GATE 2013 Electronics & Communication

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.

The set of values of p for which the roots of the equation 3x 2 + 2x + p(p - 1) = 0 are of opposite sign is

A source v s (t) = V cos 100 $$\pi$$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...

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 . When connected in series, th...

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

A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey i...

The minimum eigenvalue of the following matrix is $$\left[ {\matrix{ 3 & 5 & 2 \cr 5 & {12} & 7 \cr 2 & 7 & 5 \cr } } \right]$$

Find the sum to n terms of the series 10 + 84 + 734 +.........

The divergence of the vector field $$\,\overrightarrow A = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,$$ is

Let $$A$$ be an $$m\,\, \times \,\,n$$ matrix and $$B$$ an $$n\,\, \times \,\,m$$ matrix. It is given that determinant $$\left( {{{\rm I}_m} + AB} \right) = $$determinant $$\left(...

In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

Consider a vector field $$\overrightarrow A \left( {\overrightarrow r } \right).$$ The closed loop line integral $$\oint {\overrightarrow A \bullet \overrightarrow {dl} } $$ can be...

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

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

Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution functions of $$U$$ and $$2V$$ be $$F(x)$$ and $$G(x)$$ respective...

Let $$U$$ and $$V$$ be two independent zero mean Gaussian random variables of variances $${1 \over 4}$$ and $${1 \over 9}$$ respectively. The probability $$\,P\left( {3V \ge 2U} \r...

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one o...

What is the chance that a leap year, selected at random, will contain 53 Sundays?

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature on Thursday was 15% higher than th...

In a forward biased P-N junction diode, the sequence of events that best describes the mechanism of current flow is

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces

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

Two system with impulse responses h 1 (t) and h 2 (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

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

A system is described by the differential equation $$${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right) = x\left( t \right)$$$ Let x(t) be a rectangular pulse giv...

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

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 transform of the output is

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

For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin $${\rm{(500t + }}\,\pi /4)$$, the fundamental frequency in rad/s is

The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is