GATE'22 EE: Daily Practices Quiz 10-Sep-2021 |_00.1
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GATE’22 EE: Daily Practices Quiz 10-Sep-2021

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GATE’22 EE: Daily Practices Quiz 10-Sep-2021

Each question carries 2 marks
Negative marking: 2/3 mark

Total Questions: 05

Total marks: 10
Time: 12 min.

Q1. In a junction diode
(a) the depletion capacitance increases with an increase in the reverse bias
(b) the depletion capacitance decreases with an increase in the reverse bias
(c) the depletion capacitance increases with an increase in the forward bias
(d) the depletion capacitance is much higher than the depletion capacitance when it is forward biased

Q2. A three-phase, 4-pole, self-excited induction generator is feeding power to a load at a frequency f_1. If the load is partially removed, the frequency becomes f_2. If the speed of the generator is maintained at 1500 rpm in both the cases, then
(a) f_1,f_2>50 Hz and f_1>f_2
(b) f_1<50 Hz and f_2>50 Hz
(c) f_1,f_2<50 Hz and f_2>f_1
(d) f_1>50 Hz and f_2 <50 Hz

Q3. The output of an AND gate with three inputs, A, B, and C, is HIGH when ________:
(a) A = 1, B = 1, C = 0
(b) A = 0, B = 0, C = 0
(c) A = 1, B = 1, C = 1
(d) A = 1, B = 0, C = 1

Q4. For static electric and magnetic fields in an in homogenous source-free medium, which of the following represents the correct form of two of Maxwell’s equations?
(a) ∇. 𝐸 = 0; ∇ × 𝐵 = 0
(b) ∇. 𝐸 = 0; ∇. 𝐵 = 0
(c) ∇ × 𝐸 = 0; ∇ × 𝐵 = 0
(d) ∇ × 𝐸 = 0; ∇. 𝐵 = 0

Q5. The unit impulse response of a system is ℎ(𝑡) = e^(-t), 𝑡 ≥ 0 For this system, the steady-state value of the output for unit step input is equal to
(a) −1
(b) 0
(c) 1
(d) ∞

Solutions

S1. Ans.(b)
Sol. The depletion capacitance decreases with increase in the reverse bias.
Depletion width = W
▭((W α √(V_RB ))/(Wα √(Reverse bias voltage)))
Capacitance = C = Aξ/W
C α 1/W
C α 1/√(Reverse bias voltage)

S2. Ans.(c)
Sol. An induction generator always operates at negative slip
i.e., (N_S-N_r)/N_s = S < 0 or N_S<N_r
As the generator speed is maintained at a constant speed of 1500 rpm therefore, the synchronous speed will be less than 1500 rpm in both the cases (i.e., when at full load as well as reduced load).
N_S = 1500 rpm for P= 4 and f= 50 Hz.
Thus, for N_S. < 1500 rpm, f_1,f_2 < 50 Hz
(∵f=(N_S P)/120 or N_s=120f/P)
Also, when load decreases then, frequency increases
Hence, f_2>f_1
Therefore, option (c) is correct,

S3. Ans. (c)
Sol. The output of AND gate is HIGH only when all the inputs of the AND gate is HIGH.

GATE'22 EE: Daily Practices Quiz 10-Sep-2021 |_40.1

S5. Ans.(c)
Sol. The unit impulse response of a system is ℎ(𝑡) = e^(-t), 𝑡 ≥ 0
The steady state value of the output for unit step input
𝐻(𝑠) = 1/(s+1)
𝑋(𝑠) = 1/s
Output 𝑦(𝑠) = 𝑋(𝑠) 𝐻(𝑠) = 1/s(s+1)
𝑦(𝑠) = 1/s –1/(s+1)
𝑦(𝑡) = (1 − e^(-t))
When 𝑡 → ∞ (𝑠𝑡𝑎𝑑𝑦 𝑠𝑡𝑎𝑡𝑒), 𝑜𝑢𝑡𝑝𝑢𝑡 = 1

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