The current i_b through the base of a silicon npn transistor is 1+0.1 cos(10000$\pi t$) mA. At 300 K, the r_$\pi$ in the small signal model of the transistor is

•  (A) 250 $\Omega$
•  (B) 27.5 $\Omega$
•  (C) 25 $\Omega$
•  (D) 22.5 $\Omega$

The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X²(t)] and |E[X(t)]| , respectively, are

•  (A) 6000/$\mathrm{\pi }$, 0
•  (B) 6400/$\mathrm{\pi }$, 0
•  (C) 6400/$\mathrm{\pi }$, 20/($\pi \sqrt{2}$)
•  (D) 6000/$\mathrm{\pi }$, 20/($\pi \sqrt{2}$)

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

•  (A) 1750
•  (B) 2625
•  (C) 4000
•  (D) 5250

A plane wave propagating in air with $\overrightarrow{E}=\left(8{\hat{a}}_x+6{\hat{a}}_y+5{\hat{a}}_z\right)e^{j\left(wt+3x-4y\right) }\mathrm{V}/\mathrm{m}$ is incident on a perfectly conducting slab positioned at $x\le 0$.The $\overrightarrow{E}$ field of the reflected wave is

•  (A) $\left(-8{\hat{a}}_x-6{\hat{a}}_y-5{\hat{a}}_z\right)e^{j\left(wt+3x+4y\right)} \mathrm{V}/\mathrm{m}$
•  (B) $\left(-8{\hat{a}}_x+6{\hat{a}}_y-5{\hat{a}}_z\right)e^{j\left(wt+3x+4y\right)} \mathrm{V}/\mathrm{m}$
•  (C) $\left(-8{\hat{a}}_x-6{\hat{a}}_y-5{\hat{a}}_z\right)e^{j\left(wt-3x-4y\right)} \mathrm{V}/\mathrm{m}$
•  (D) $\left(-8{\hat{a}}_x+6{\hat{a}}_y-5{\hat{a}}_z\right)e^{j\left(wt-3x-4y\right)} \mathrm{V}/\mathrm{m}$

The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10\left({\hat{a}}_y+j{\hat{a}}_z\right)e^{-j25x}$.The frequency and polarization of the wave, respectively, are

•  (A) 1.2 GHz and left circular
•  (B) 4 Hz and left circular
•  (C) 1.2 GHz and right circular
•  (D) 4 Hz and right circular

Consider the given circuit.

In this circuit, the race around

•  (A) does not occur
•  (B) occurs when CLK = 0
•  (C) occurs when CLK = 1 and A = B = 1
•  (D) occurs when CLK = 1 and A = B = 0

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

•  (A) 4
•  (B) 6
•  (C) 8
•  (D) 10

The i-v characteristics of the diode in the circuit given below are

$i=\left\{\begin{array}{ll}\frac{v-0.7}{500}A,& v\ge 0.7v\\ 0 A,& v<0.7v\end{array}\right.$

The current in the circuit is

•  (A) 10 mA
•  (B) 9.3 mA
•  (C) 6.67 mA
•  (D) 6.2 mA

In the following figure, C₁ and C₂ are ideal capacitors. C₁ has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

•  (A) zero
•  (B) a step function
•  (C) an exponentially decaying function
•  (D) an impulse function

The average power delivered to an impedance (4-j3)$\Omega$ by a current $5\cos \left(100\pi t+100\right)A$ is

•  (A) 44.2 W
•  (B) 50 W
•  (C) 62.5 W
•  (D) 125 W

The unilateral Laplace transform of f (t) is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of t f (t) is

•  (A) $-\frac{s}{{\left(s^2+s+1\right)}^2}$
•  (B) $-\frac{2s+1}{{\left(s^2+s+1\right)}^2}$
•  (C) $\frac{s}{{\left(s^2+s+1\right)}^2}$
•  (D) $\frac{2s+1}{{\left(s^2+s+1\right)}^2}$

With initial condition $x\left(1\right)=0.5$ , the solution of the differential equation,

$t\frac{dx}{dt}+x=t$ is

•  (A) $x=t-\frac{1}{2}$
•  (B) $x=t^2-\frac{1}{2}$
•  (C) $x=\frac{t^2}{2}$
•  (D) $x=\frac{t}{2}$

The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is

•  (A) $\cos \left(\omega t\right)-1$
•  (B) $\sin \left(\omega t\right)$
•  (C) $1-\cos \left(\omega t\right)$
•  (D) $1-\sin \left(\omega t\right)$

In the circuit shown

•  (A) $Y=\overline{A} \overline{B}+\overline{C}$
•  (B) $Y=\left(A+B\right)C$
•  (C) $Y=\left(\overline{A}+\overline{B}\right)\overline{C}$
•  (D) $Y=AB+C$

A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $\epsilon$ and decreases that of the second by $\epsilon$. After encoding, the entropy of the source

•  (A) increases
•  (B) remains the same
•  (C) increases only if N = 2
•  (D) decreases

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given ${\mu }_0=4\pi \times {10}^{-7}H/m, {\epsilon }_0=\frac{{10}^{-9}}{36\pi }F/m$, the characteristic impedance of the cable is

•  (A) 330$\Omega$
•  (B) 100$\Omega$
•  (C) 143.3$\Omega$
•  (D) 43.4$\Omega$

The radiation pattern of an antenna in spherical co-ordinates is given by

$F\left(\theta \right)={\cos }^4\theta ;0\le \theta \le \mathrm{\pi }/2$

The directivity of the antenna is

•  (A) 10 dB
•  (B) 12.6 dB
•  (C) 11.5 dB
•  (D) 18 dB

If $x\left[n\right]={\left(1/3\right)}^{\left|n\right|}-{\left(1/2\right)}^{n}u\left[n\right]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be

•  (A) $\frac{1}{3}<\left|z\right|<3$
•  (B) $\frac{1}{3}<\left|z\right|<\frac{1}{2}$
•  (C) $\frac{1}{2}<\left|z\right|<3$
•  (D) $\frac{1}{3}<\left|z\right|$

In the sum of products function f(X,Y,Z)=$\sum \left(2,3,4,5\right)$,the prime implicants are

•  (A) $\overline{X}Y,X\overline{Y}$
•  (B) $\overline{X}Y,X\overline{Y}\overline{Z},X\overline{Y}Z$
•  (C) $\overline{X}Y\overline{Z},\overline{X}YZ,X\overline{Y}$
•  (D) $\overline{X}Y\overline{Z},\overline{X}YZ,X\overline{Y}\overline{Z},X\overline{Y}Z$

A system with transfer function

G(s)=$\frac{\left(s^2+9\right)\left(s+2\right)}{\left(s+1\right)\left(s+3\right)\left(s+4\right)}$

is excited by $\sin \left(\omega t\right)$. The steady-state output of the system is zero at

•  (A) $\omega$=1 rad/s
•  (B) $\omega$=2 rad/s
•  (C) $\omega$=3 rad/s
•  (D) $\omega$=4 rad/s