GATE EC question library

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor $k, \: k> 0,$ the elements of the corresponding star equivalent will be scaled by a factor of

For $8085$ microprocessor, the following program is executed. $\begin{array}{ll} & MVI\: A, 05H; \\ & MVI\: B, 05H; \\ PTR: & ADD \:B; \\ & DCR \:B; \\ & JNZ\: PTR; \\ & ADI\: 03H; \\ & HLT; \end{array}$ At the end of program, accumulator contains

The bit rate of a digital communication system is $R$ kbits/s. The modulation used is $32$-QAM. The minimum bandwidth required for ISI free transmission is

For a periodic signal $v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),$ the fundamental frequency in $rad/s$ is

In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased?

A band-limited signal with a maximum frequency of $5\: kHz$ is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is

In a MOSFET operating in the saturation region, the channel length modulation effect causes

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

The minimum eigenvalue of the following matrix is $$\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$$

A polynomial $f(x) = a_{4}x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x - a_{0}$ with all coefficients positive has

Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is

The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is

A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be

The return loss of a device is found to be $20\:dB.$ The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively

Let $g(t) = e^{-\pi t^{2}},$ and $h(t)$ is a filter matched to $g(t).$ If $g(t)$ is applied as input to $h(t),$ then the Fourier transformation of the output is

Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is

Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ identity matrix. Using the above property, the determinant of the matrix given below is …

In the circuit shown below, if the source voltage $V_S = 100\angle 53.13^{\circ}\: V$ then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_{L}$ is

The open-loop transfer function of a dc motor is given as $\dfrac{\omega(s)}{V_{a}(s)} = \dfrac{10}{1+10s}.$ When connected in feedback as shown below, the approximate value of $K_{a}$ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

In the circuit shown below, the knee current of the ideal Zener diode is $10\: mA.$ To maintain $5\: V$ across $R_{L},$ the minimum value of $R_{L}$ in $\Omega$ and the minimum power rating of the Zener diode in $mW,$ respectively, are