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GATE 2021: Toppers Quiz-23 (App update required to attempt this test)

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Question 1

In a full-wave rectifier using two ideal diodes and center tapped transformer, V_dc and V_m are the dc and peak values of the voltage respectively across a resistive load. If PIV is the peak inverse voltage of the diode, then the appropriate relationships for this rectifier are

Question 2

For the circuit shown in the figure,

and

If the input

then the overall voltage gain

of the circuit is ______.

Question 3

The small signal resistance (i.e., dV_B/dI_D) in kΩ offered by the n-channel MOSFET M shown in the figure below, at a bias point of V_B = 2 V is (devise data for M: device transconductance parameter

, threshold voltage

, and neglect body effect and channel length modulation effects)

Question 4

In the circuit shown, assume that the opamp is ideal. If the gain (V₀ / V_in) is –12, the value of R (in kΩ) is _____.
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Question 5

A linear voltage controller is construct using discrete components as shown in figure. Then the output voltage V₀ is (in Volts)

Question 6

From the given direct form structure, find the input-output relation equation;

Question 7

Find the determinant of

Question 8

If x(t)= 5exp[j50ᴨt(2+

)], then determine the instantaneous frequency (in Hz).

Question 9

Let

be an input to the system and

is DTFT of

The output of the system is

and the DTFT

. If

the energy of the signal

Question 10

The closed loop transfer function of a system is

The number of poles having positive real part is

Question 11

A negative resistance R_neg is connected to a passive network N having driving point impedance Z₁(s) as shown below. For Z₂(s) to be positive real,

Question 12

What is the rise time (

) of a 2nd order system if damping ratio (ξ) = 0.40 and natural frequency (

) =2 rad/sec?

Question 13

The switch has been in position 1 for a long time and abruptly changes to position 2 at t= 0.

If time t is in seconds, the capacitor voltage Vc (in volts) for t>0 is given by

Question 14

A non-linear device has transfer characteristic given by I = (4 + v_i + v_i²) mA is supplied with a carrier of 2 V amplitude and a sinusoidal signal of 1 V amplitude in series. The modulation index is

Question 15

If the radius of a sphere is increased by 4cm, its surface area is increased by 464π cm². What is the volume (in m³)

Question 16

Direction: Find out a set of numbers amongst the four sets of numbers given in the alternatives, which is most like the set given in the question.
(14, 20, 3)

Question 17

A feedback system employing output rate damping is shown below

In the absence of derivative feedback, the rise time for the system response is _______ sec.

Question 18

Group I lists a set of four transfer functions. Group II gives a list of Possible step responses y(t). Match the step responses with the corresponding transfer functions
Group–I

Group-II
(1)

(2)

(3)

(4)

Question 19

A super-heterodyne receiver is to operate in the frequency range of 90 MHz – 110.5 MHz. If C = C_max/C_min = 1.45 is the required capacitance ratio of the local oscillator. If the image frequency is 125 MHz, then the receiver is tuned at ________ MHz.

Question 20

If x⁴ - 79x² + 1 = 0, then the value of x³ + x^-3 is:

Question 21

For the source follower circuit shown in the figure below, the transistor parameters are V_T = 1V,

A/V² and neglect channel length modulation. The small signal voltage gain to be

The value of

ratio if

mA is

Question 22

The angle of asymptotes for the system shown below are

Question 23

Two ideal pn junction have exactly the same electrical and physical parameters except for the band gap of the semiconductor materials. The first has a bandgap energy of 0.525 eV and a forward-bias current of 10 mA with V_a =0.255 V. The second pn junction diode is to be designed such that the diode current I=10

at a forward-bias voltage of V_a =0.32 V. The bandgap energy of second diode would be_____ (eV)

Question 24

The open loop transfer function of a unity feedback system is

The number of roots having positive real part is

Question 25

Two pn silicon junction is reverse biased at V_r=5V. The impurity doping concentration in junction A are N_a=10¹⁸ cm^-3 and N_d=10¹⁵ cm^-3 and impurity doping concentration in junction B are Na=10¹⁸ cm^-3 and N_d=10¹⁶ cm^-3.The ratio of the space charge width is _____

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