GATE EC question library

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) and (ⅱ) (ⅲ) and (ⅳ) (ⅲ) only …

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 …

Let $M^4$= $I$,(where $I$ denotes the identity matrix) and $M \neq I$, $M^2\neq I$ and $M^3\neq I$. 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 $f: \Bbb R \rightarrow \Bbb R$, 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 …

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

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

Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems ($u(t)$ 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 $T_s$. In which one of the following cases is the sampled signal periodic?

Consider the sequence $x[n] = a^nu[n] + b^nu[n]$, where $u[n]$ denotes the unit-step sequence and $0<\mid a \mid < \mid b \mid<1$. The region of convergence (ROC) of the $Z$-transform of $x[n]$ is

Consider a two-port network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then

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

A small percentage of impurity is added to an intrinsic semiconductor at $300 \: K$. Which one of the following statements is true for the energy band diagram shown in the following figure?

Consider the following statements for a metal oxide semiconductor field effect transistor (MOSFET): Which of the above statements are INCORRECT? P and Q P and S Q and R R and S

Consider the constant current source shown in the figure below. Let $\beta$ represent the current gain of the transistor. The load current $I_0$ through $R_L$ is

The following signal $V_i$ of peak voltage $8 \: V$ is applied to the non-inverting terminal of an ideal Op-amp.The transistor has $V_{EE}=0.7 \: V$, $\beta=100; \: V_{LED}=1.5 \: V$, $V_{CC}=10 \: V$ and $– V_{CC}= – 10 \:V$. The number of times the LED glows is ________

Consider the oscillator circuit shown in the figure. The function of the network (shown in dotted lines) consisting of the $100 \: k \Omega$ resistor in series with the two diodes connected back-to-back is to: