GATE EC question library

Find the next term in the sequence: $13M, 17Q, 19S$, ___

If $\text{‘KCLFTSB’}$ stands for ‘best of luck’ and $\text{‘SHSWDG’}$ stands for ‘good wishes’, which of the following indicates ‘ace the exam’?

Industrial consumption of power doubled from $2000$-$2001$ to $2010$-$2011$. Find the annual rate of increase in percent assuming it to be uniform over the years.

A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in $2012$. The expenditure on labour in $2012$ is $Rs$. $4,50,000$. In $2013$, the raw material expenses increased by …

A five digit number is formed using the digits $1,3,5,7$ and $9$ without repeating any of them. What is the sum of all such possible five digit numbers?

The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to

The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.

Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________

If $a$ and $b$ are constants, the most general solution of the differential equation $$\frac{d^2x}{dt^2}+2 \frac{dx}{dt}+x=0$$ is

The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by _________.

The circuit shown in the figure represents a

The magnitude of current (in mA) through the resistor $R_2$ in the figure shown is __________

At $T=300 \:K$, the band gap and the intrinsic carrier concentration of GaAs are $1.42$ eV and $10^6 \: cm^{-3}$, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength $(\lambda_C)$ ranges of incident radiation, is most suitable? (Given that: Plank’s constant is $6.62 \times 10^{-34} \: J-s$, velocity of light …

In the figure, $\text{ln }(\rho _i)$ is plotted as a function of $1/T$, where $\rho_i$ is the intrinsic resistivity of silicon, $T$ is the temperature, and the plot is almost linear. The slope of the line can be used to estimate

The cut-off wavelength (in $\mu m$) of light that can be used for intrinsic excitation of a semiconductor material of bandgap $E_g = 1.1 \: eV$ is ______________

If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

Two silicon diodes, with a forward voltage drop of $0.7 \: V$, are used in the circuit shown in the figure. The range of input voltage $V_i$ for which the output voltage $V_o=V_i$, is

The circuit shown represents

For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then

In the circuit shown in the figure, if $C=0$, the expression for $Y$ is