Paper Solution, Question Answer | EC | Electronics and Communication Engg

Question No. 1

SET - 1

Which of the following is CORRECT with respect to grammar and usage?

Mount Everest is ____________.

(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world

(A) the highest peak in the world

Subject : Language Skills

Question No. 2

The policeman asked the victim of a theft, “What did you ___________ ?”

(A) loose
(B) lose
(C) loss
(D) louse

(B) lose

Subject : Language Skills

Question No. 3

Despite the new medicine’s ______________ in treating diabetes, it is not ______________widely.

(A) effectiveness --- prescribed
(B) availability --- used
(C) prescription --- available
(D) acceptance --- proscribed

(A) effectiveness --- prescribed

Subject : Language Skills

Question No. 4

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples?

(A) 2029198
(B) 2467482
(C) 2789080
(D) 3577422

Show Answer

(A) 2029198

Subject : Analytical Skills

Question No. 5

Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

(A) 3.00
(B) 4.99
(C) 6.02
(D) 7.01

Show Answer

(C) 6.02

Subject : Analytical Skills

Question No. 6

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

(A) 15
(B) 33
(C) 35
(D) 37

Show Answer

(C) 35

Subject : Analytical Skills

Question No. 7

In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong.

Which of the following inference(s) is/are logically valid and can be inferred from the above passage?

(i) His friends were always asking him to help them.

(ii) He felt that when in need of help, his friends would let him down.

(iii) He was sure that his friends would help him when in need.

(iv) His friends did not help him last week.

(A) (i) and (ii)
(B) (iii) and (iv)
(C) (iii) only
(D) (iv) only

Show Answer

(B) (iii) and (iv)

Subject : Language Skills

Question No. 8

Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.

Which one of the following statements must be TRUE based on the above?

(A) When Shiva plays chess with Leela and Pavithra, he often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better chess player than Pavithra.
(D) Pavithra is the youngest of the three.

Show Answer

(D) Pavithra is the youngest of the three.

Subject : Language Skills

Question No. 9

q^{- a} = \frac{1}{r}

and

r^{- b} = \frac{1}{s}

and

s^{- c} = \frac{1}{q}

, the value of $abc$ is ___________ .

(A) (rqs)^-1
(B) 0
(C) 1
(D) r+q+s

Show Answer

(C) 1

Subject : Analytical Skills

Question No. 10

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

(A) 10:11
(B) 11:10
(C) 20:21
(D) 21:20

Show Answer

(C) 20:21

Subject : Analytical Skills

Question No. 11

L et M⁴ = I, (where I denotes the identity matrix) and M ≠ I, M² ≠ I and M³ ≠ I. Then, for any natural number k, M⁻¹ equals:

(A) M^{4k + 1}
(B) M^{4k + 2}
(C) M^{4k + 3}
(D) M^4k

Show Answer

(C) M^{4k + 3}

Subject : Linear Algebra

Question No. 12

The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is _______

Show Answer

0.9 : 1.1

Subject : Probability and Statistics

Question No. 13

Given the following statements about a function $\style{font-family:'Times New Roman'}{f:\mathbb{R}\rightarrow\mathbb{R}}$, select the right option:

P: If $f(x)$is continuous at

x = x_{0}

, then it is also differentiable at

x = x_{0}

Q: If $f(x)$ is continuous at

x = x_{0}

, then it may not be differentiable at

x = x_{0}

R: If $f(x)$is differentiable at

x = x_{0}

, then it is also continuous at

x = x_{0}

(A) P is true, Q is false, R is false
(B) P is false, Q is true, R is true
(C) P is false, Q is true, R is false
(D) P is true, Q is false, R is true

Show Answer

(B) P is false, Q is true, R is true

Subject : Calculus

Question No. 14

Which one of the following is a property of the solutions to the Laplace equation: $ \nabla^2f=0? $

(A) The solutions have neither maxima nor minima anywhere except at the boundaries.
(B) The solutions are not separable in the coordinates.
(C) The solutions are not continuous.
(D) The solutions are not dependent on the boundary conditions.

Show Answer

(A) The solutions have neither maxima nor minima anywhere except at the boundaries.

Subject : Differential equations

Question No. 15

Consider the plot of $f (x)$ versus $x$ as shown below.

Suppose $F (x) = \int_{- 5}^{x} f (y) d y .$ Which one of the following is a graph of $F\left(x\right)?$

Show Answer

(C)

Subject : Calculus

Question No. 16

Which one of the following is an eigen function of the class of all continuous-time, linear, timeinvariant systems (

u (t)

denotes the unit-step function)?

(A) $e^{j ω_{0} t} u (t)$
(B) $\cos (ω_{0} t)$
(C) $e^{j ω_{0} t}$
(D) $\sin (ω_{0} t)$

Show Answer

(C) $e^{j ω_{0} t}$

Subject : Signals and Systems

Topic : Linear Time-Invariant (LTI) Systems

Question No. 17

A continuous-time function $ x(t) $ is periodic with period T. The function is sampled uniformly with a sampling period T_s. In which one of the following cases is the sampled signal periodic?

(A) $T = \sqrt{2} T_{s}$
(B) $T = 1.2 T_{s}$
(C) Always
(D) Never

Show Answer

(B) $T = 1.2 T_{s}$

Subject : Signals and Systems

Question No. 18

Consider the sequence

x [n] = a^{n} u [n] + b^{n} u [n]

, where

u [n]

denotes the unit-step sequence and

0 < |a| < |b| < 1

. The region of convergence (ROC) of the z-transform of

x [n]

(A) $|z| > |a|$
(B) $|z| > |b|$
(C) $|z| < |a|$
(D) $|a| < |z| < |b|$

Show Answer

(B) $|z| > |b|$

Subject : Signals and Systems

Topic : Z-transform

Question No. 19

Consider a two-port network with the transmission matrix:

T = (\begin{matrix} A & B \\ C & D \end{matrix})

. If the network is reciprocal, then

(A) $T^{- 1} = 1$
(B) $T^{2} = T$
(C) Determinant $(T) = 0$
(D) Determinant $(T) = 1$

Show Answer

(D) Determinant $(T) = 1$

Subject : Networks

Topic : Linear 2-Port Network Parameters

Question No. 20

A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23 Hz. The fundamental frequency (in Hz) of the output is _________

Show Answer

12 : 14

Subject : Signals and Systems

Topic : Sampling theorem

Electronics and Communication Engg - GATE 2016 Paper Solution

SET - 1

(A) the highest peak in the world

(B) lose

(A) effectiveness --- prescribed

(A) 2029198

(C) 6.02

(C) 35

(B) (iii) and (iv)

(D) Pavithra is the youngest of the three.

(C) 1

(C) 20:21

(C) M4k + 3

0.9 : 1.1

(B) P is false, Q is true, R is true

(A) The solutions have neither maxima nor minima anywhere except at the boundaries.

(C)

(C) ejω0t

(B) T=1.2Ts

(B) z>b

(D) Determinant T=1

12 : 14

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(C) M^{4k + 3}

(C) $e^{j ω_{0} t}$

(B) $T = 1.2 T_{s}$

(B) $|z| > |b|$

(D) Determinant $(T) = 1$