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

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

The voltage gain A_v of the circuit shown below is

The circuit shown is a

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 $$\varepsilon $$ and decreases that of the second by $$\varepsilon $$. After encoding, the entropy of the source

In a base band communications link, frequencies up to 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

Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X, Y] is less than 1/2 is

The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X^2}\,(t)} \right]$$ and $$E\,\left[ {X\,(t)} \right]$$, respectively, are

A BPSK scheme operating over an AWGN channel with noise power spectral density of N₀2, uses equi-probable signals $$${s_1}\left( t \right) = \sqrt {{{2E} \over T}\,\sin \left( {{\omega _c}t} \right)} $$$
and $$${s_2}\left( t \right) = - \sqrt {{{2E} \over T}\,\sin \left( {{\omega _c}t} \right)} $$$

over the symbol interval, $$(0, T)$$. If the local oscillator in a coherent receiver is ahead in phase by 45⁰ with respect to the received signal, the probability of error in the resulting system is

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X =0) = 9/10, then the probability of error for an optimum receiver will be

The signal m(t) as shown is applied both to a phase modulator (with k_p as the phase constant) and a frequency modulator (with k_f as the frequency constant) having the same carrier frequency.

The ratio k_p/k_f (in rad/Hz) for the same maximum phase deviation is

The feedback system shown below oscillates at 2 rad/s when

A system with transfer function g(s) = $${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}},$$ is excited by $$\sin \left( {\omega t} \right).$$ The steady-state output of the system is zero at

The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$

$${G_C}(s)$$ is a lead compensator if

The state variable description of an LTI system is given by

where y is the output and u is input. The system is controllable for

The state transition diagram for the logic circuit shown is

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

Consider the given circuit. In this circuit, the race around

The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is $${H_Z} = 3\,\,\cos \,\,(2.094\,\, \times \,\,{10^2}x)\,\,\,\cos \,(2.618\,\, \times \,\,{10^2}y)$$
$$\cos \,\,(6.283\,\, \times \,\,{10^{10}}t\, - \beta \,z)$$
The phase velocity $${V_p}$$ of the wave inside the waveguide satisfies

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

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 $${\mu _0} = \,4\,\pi \, \times \,{10^{ - 7}}$$
$$H/m,\,\,{\varepsilon _0} = {{{{10}^{ - 9}}\,} \over {36\,\pi }}\,F/m,$$ the characteristic impedance of the cable is

A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$ is incident on a perfectly conducting slab positioned at $$x \le 0$$. The $$\overrightarrow E $$ field of the reflected wave is

A transmission line with a characteristic impedance of 100 $$\Omega $$ is used to match a 50 $$\Omega $$ section to a 200 $$\Omega $$ section. If the matching is to be done both at 429 MHz and 1 GHz, the tength of the transmission line can be approximately

The radiation pattern of an antenna in spherical co-ordinates is given by $$$F\,(\theta )\, = {\cos ^4}\,\theta \,\,\,;\,\,0\,\, \le \,\,\theta \,\, \le \,\,\pi /2$$$ The directivity of the antenna is

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$

The magnetic field at a distance r from the center of the wire is proportional to

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$.

A hole of radius b (b < a) is now drilled along the length of the wire at a distance d from the center of the wire as shown below.

The magnetic field inside the hole is

In the circuit shown

The source of a silicon (n_i = 10¹⁰ per cm³) n - channel MOS transistor has an aewa of 1 sq $$\mu m$$ and a depth of 1 $$\mu m$$ . If the dopant density in the source is 10¹⁹/cm³, the number of holes in the source region with the above volume is approximately

In the three dimensional view of a silicon n-channel MOS transistor shown below, $$\delta = 20$$ nm. The transistor is of width 1 $$\mu m$$. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of Si and SiO₂, respectively, are 11.7 and 3.9, and $${\varepsilon _0}$$ = 8.9 $$ \times {10^{ - 12}}$$ F/m.

The source-body junction capacitance is approximately

In the three dimensional view of a silicon n-channel MOS transistor shown below, $$\delta = 20$$ nm. The transistor is of width 1 $$\mu m$$. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of Si and SiO₂, respectively, are 11.7 and 3.9, and $${\varepsilon _0}$$ = 8.9 $$ \times {10^{ - 12}}$$ F/m.

The gate-source overlap capacitance is approximately

In the CMOS circuit shown, electron and hole mobilities are equal, and M₁ and M₂ are equally sized. The device M₁ is in the linear region if

Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is

The direction of vector $$A$$ is radially outward
from the origin, with $$\left| A \right| = K\,{r^n}$$
where $${r^2} = {x^2} + {y^2} + {z^2}$$ and $$K$$ is constant.
The value of $$n$$ for which $$\nabla .A = 0\,\,$$ is

Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less than $$1/2$$ is

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is

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

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

Consider the differential equation
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
with $$y\left( t \right)\left| {_{t = 0} = - 2} \right.$$ and $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$

The numerical value of $${{dy} \over {dt}}\left| {_{t = 0}.} \right.$$ is

If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is

Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that
$$\left| {z + 1} \right| = 1,$$ the value of $${1 \over {2\,\pi \,j}}\oint\limits_c {f\left( z \right)dz} $$ is

The impedance looking into nodes 1 and 2 in the given circuit is

In the circuit shown below, current through the inductor is

If V_A - V_B = 6 V then V_C - V_D is

Assuming both the voltage sources are in phase the value of R for which maximum power is transferred from circuit A to circuit B is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:
(i) 1Ω connected at port B draws a current of 3 A
(ii) 2.5Ω connected at port B draws a current of 2 A

For the same network, with 6 V dc connected at port A, 1Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:
(i) 1Ω connected at port B draws a current of 3 A
(ii) 2.5Ω connected at port B draws a current of 2 A

With 10 V dc connected at port A, the current drawn by 7Ω connected at port B is

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.

The average power delivered to an impedance $(4-j 3) \Omega$ by a current $5 \cos (100 \pi t+100) A$ is

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

The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$.

The system is

The Fourier transform of a signal h(t) is $$H(j\omega )$$ =(2 cos $$\omega $$) (sin 2$$\omega $$) / $$\omega $$. The value of h(0) is

Let $$y\left[ n \right]$$ denote the convolution of $$h\left[ n \right]$$ and $$g\left[ n \right]$$, where $$h\left[ n \right]$$ $$ = \,{\left( {1/2} \right)^2}\,\,u\left[ n \right]$$ and $$g\left[ n \right]\,$$ is a causal sequence. If $$y\left[ 0 \right]\,$$ $$ = \,1$$ and $$y\left[ 1 \right]\,$$ $$ = \,1/2,$$ then $$g\left[ 1 \right]$$ equals

Choose the most appropriate alternative from the options given below to complete the following sentence:

If the tired soldier wanted to lie down, he _______ the mattress out on the balcony.

Choose the most appropriate word from the options given below to complete the following sentence:

Given the seriousness of the situation that he had to face, his ________ was impressive.

Which one of the following options is the closest in meaning to the word given below?

Latitude

One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT?

I requested that he should be given the driving test today instead of tomorrow.

If (1.001)¹²⁵⁹ = 3.52 and (1.001)²⁰⁶² = 7.85, then (1.001)³³²¹ =

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

The data given in the following table summarizes the monthly budget of an average household.

The approximate percentage of the monthly budget NOT spent on savings is

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them.

Which one of the following statements best sums up the meaning of the above passage?