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English SSC CGL Tier I papers. Free 60-minute mocks, 100 questions, 200 marks; +2 correct and −0.5 incorrect. Source: SSC response sheets preserved by SSC Portal. The marked archived keys have not been independently revalidated against final SSC keys; worked explanations are pending review. A/B/C/D correspond to source options 1/2/3/4.

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Civil Engineering (SSC JE)

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Question 1 · Electrical Engineering (SSC JE) · Signals and Systems
A signal has a maximum frequency component of 5 kHz. The minimum sampling frequency (Nyquist rate) is
Choose your answer for question 1
Answer and explanation

Correct answer: B

The Nyquist rate is twice the highest frequency, 2 × 5 = 10 kHz.

Question 2 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of a unit step function is
Choose your answer for question 2
Answer and explanation

Correct answer: B

L{u(t)} = ∫ e^(−st) dt from 0 to ∞ = 1/s.

Question 3 · Electrical Engineering (SSC JE) · Signals and Systems
A system is linear if it satisfies the principle of
Choose your answer for question 3
Answer and explanation

Correct answer: B

The response to a sum of inputs is the sum of responses (additivity), and scaling the input scales the output (homogeneity).

Question 4 · Electrical Engineering (SSC JE) · Signals and Systems
The period of the signal x(t) = sin(100πt) is
Choose your answer for question 4
Answer and explanation

Correct answer: A

ω = 100π rad/s, so T = 2π/ω = 2π/(100π) = 0.02 s.

Question 5 · Electrical Engineering (SSC JE) · Signals and Systems
The Fourier transform of a rectangular pulse is a
Choose your answer for question 5
Answer and explanation

Correct answer: A

A pulse of width T has a spectrum proportional to sin(ωT/2)/(ω/2).

Question 6 · Electrical Engineering (SSC JE) · Signals and Systems
Convolution of two signals in the time domain corresponds to which operation in the frequency domain?
Choose your answer for question 6
Answer and explanation

Correct answer: B

If y(t) = x(t) * h(t), then Y(ω) = X(ω) H(ω). This is why filtering is easier in the frequency domain.

Question 7 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of e^(−at) u(t) is
Choose your answer for question 7
Answer and explanation

Correct answer: B

∫ e^(−at) e^(−st) dt from 0 to ∞ = 1 / (s + a).

Question 8 · Electrical Engineering (SSC JE) · Signals and Systems
The energy of the signal x(t) = e^(−t) u(t) is
Choose your answer for question 8
Answer and explanation

Correct answer: B

E = ∫ e^(−2t) dt from 0 to ∞ = 1/2.

Question 9 · Electrical Engineering (SSC JE) · Signals and Systems
The average power of the signal x(t) = 54 sin(ωt) is
Choose your answer for question 9
Answer and explanation

Correct answer: C

Power = A²/2 = 54²/2 = 1458.

Question 10 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of e^(−47t) u(t) is
Choose your answer for question 10
Answer and explanation

Correct answer: A

The Laplace transform of e^(−47t) u(t) = 1/(s + 47).

Question 11 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of e^(−25t) u(t) is 1/(s + a). For the signal e^(−25t) u(t), the pole is at s =
Choose your answer for question 11
Answer and explanation

Correct answer: C

The transform is 1/(s + 25), whose pole is at s = −25.

Question 12 · Electrical Engineering (SSC JE) · Signals and Systems
The average power of the signal x(t) = 16 sin(ωt) is
Choose your answer for question 12
Answer and explanation

Correct answer: B

Power = A²/2 = 16²/2 = 128.

Question 13 · Electrical Engineering (SSC JE) · Signals and Systems
The sequences x[n] = {2, 4} and h[n] = {1, 1} both start at n = 0. The value of y[1] in their convolution y[n] = x[n] * h[n] is
Choose your answer for question 13
Answer and explanation

Correct answer: B

y[n] = Σ x[k] h[n − k]. The full convolution is {2, 6, 4}, so y[1] = 6.

Question 14 · Electrical Engineering (SSC JE) · Signals and Systems
The sequences x[n] = {4, 4, 4} and h[n] = {2, 1} both start at n = 0. The value of y[0] in their convolution y[n] = x[n] * h[n] is
Choose your answer for question 14
Answer and explanation

Correct answer: D

y[n] = Σ x[k] h[n − k]. The full convolution is {8, 12, 12, 4}, so y[0] = 8.

Question 15 · Electrical Engineering (SSC JE) · Signals and Systems
The sequences x[n] = {3, 2} and h[n] = {4, 3} both start at n = 0. The value of y[2] in their convolution y[n] = x[n] * h[n] is
Choose your answer for question 15
Answer and explanation

Correct answer: C

y[n] = Σ x[k] h[n − k]. The full convolution is {12, 17, 6}, so y[2] = 6.

Question 16 · Electrical Engineering (SSC JE) · Signals and Systems
The sequences x[n] = {1, 4} and h[n] = {4, 2, 4} both start at n = 0. The value of y[0] in their convolution y[n] = x[n] * h[n] is
Choose your answer for question 16
Answer and explanation

Correct answer: A

y[n] = Σ x[k] h[n − k]. The full convolution is {4, 18, 12, 16}, so y[0] = 4.

Question 17 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of e^(−5t) u(t) is
Choose your answer for question 17
Answer and explanation

Correct answer: A

The Laplace transform of e^(−5t) u(t) = 1/(s + 5).

Question 18 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of e^(−39t) u(t) is 1/(s + a). For the signal e^(−39t) u(t), the pole is at s =
Choose your answer for question 18
Answer and explanation

Correct answer: A

The transform is 1/(s + 39), whose pole is at s = −39.

Question 19 · Electrical Engineering (SSC JE) · Signals and Systems
The average power of the signal x(t) = 56 sin(ωt) is
Choose your answer for question 19
Answer and explanation

Correct answer: C

Power = A²/2 = 56²/2 = 1568.

Question 20 · Electrical Engineering (SSC JE) · Signals and Systems
The Laplace transform of e^(−8t) u(t) is
Choose your answer for question 20
Answer and explanation

Correct answer: C

The Laplace transform of e^(−8t) u(t) = 1/(s + 8).

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