GATE EC question library

If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

Two silicon diodes, with a forward voltage drop of $0.7 \: V$, are used in the circuit shown in the figure. The range of input voltage $V_i$ for which the output voltage $V_o=V_i$, is

The circuit shown represents

For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then

In the circuit shown in the figure, if $C=0$, the expression for $Y$ is

The output $(Y)$ of the circuit shown in the figure is

A Fourier transform pair is given by $$\left ( \frac{2}{3} \right ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{-j6 \pi f}}{1- (\frac{2}{3} ) e^{-j2 \pi f}}$$ where $u[n]$ denotes the unit step sequence. The values of $A$ is ____________

A real-valued signal $x(t)$ limited to the frequency band $\mid f \mid \leq \frac{W}{2}$ is passed through a linear time invariant system whose frequency response is $$H(f) = \begin{cases} e^{-j 4 \pi f}, & \mid f \mid \leq \frac{W}{2} \\ 0, & \mid f \mid > \frac{W}{2} \end{cases}.$$ The output of the system is

The sequence $x[n] = 0.5^n \: u[n]$, where $u[n]$ is the unit step sequence, is convolved with itself to obtain $y[n]$. Then $\Sigma_{n= -\infty}^{+ \infty} y[n]$ is _________.

In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a $4$th order all-pole system?

For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is

If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be

In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of __________.

For an antenna radiating in free space, the electric field at a distance of $1$ km is found to be $12 \: mV/m$. Given that intrinsic impedance of the free space is $120 \pi \: \Omega$, the magnitude of average power density due to this antenna at a distance of $2$ km from the antenna (in $nW/m^2$) is _________.

Match column A with column B. $\begin{array}{ll} \textbf{Column A} & \textbf{Column B} \\ \text{1. Point electromagnetic source} & \text{P. Highly directional} \\ \text{2. Dish antenna} & \text{Q. End fire} \\ \text{3. Yagi-Uda antenna} & \text{R. Isotrophic} \end{array}$

With initial values $y(0) =y’(0)=1$, the solution of the differential equation $$\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$$ at $x=1$ is ________

Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is _________

The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. Which one of the following is the unilateral Laplace transform of $g(t) = t \cdot f(t)$?

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the angle between the hypotenuse and the side is

The steady state output of the circuit shown in the figure is given by $y(t)=A(\omega) \sin (\omega t + \phi ( \omega))$. If the amplitude $\mid A (\omega ) \mid =0.25$, then the frequency $\omega$ is