Electronics & Communication Gate Yearwise
Electronics and Communication Gate 2022 Questions with Answer
Ques 53 GATE 2022
The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler has taken 5 wickets each. The median number of wickets taken by the bowler in a match is ________ (rounded off to one decimal place).
Ques 54 GATE 2022
A simple closed path C in the complex plane is shown in the figure. If
∮C (2z)/(z2 − 1) dz = −iπA,
where i = √−1, then the value of A is ______ (rounded off to two decimal places).
Ques 55 GATE 2022
The function f(x) = 8 loge x − x2 + 3 attains its minimum over the interval [1, e] at x = _______.
(Here loge x is the natural logarithm of x.)
Ques 56 GATE 2022
Let α, β be two non-zero real numbers and v1, v2 be two non-zero real vectors of size 3 × 1. Suppose that v1 and v2 satisfy v1T v2 = 0, v1T v1 = 1, and v2T v2 = 1. Let A be the 3 × 3 matrix given by:
A = αv1v1T + βv2v2T
The eigenvalues of A are __________.
Ques 57 GATE 2022
Consider the following series:
∑n=1∞ ndcn
For which of the following combinations of c, d values does this series converge?
Ques 58 GATE 2022
The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
Ques 59 GATE 2022
An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360o view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.
Ques 60 GATE 2022
Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following operations:
X: rotation of the square by 180 degree with respect to the S-Q axis.
Y: rotation of the square by 180 degree with respect to the P-R axis.
Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied in the left to right order).
(1) XYZZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?
Ques 61 GATE 2022
The outputs of four systems (S1, S2, S3, and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure.
Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?
Ques 62 GATE 2022
For a vector x̄ = [x[0], x[1], …, x[7]], the 8-point discrete Fourier transform (DFT) is denoted by X̄ = DFT(x̄) = [X[0], X[1], …, X[7]], where
X[k] = ∑n=07 x[n] exp(−j(2π/8)nk).
Here, j = √−1. If x̄ = [1, 0, 0, 0, 2, 0, 0, 0] and ȳ = DFT(DFT(x̄)), then the value of y[0] is _________ (rounded off to one decimal place).
Ques 63 GATE 2022
The Fourier transform X(jω) of the signal
x(t) = t/(1 + t2)2
is _______
Ques 64 GATE 2022
The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.
Statement I: The system is necessarily a pure delay system for inputs which are bandlimited to −α ≤ f ≤ α.
Statement II: For any wide-sense stationary input process with power spectral density SX(f), the output power spectral density SY(f) obeys SY(f) = SX(f) for −α ≤ f ≤ α.
Which one of the following combinations is true?
Ques 65 GATE 2022
Let x1(t) = e−tu(t) and x2(t) = u(t) − u(t − 2), where u(⋅) denotes the unit step function.
If y(t) denotes the convolution of x1(t) and x2(t), then limt→∞ y(t) = _________ (rounded off to one decimal place).
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