For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector current are equal. Given that V_T = 25mV, V_BE = 0.7V, and the BJT output r₀ is practically infinite. Under these conditions the midband voltage gain magnitude, a_v = $$\left| {{v_0}/{v_i}} \right|\,\,\,V/V,$$ is _____

In the figure shown, the npn transistor acts as a switch.

For the input v_in(t)as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage saturation V_CE(sat) = 0.2V and base-to-emitter voltage V_BE = 0.7V. The minimum value of the common-base current gain$$\left( \alpha \right)$$ of the transistor for the switching should be _________.

The Miller effect in the context of a Common Emitter amplifier explains

For the operational amplifier circuit shown, the output saturation voltages are $$ \pm \,\,15V$$. The upper and lower threshold voltages for the circuit are, respectively.

The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, A₀ 10⁵ V/V and an open-loop cut-off frequency, f_C = 8 Hz. The voltage gain of the amplifier at 15 kHz, in V/V, is __________.

In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is inter symbol interference zero?

Which one of the following statements about differential pulse code modulation (DPCM) is true?

Let $$X(t)$$ be a wide sense stationary random process with the power spectral density $${S_x}\left( f \right)$$ as shown in figure (a), where $$f$$ is in Hertz $$(Hz)$$. The random process $$X(t)$$ is input to an ideal low pass filter with the frequency response $$$H\left( f \right) = \left\{ {\matrix{ {1,} & {\left| f \right| \le {1 \over 2}Hz} \cr {0,} & {\left| f \right| > {1 \over 2}Hz} \cr } } \right.$$$

As shown in Figure (b). The output of the low pass filter is $$y(t)$$.

Let $$E$$ be the expectation operator and consider the following statements :
$$\left( {\rm I} \right)$$ $$E\left( {X\left( t \right)} \right) = E\left( {Y\left( t \right)} \right)$$
$$\left( {{\rm I}{\rm I}} \right)$$ $$\,\,\,\,\,\,\,\,E\left( {{X^2}\left( t \right)} \right) = E\left( {{Y^2}\left( t \right)} \right)$$
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\,$$ $$\,\,\,\,\,\,E\left( {{Y^2}\left( t \right)} \right) = 2$$

Select the correct option:

In binary frequency shift keying (FSK), the given signal wave forms are
$$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and
$${u_o}(t) = 5\,\cos \,(22000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$

where T is the bit-duration interval and t is in seconds. Both $${u_o}(t)$$ and $${u_1}(t)$$ are zero output the interval $$0 \le \,\,t\, \le \,T$$. With a matched filter (correlator ) based receiver, the smallest positive value of T (in milliseconds) required to have $${u_o}(t)$$ and $${u_1}(t)$$ uncorrelated is

Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_2}$$ has mean 1 and variance 4. The mutual information I $$\left( {{X_1},\,{X_2}} \right)$$ between $${{X_1}}$$ and $${{X_2}}$$ in bits is ________________.

The open loop transfer function $$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\mathrm p\left(\mathrm s\;+\;2\right)\left(\mathrm s\;+\;3\right)}$$$ Where p is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.

Which one of the following options correctly describes the locations of the roots of the equation s⁴ + s² + 1 = 0 on the complex plane?

A linear time invariant (LTI) system with the transfer function $$$G\left(s\right)=\frac{K\left(s^2+2s+2\right)}{s^2-3s+2}$$$ is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < $$\infty$$ intersects the imaginary axis for K = 1.5. The closed loop system is stable for

Consider a stable system with transfer function $$$G\left(s\right)=\frac{s^p+b_1s^{p-1}+....+b_p}{s^q+a_1s^{q-1}+....+a_q}$$$ Where $$b_1,.......,b_p$$ and $$a_1,.......,a_q$$ are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB/decade as $$\omega\rightarrow\infty$$ . A possible pair of values for p and q is

The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ does not encircle the point (-1+j0) for K = 10 but does encircle the point (-1+j0) for K = 100. Then the closed loop system (having unity gain feedback) is

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output latch in percentage is ___________.

In the latch circuit shown, the NAND gates have non-zero, but unequal propagation delays. The present input condition is: P = Q = "0‟. If the input condition is changed simultaneously to P = Q = "1", the outputs X and Y are

A 4-bit shift register circuit configured for right-shift operation is $${D_{in}}\, \to \,A,\,A\, \to B,\,B \to C,\,C \to D,$$ is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is

A finite state machine (FSM) is implemented using the D flip-flops A and B and logic gates, as shown in the figure below. The four possible states of the FSM are Q_A Q_B = 00, 01, 10, and 11.

