Recent questions tagged gate2013-ec

The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ consider the...

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 v...

The small-signal resistance $(i.e., dV_{B}/dI_{D})$ in $k\Omega$ offered by the $n$-channel $MOSFET\: M$ shown in the figure below, at a bias point of $V_{B} = 2\: V$ is ...

The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$$1$$2$$3$

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of $0.8.$ An ac voltage $V_{WX1} = 100V$ is applied across $WX$ ...

Two magnetically uncoupled inductive coils have $Q$ factors $q_{1}$ and $q_{2}$ at the chosen operating frequency. Their respective resistances are $R_{1}$ and $R_{2}.$ W...

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 m...

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$4/9$...

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 \time...

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

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 powe...

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$ e^{-\pi ...

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 $1.22$ and $0.1$$0.81...

The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is$\frac{0.5s+1}{s+1} \\ $$\frac{3s+6}{s+2} \\ $$\frac{s+2}{s+1} \\ $$\frac{s+1}{s+2}$

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 hasno real rootsno negative real rootodd number of real roots a...

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? All the poles of the system must lie on the left side of the $j\omeg...

Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is$u(t)$$tu(t)$$\frac{t^{2}}{2}u(t)$$e^{-t}u(t)$

In a MOSFET operating in the saturation region, the channel length modulation effect causes an increase in the gate-source capacitancea decrease in the transconductance a...

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 $R/10\: Hz$$R/...

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 $k, \: k 0,$ th...

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$5\: kHz $$12...

In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased? The input impedance increases and output impedan...

For $8085$ microprocessor, the following program is executed.$\begin{array}{ll} & MVI\: A, 05H; \\ & MVI\: B, 05H; \\ PTR: & ADD \:B; \\ & DCR \:B; \\ & JNZ\: PTR; \\ & ...

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$100$$300$$500$$1500$

The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is$10^{\circ}$$18^{\circ}$$50^{\circ}$$90^{\circ}$

The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is$\frac{t^{2}}{2}u(t)$$\frac{t(t-1)}{2}u(t-1)$$\frac{(t-1)^{2}}{2}u(t-1)$$\frac{t...

The Bode plot of a transfer function $G(s)$ is shown in the figure below.The gain $(20\log \mid G(s)\mid)$ is $32\:dB$ and $-8\:dB$ at $1\:rad/s$ and $10\:rad/s$ respecti...

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces superior quality oxide with a higher growth rate inf...

In the circuit shown below what is the output voltage $(V_{\text{out}})$ if a silicon transistor $Q$ and an ideal op-amp are used?$-15\: V$$-0.7\: V$$+0.7\: V$$+15\: V$