GATE EC question library

In the following sentence certain parts are underlined and marked P,Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication.select the part containing an error. Choose D as your answer if there is no error. …

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: All film stars are playback singers. All film directors are film stars Conclusions: All film directors are playback singers some film stars are film director

A tiger is $50$ leaps of its own behind a tree. The tiger takes $5$ leaps per minute to the deer's $4$. If the tiger and the deer cover $8$ meter and $5$ meter per leap respectively, what distance in meters will the tiger have to run before it catches the deer?

if $a^2+b^2+c^2=1$ then $ab+bc+ac$ lies in the interval

Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the chief minister last year, asking him to allocate more funds to support art education in schools. However, no such increase has been announced in this year's Budget. The artists expressed their deep anguish at their request not being approved, but many …

The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is

The value of $x$ for which all the eigen-values of the matrix given below are real is $$\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &-10 \end{bmatrix}$$

Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.

The general solution of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x} = \dfrac{1+\cos 2y}{1-\cos 2x}$ is

The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the four choices given. Notation: $C$ is the set of complex numbers, ܴ$R$ is the set of purely real numbers, and $P$ ܲis the set of purely imaginary numbers.

The voltage $(ܸV_{C})$ across the capacitor (in Volts) in the network shown is ______.

In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.

The $2$-port admittance matrix of the circuit shown is given by

An $n$-type silicon sample is uniformly illuminated with light which generates $10^{20}$ electron-hole pairs per $cm^{3}$ per second. The minority carrier lifetime in the sample is $1\mu s$. In the steady state, the hole concentration in the sample is approximately $10^{x}$, where $x$ is an integer. The value of $x$ is _______.

A piece of silicon is doped uniformly with phosphorous with a doping concentration of $10^{16}/cm^{3}.$ The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is $1.6 \times 10^{-19} \:C.$ The conductivity $\text{(in S } cm^{-1})$ of the silicon sample at …

If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period $T?$

In the circuit shown, $V_{0} = V_{0A}$ for switch $SW$ in position $A$ and $V_{0} = V_{0B}$ for $SW$ in position $B$. Assume that the opamp is ideal. The value of $\dfrac{V_{0B}}{V_{0A}}$ is ___________.

In the bistable circuit shown, the ideal opamp has saturation levels of $\pm\: 5\: V.$ The value of $R_{1} \text{(in}\: k\Omega)$ that gives a hysteresis width of $500\: mV$ is ________.

In the figure shown, the output ܻ$Y = AB + \overline{C}\:\:\overline{D}$ is required to be ܻ The gates $G1$ and $G2$ must be, respectively,

In an $8085$ microprocessor, which one of the following instructions changes the content of the accumulator?