Assume that X_IN is held at a logic level throughout the operation of the FSM. When the FSM is initialized to the state Q_A Q_B = 100 and clocked, after a few clock cycles, it starts cycling through

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $$V(l) = {e^{ - \gamma l\, + \,j\,\omega \,t}}$$ Volts, where $$l$$ is the distance along the length of the cable in metres, $$\gamma = (0.1\, + \,j40)\,\,{m^{ - 1}}$$ is the complex propagation constant, and $$\omega = \,2\,\pi \,\, \times \,\,{10^9}$$ rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/metre is ___________________.

The expression for an electric field in free space is $$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right){e^{ - j\left( {\omega t - kx + ky} \right)}},$$ where $$x,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} y,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} z\,\,\,\,\,\,\,$$ represent the spatial coordinates, $$t$$ represents time, and $$\omega ,\,\,k$$ are contants. This electric field

A half wavelength dipole is kept in the x-y plane and oriented along $${45^ \circ }$$ from the x-axis. Determine the direction of null in the radiation pattern for $$0 \le \phi \le \pi $$. Here the angle $$\theta \left( {0 \le \theta \le \pi } \right)$$ is measured from the z-axis, and the angle $$\phi \left( {0 \le \phi \le 2\pi } \right)$$ is measured from the x-axis in the x-y plane.

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

An optical fiber is kept along the$$\widehat Z$$ direction. The refractive indices for the electric fields along $$\widehat X$$ and $$\widehat Y$$ directions in the fiber are $${n_x} = 1.5000$$ and $${n_y} = 1.5001$$, respectively ($${n_x} \ne {n_y}$$ due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is $$1.5\,\,\,\mu m$$. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters, is _______ .

A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement is true?

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n = 1x10¹⁶ $$cm^{-3}$$ and electronic charge q = 1.6x10^-19 C. If a bias of 5V is applied across a 1 $$\mu$$m region of this semiconductor, the resulting current density in this region, in kA/cm², is _________.

For a narrow base PNP BJT, the excess minority carrier concentration ($$\bigtriangleup n_E$$ for emitter, $$\bigtriangleup p_B$$ for base, $$\bigtriangleup n_E$$ for collector) normalized to equilibrium minority carrier concentration ($$\bigtriangleup n_{E0}$$ for emitter, $$\bigtriangleup p_{B0}$$ for base, $$\bigtriangleup n_{C0}$$ for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage V_tn = 1 V and its trans-conductance parameter $${\mu _n}{C_{ox}}\left( {{W \over L}} \right) = 1m{\rm A}/{V^2}.$$ Neglect channel length modulation and body bias effects. Under these conditions the drain current I_D in mA is______.

Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series approximation of $$f$$ $$(x)$$ around $$x=0,$$ which includes all powers of $$x$$ less than or equal to $$3.$$

The rank of the matrix $$M = \left[ {\matrix{ 5 & {10} & {10} \cr 1 & 0 & 2 \cr 3 & 6 & 6 \cr } } \right]$$ is

Consider the $$5 \times 5$$ matrix $$A = \left[ {\matrix{ 1 & 2 & 3 & 4 & 5 \cr 5 & 1 & 2 & 3 & 4 \cr 4 & 5 & 1 & 2 & 3 \cr 3 & 4 & 5 & 1 & 2 \cr 2 & 3 & 4 & 5 & 1 \cr } } \right]$$
It is given that $$A$$ has only one real eigen value. Then the real eigen value of $$A$$ is

A three dimensional region $$R$$ of finite volume is described by $$\,\,{x^2} + {y^2} \le {z^3},\,\,\,0 \le z \le 1$$
Where $$x, y, z$$ are real. The volume of $$R$$ correct to two decimal places is __________.

If the vector function
$$\,\,\overrightarrow F = \widehat a{}_x\left( {3y - k{}_1z} \right) + \widehat a{}_y\left( {k{}_2x - 2z} \right) - \widehat a{}_z\left( {k{}_3y + z} \right)\,\,\,$$
is irrotational, then the values of the constants $$\,{k_1},\,{k_2}\,\,$$ and $$\,{k_3}$$ respectively, are

Let $$\,\,\,{\rm I} = \int_c {\left( {2z\,dx + 2y\,dy + 2x\,dz} \right)} \,\,\,\,$$ where $$x, y, z$$ are real, and let $$C$$ be the straight line segment from point $$A: (0, 2, 1)$$ to point $$B: (4,1,-1).$$ The value of $${\rm I}$$ is ___________.

