GATE EC question library

An M-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth $100$ kHz. The bit rate is $200$ kbps and the system characteristic is a raised-cosine spectrum with $100 \%$ excess bandwidth. The minimum value of M is __________

Consider a discrete-time channel $Y=X +Z$, where the additive noise $Z$ is signal-dependent. In particular, given the transmitted symbol $X \in \{-a , +a\}$ at any instant, the noise sample $Z$ is chosen independently from a Gaussian distribution with mean $\beta X$ and unit variance. Assume a threshold detector with zero threshold at the receiver. …

The electric field (assumed to be one-dimensional) between two points $A$ and $B$ is shown. Let $\psi _A$ and $\psi _B$ be the electrostatic potentials at $A$ and $B$, respectively. The value of $\psi _B – \psi _A$ in Volts is ____________

Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \times \overrightarrow{F} \cdot \overrightarrow{ds}$ is __________.

If $\overrightarrow{E} = -(2y^3 – 3yz^2)\hat{x} – (6xy^2-3xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is

Choose the grammatically CORRECT sentence:

Statement: You can always give me a ring whenever you need. Which one of the following is the best inference from the above statement?

In the summer of $2012,$ in New Delhi, the mean temperature of Monday to Wednesday was $41^{\circ}C$ and of Tuesday to Thursday was $43^{\circ}C$. If the temperature on Thursday was $15\%$ higher than that of Monday, then the temperature in $^{\circ}C$ on Thursday was

Complete the sentence: Dare _______________ mistakes.

They were requested not to $\textbf{quarrel}$ with others. Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$?

A car travels $8 \: km$ in the first quarter of an hour, $6\: km$ in the second quarter and $16\: km$ in the third quarter. The average speed of the car in $km$ per hour over the entire journey is

Find the sum to $n$ terms of the series $10+84+ 734 +\dots$

Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement?

The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is

What is the chance that a leap year, selected at random, will contain $53$ Saturdays?

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

Consider a vector field $\vec{A}(\vec{r}).$ The closed loop line integral $\displaystyle {} \int \vec{A}\bullet\vec{dl}$ can be expressed as

Two systems with impulse responses $h_{1}(t)$ and $h_{2}(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given by

In a forward biased $pn$ junction diode, the sequence of events that best describes the mechanism of current flow is

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces