GATE EC question library

The maximum value of the function $f(x) = \text{ln } (1+x) – x$ (where $x >-1$) occurs at $x=$_______.

Which $ONE$ of the following is a linear non-homogeneous differential equation, where $x$ and $y$ are the independent and dependent variables respectively?

Match the application to appropriate numerical method. …

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

If $z= xy \text{ ln} (xy)$, then

A series $RC$ circuit is connected to a $DC$ voltage source at time $t= 0$. The relation between the source voltage $V_{s},$ the resistance $R$, the capacitance $C$, and the current $i(t)$ is given below. $V_{s}= R \: i(t)+\frac{1}{c}\int ^{t}_{o}i(u)du$. Which one of the following represents the current $i(t)$?

In the figure shown, the value of the current $I$ (in Amperes) is __________.

In MOSFET fabrication, the channel length is defined during the process of

A thin $P$-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

At $T= 300 \: K$, the hole mobility of a semiconductor $\mu _{p}= 500$ $cm^{2}$$/V-s$ and $\frac{kT}{q}= 26$ $mV$. The hole diffusion constant $D_{p}$ in $cm^{2}$$/s$ is _________

The desirable characteristics of a transconductance amplifier are

In the circuit shown, the $PNP$ transistor has $\mid V_{BE} \mid = 0.7 \:V$ and $\beta = 50$. Assume that $R_{B}= 100 \: k \Omega$. For $V_{0}$ to be $5 \: V$, the value of $R_{C}$ (in $k \Omega$) is ________

The figure shows a half-wave rectifier. The diode $D$ is ideal. The average steady-state current (in Amperes) through the diode is approximately ___________.

An analog voltage in the range $0$ to $8$ V is divided in $16$ equal intervals for conversion to $4$-bit digital output. The maximum quantization error (in V) is __________

The circuit shown in the figure is a

Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit?

Let $x(t)= \cos(10\pi t)+\cos(30\pi t)$ be sampled at $20 Hz$ and reconstructed using an ideal low-pass filter with cut-off frequency of $20 Hz$. The frequency/frequencies present in the reconstructed signal is/are

For an all-pass system $H(z)= \frac{(z^{-1}-b)}{(1-az^{-1})}$, where $\mid H(e^{-j\omega }) \mid= 1,$ for all $\omega$. If $\text{Re}(a)\neq 0, \: \text{Im}(a)\neq 0,$then $b$ equals

A modulated signal is $y(t)= m(t)\cos(40000\pi t)$, where the baseband signal $m(t)$ has frequency components less than $5$ KHz only. The minimum required rate (in KHz) at which $y(t)$ should be sampled to recover $m(t)$ is _______.

Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is