GATE EC question library

The PDF of a Gaussian random variable $X$ is given by $\operatorname{Px}(x)=\frac{1}{3 \sqrt{2 \pi}} e^{\frac{-(x-4)^{2}}{18}}$ The probability of the event $\{X=4\}$ is

A bandlimited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through

Let $\delta(t)$ denote the delta function. The value of the integral $\int_{-\infty}^{\infty} \delta(t) \cos \left(\frac{3 t}{2}\right) d t$ is

The Nyquist plot for the open-loop transfer function $G(s)$ of a unity negative feedback system is shown in the figure, if $G(s)$ has no pole in the right-half of $s$-plane, the number of roots of the system characteristic equation in the right-half of $s$-plane is

The root-locus diagram for a closed-loop feedback system is shown in the figure is. The system is overdamped.

If the characteristic equation of a closed-loop system is $s^{2}+2 s+2=0$, then the system is

An $8085$ microprocessor based system uses a $4 \mathrm{K} \times 8 \text{bit RAM}$ whose starting address is $\text{AA00 H}$. The address of the last byte in this $\text{RAM}$ is

For the ring oscillator shown in the figure, the propagation delay of each inverter is $100$ pico sec. What is the fundamental frequency of the oscillator output?

Consider the following two statements : $\text{Statement 1: A}$ stable multivibrator can be used for generating square wave. $\text{Statement 1: B}$ stable multivibrator can be used for storing binary information.

The $2$'s complement representation of $-17$ is

The ideal $\text{OP-AMP}$ has the following characteristics.

The effective channel length of a MOSFET in saturation decreases with increase in

MOSFET can be used as a

The current gain of a BJT is

The region of convergence of the $z$-transform of a unit step function is

The admittance parameter $\mathrm{Y}_{12}$ in the $2$-port network in the figure,

The transfer function of a system is given by $H(s)=\frac{1}{s^{2}(s-2)}$. The impulse response of the system is

If each branch of a Delta circuit has impedance $\sqrt{3} Z$, then each branch of the equivalent Wye circuit has impedance.

This question consists of TWENTY FIVE sub-questions $(1.1 - 1.25)$ of ONE mark each. For each of these sub-questions, four possible answers ( $\text{A, B, C}$ and $\text{D}$ ) are given, out of which only one is correct. Answer each sub-question by darkening the appropriate bubble on the OBJECTIVE RESPONSE SHEET (ORS) using a soft HB pencil. Do not use …

In a uniform linear array, four isotropic radiating elements are spaced $\frac{\lambda}{4}$ apart. The progressive phase shift between the elements required for forming the main beam at $60^{\circ}$ off the end-fire is