GATE EC question library

If the open-loop transfer function is a ratio of a numerator polynomial of degree ' $m$ ' and a denominator polynomial of degree '$n$', then the integer $(n-m)$ represents the number of

The $3-d \mathrm{B}$ bandwidth of a typical second-order system with the transfer function $\frac{\mathrm{C}(s)}{\mathrm{R}(s)}=\frac{w_{n}^{2}}{s^{2} \mathrm{t}+2 x w_{n} s+w_{n}^{2}}$ is given by

A ramp voltage, $v(t)=100$ volts, is applied to an $R C$ differentiating circuit with $R=5 \; \mathrm{k} \Omega$ and $C=4$ $\mu \mathrm{F}$. The maximum output voltage is

A series $\text{LCR}$ circuit consisting of $R=10 \; \Omega$, $\left|X_{L}\right|=20 \; \Omega$ and $\left|X_{C}\right|=20 \; \Omega$, is connected across an $a . c$. supply of $200 \text{V rms}$ . The $\text{rms}$ voltage across the capacitor is

The Fourice Series of a odd periọdic function, contains only

The Laplace transform of a unit ramp function starting at $t=a$, is

$2$'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