# Electronics and Communication Engg - GATE 2016 Paper Solution

#### SET - 1

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

Mount Everest is ____________.

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

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

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?

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 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?

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.

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?

If ${q}^{-a}=\frac{1}{r}$ and ${r}^{-b}=\frac{1}{s}$ and ${s}^{-c}=\frac{1}{q}$, the value of $abc$ is ___________ .

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?

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:

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

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 $x={x}_{0}$.

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

Consider the plot of $f\left(x\right)$ versus $x$ as shown below. Suppose $F\left(x\right)={\int }_{-5}^{x}f\left(y\right)dy.$ Which one of the following is a graph of $F\left(x\right)?$

Which one of the following is an eigen function of the class of all continuous-time, linear, timeinvariant systems ($u\left(t\right)$ denotes the unit-step function)?

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

Consider the sequence $x\left[n\right]={a}^{n}u\left[n\right]+{b}^{n}u\left[n\right]$, where $u\left[n\right]$ denotes the unit-step sequence and $0<\left|a\right|<\left|b\right|<1$. The region of convergence (ROC) of the z-transform of $x\left[n\right]$ is
Consider a two-port network with the transmission matrix: $T=\left(\begin{array}{cc}A& B\\ C& D\end{array}\right)$. If the network is reciprocal, then