GATE EC question library

The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta$ holds to within $10\%$ error is

The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is

The impulse response of a system is $h(t) = tu(t).$ For an input $u(t − 1),$ the output is

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 $10\:rad/s$ respectively. The phase is negative for all $\omega.$ Then $G(s)$ is

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?

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