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _________.

Consider the following statements about the linear dependence of the real valued functions $${y_1} = 1,\,\,{y_2} = x$$ and $${y_3} = {x^2}$$. Over the field of real numbers.

$${\rm I}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly independent on $$ - 1 \le x \le 0$$
$${\rm II}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly dependent on $$0 \le x \le 1$$
$${\rm III}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly independent on $$0 \le x \le 1$$
$${\rm IV}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly dependent on $$ - 1 \le x \le 0$$

Which one among the following is correct?

Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?

Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's method (up to two decimal places) is ______________

The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 $$\mu $$s, then the number of T-states needed for executing the instruction is

The following five instructions were executed on an 8085 microprocessor.
MVI A, 33H
MVI B, 78H
ADD B
CMA
ANI 32H

The Accumulator value immediately after the execution of the fifth instruction is

In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $$${V_{IN}}\,\left( t \right) = \left\{ {\matrix{ {0,} & {for\,\,\,t < 0} \cr {15Volts,} & {for\,\,\,t \ge 0} \cr } } \right.$$$

where $$'t'$$ is in seconds. The time (in seconds) at which the current $${\rm I}$$ in the circuit will reach the value $$2$$ Ampere is ______ .

The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The ratio $${{amplitude\,\,of\,\,{V_2}} \over {amplitude\,\,of\,\,{V_1}}}\,\,$$ is ________ .

In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which magnitude of the phase difference between the voltages $$V_1$$ and $$V_2$$ equals $$\frac{\mathrm\pi}4$$ radians, is __________.

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as
$$y\left[ n \right]\, = \left\{ {\matrix{ {n\left| {x\left[ n \right]} \right|,} & {for\,\,0 \le n \le 10} \cr {x\left[ n \right] - x\left[ {n - 1} \right],} & {otherwise,} \cr } } \right.$$

Which one of the following statements is true about the system?

A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $$h(t) = \left\{ {{{2\sin (300\pi t)} \over {\matrix{ {\pi t} \cr {600} \cr } }}} \right.\,,\,\matrix{ t \cr t \cr } \,\matrix{ \ne \cr = \cr } \,\matrix{ 0 \cr 0 \cr } $$

Let y(t) be the output of this filter. The maximum value of $$\left| {y(t)} \right|$$ is ________________________.

A periodic signal x(t) has a trigonometric Fourier series expansion $$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_n\cos\;n\omega_0t\;+\;b_n\sin\;n\omega_0t\right)$$$ If $$x\left(t\right)=-x\left(-t\right)=-x\left(t-\mathrm\pi/{\mathrm\omega}_0\right)$$, we can conclude that

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a_k} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3a_k} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6$$\mathrm\pi$$ rad/s

For the three statements above, which one of the following is correct?

Let h[n] be the impulse response of a discrete time linear time invariant (LTI) filter. The impulse response is given by h(0)= $${1 \over 3};h\left[ 1 \right] = {1 \over 3};h\left[ 2 \right] = {1 \over 3};\,and\,h\,\left[ n \right]$$ =0 for n < 0 and n > 2. Let H ($$\omega $$) be the Discrete- time Fourier transform (DTFT) of h[n], where $$\omega $$ is the normalized angular frequency in radians. Given that ($${\omega _o}$$) = 0 and 0 < $${\omega _0}$$ < $$\pi $$, the value of $${\omega _o}$$ (in ratians ) is equal to ____________.

Two discrete-time signals x [n] and h [n] are both non-zero only for n = 0, 1, 2 and are zero otherwise. It is given that x(0)=1, x[1] = 2, x [2] =1, h[0] = 1, let y [n] be the linear convolution of x[n] and h [n]. Given that y[1]= 3 and y [2] = 4, the value of the expression (10y[3] +y[4]) is _____________________.

Consider the following statements for continuous-time linear time invariant (LTI) system.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

S, T, U, V, W, X, Y and Z are seated around a circular table. T's neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U's neighbors are S and Y: and T and W are not seated opposite each other. Who is third to the left of V?

She has a sharp tongue and it can occasionally turn

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

I ___________ made arrangements had I ___________informed earlier.

Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages: for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word ‘antagonistic’ is closest in meaning to

In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statement is correct?

40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?

(i) At least one bench is a table
(ii) At least one shelf is a bench
(iii) At least one chair is a table
(iv) All benches are chairs