-circuit voltage of 10 Vp−pV_{p-p}... The capacitance of the capacitor (in microfarads) is (round off to two decimal places).
GATE→2022→Measurements→Measurements and Instruments
Q56
NAT[2 Marks]
The bridge shown is balanced when R1=100R_{1} = 100 \Omega, R2=210R_{2} = 210 \Omega, C2=2.9C_{2} = 2.9 \mu\text{F}, and R4=50R_{4} = 50 \Omega... The value of L3L_{3} (in millihenry) is (round off to two decimal places).
Figure for Question 56
GATE→2022→Measurements→Measurements and Instruments
Q57
NAT[2 Marks]
In the Wheatstone bridge circuit shown... The sensitivity of the bridge (in volt/kiloohm), defined as ∣δVCDδR1∣|\frac{\delta V_{CD}}{\delta R_{1}}|, is (round off to two decimal places).
Figure for Question 57

Sensors and Industrial Instrumentation

4 Questions
GATE→2022→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation
Q58
MCQ[1 Mark]
A pneumatic nozzle-flapper system is conventionally used to convert
GATE→2022→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation
Q59
MCQ[1 Mark]
A Hall sensor is based on the principle of
GATE→2022→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation
Q60
MCQ[1 Mark]
The figure shows a Chromel-Alumel thermocouple... When C1 and C2 are held at temperature TCT_{C}, the voltmeter reads a thermal emf E2E_{2}. Then,
Figure for Question 60
GATE→2022→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation
Q61
NAT[2 Marks]
Monochromatic light of wavelength 532 nm... The absorption coefficient (in cm−1\text{cm}^{-1}) of the material is (round off to two decimal places).

Communication and Optical Instrumentation

4 Questions
GATE→2022→Communication and Optical Instrumentation→Communication and Optical Instrumentation
Q62
MCQ[1 Mark]
A sinusoidal carrier wave with amplitude AcA_{c} and frequency fcf_{c} is amplitude modulated... The message signal that can be retrieved completely using envelope detection is
GATE→2022→Communication and Optical Instrumentation→Communication and Optical Instrumentation
Q63
NAT[1 Mark]
Consider 24 voice signals being transmitted without latency using time-division multiplexing... the bit-duration (in microseconds) is (round off to two decimal places).
GATE→2022→Communication and Optical Instrumentation→Communication and Optical Instrumentation
Q64
NAT[1 Mark]
A photodiode is made of a semiconductor with a bandgap of 1.42 eV... the cut-off wavelength (in nanometers) of the photodiode is (round off to one decimal place).
GATE→2022→Communication and Optical Instrumentation→Communication and Optical Instrumentation
Q65
MCQ[2 Marks]
A car is moving collinearly with a laser beam emitted by a transceiver... the average speed of the car in this interval is