GATE EC question library

$2$'s complement representation of a $16$ – bit number (one sign bit and $15$ magnitude bits) is $\text{FFFI}$. Its magnitude in decimal representation is

$\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is

A plane wave is incident normally on a perfect conductor as shown in figure. Here $E_{x}^{r}=\mathrm{H}^{\prime}$, and $\overrightarrow{\mathrm{P}}$ are electric field, magnetic field and Poynting vector respectively, for the incident wave. The reflected wave should be

Consider a transmission line of characteristic impedance of $50 \; \mathrm{ohm}$. Let it be terminated at one end by $+j \; 50 \; \mathrm{ohm}$. The $\text{VSWR}$ produced by it in the transmission line will be

Which of the following demodulator(s) can be used for demodulating the signal $x(t)=5(1+2 \cos 2000 \pi t) \cos 2000 \pi t .$

In a microprocessor, the register which holds the address of the next instruction to be fetched is

A pulse train with a frequency of $1 \; \mathrm{MHz}$ is counted using a modulo $1024$ ripple-counter built with $\text{JK}$ flip flops. For proper operation of the counter, the maximum permissible propagation delay per flip flop stage is $\dots n \mathrm{Sec}$.

In a transistor push-pull amplifier

The bandwidth of an $n$-stage tuned amplifier, with each stage having a band width of $B$, is given by

In a multi-stage $\text{R-C}$ coupled amplifier the coupling capacitor

Negative feedback in amplifiers

$\alpha$ - cut off frequency of a bipolar junction transistor

If $s^{3}+3 s^{2}+4 s+A=0$, then all the roots of this equation are in the left half plane provided that

If $\tau \mathrm{F}(\mathrm{s})=[f(t)]=\frac{\mathrm{K}}{(\mathrm{s}+1)\left(\mathrm{s}^{2}+4\right)}$ then $\lim _{t \rightarrow \infty} f(t)$ is given by

In the figure is $\mathrm{A}^{1} \mathrm{~A}^{2}$ and $\mathrm{A}^{3}$ are ideal ammeters. If $\mathrm{A}^{1}$ reads $5 \mathrm{A}, \mathrm{~A}^{2}$ reads $12 \mathrm{A}$, then $\mathrm{A}^{3}$ should read.

The two electrical sub network $N^{1}$ and $N^{2}$ are connected through three resistors as shown in the figure. The voltage across $5 \; \mathrm{ohm}$ resistor and $1 \; \mathrm{ohm}$ resistor are given to be $10 \mathrm{~V}$ and $5 \mathrm{~V}$, respectively. Then voltage across $15 \; \mathrm{ohm}$ resistor is

A network contains linear resistors and ideal voltage sources. If values of all the resistors are doubled, then the voltage across each resistor is

The built-in potential (Diffusion Potential) in a $p-n$ junction