GATE EC question library

For a narrow base PNP BJT , the excess minority carrier concentrations($\Delta n_{E}$ for emitter,$\Delta p_{B}$ for base ,$\Delta n_{c}$ for collector) normalized to equilibrium minority carrier concentrations($n_{E0}$ for emitter, , $\Delta p_{B0}$ for base ,$\Delta n_{C0}$ for collector) in the quasi-neutral emitter,base and collector regions …

For the operational amplifier circuit shown, the output saturation voltage are $\pm 15 \:V$. The upper and lower threshold voltages for the circuit are,respectively,

A good transconductance amplifier should have

The Miller effect in the context of a Common Emitter amplifier explains

In the latch circuit shown, the $NAND$ gates have non-zero, but unequal propagation delays. The present input condition is $P=Q=’0’$. If the input condition is changed simultaneously to $P=Q=’1’$, the outputs $X$ and $Y$ are,

The clock frequency of an $8085$ microprocessor is $5$ MHz . If the time required to execute an instruction is $1.4 \: \mu s$, then the number of T-states needed for executing the instruction is

Consider the D-Latch shown in the figure, which is transparent when its clock input $CK$ is high and has zero propagation delay. In the figure , the clock signal $CLK$ has a $50 \%$ duty cycle and $CLK2$ is a one-fifth period delayed version of $CLK1$.The duty cycle at the output of the latch in percentage is _________.

The open loop transfer function $$G(s)=\frac{(s+1)}{s^{p}(s+2)(s+3)}$$ where $p$ is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is $6$ for unit ramp input, the parameter $p$ is__________.

Consider a stable system with transfer function,$$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$$, where $b_1, \dots ,b_p$ and $a_1, \dots ,a_q$ are real valued constants.The slope of the Bode log magnitude curve of $G(s)$ converges to $-60 \text{dB/decade}$ as $ω\to \infty$.A possible pair of values for $p$ and …

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

Let $\left ( X_{1},X_{2} \right )$ be independent random variables. $\left ( X_{1} \right )$ has mean $0$ and variance $1$, while $\left ( X_{2} \right )$ has mean $1$ and variance $4$. The mutual information $I\left (X_{1},X_{2} \right )$ between $X1$ and $X2$ in bits is_______.

Which one of the following statements about differential pulse code modulation (DPCM) is true?

In a digital communication system, the overall pulse shape $p(t)$ at the receiver before the sampler has the Fourier transform $P(f)$. If the symbols are transmitted at the rate of $2000$ symbols per second, for which of the following cases is the inter symbol interference zero?

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(l)= e^{-\gamma l +j\omega t }$ Volts, where $l$ is the distance along the length of the cable in meters, $\gamma=(0.1+j40)m^{-1}$ is the complex propagation constant, and $\omega=2 \pi \times 10^{9}$ rad/s is the angular frequency. The …

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged , the maximum capacity of the wireless link

Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$.

A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal places) is _________

Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,-1)$.The value of $I$ is ____________.

Which one of the following is the general solution of the first order differential equation $$\frac{dy}{dx}=(x+y-1)^{2},$$ where $x,y$ are real?

Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.