A small signal source V_i(t) = A cos 20t + B sin 10⁶ t, is applied to a transistor Amplifier as shown in fig. The transistor has $$\beta $$ = 150 and h_ie = 3k$$\Omega $$ , which expression best approximates $${V_0}\left( t \right)$$ ?

A communication channel with AWGN operating at a signal to noise ratio SNR > > 1 and band width B has capacity $${{C_1}}$$ . If the SNR is doubled keeping B constant, the resulting capacity $${{C_2}}$$ is given

The amplitude of random signal is uniformly distributed between $$-$$5V and 5V

If the signal to quantization noise ratio required in uniformly quantizing the signals is 43.5 dB, the step size of the quantization is approximately

The amplitude of random signal is uniformly distributed between $$-$$5V and 5V

If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with a step size of 0.1V, the resulting signal to quantization noise ratio is approximately

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown. The gain and phase margins of G(s) for closed loop stability are

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer function has these properties?

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown. Which of the foloowing statements is true?

The magnitude plot of a rational transfer function G(s), with real coefficient is shown in figure. Which of the following compensators has such a magnitude plot?

Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\,\,{\rm B} = \left[ {\matrix{ p \cr q \cr } } \right],$$

where p and q are arbitrary real numbers. Which of the following statesments about the controllability of the system is true?

If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$$ then

What are the minimum number of 2-to 1 multiplexers required to generate a 2-input AND gate and a 2-input EX-OR gate?

The full forms of the abbreviations TTL and COMS in reference to logic families are

What are the counting states (Q₁, Q₂) for the counter shown in the figure below?

A transmission line terminates in two branches, each of length $$\lambda /4$$, as shown.The branches are terminated by 50 $$\Omega $$ loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance $${Z_i}$$ as seen by the source.

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y-axis. The other wire is in the x-y plane and parallel to the x-axis. Which components of the resulting magnetic field are non-zero at the origin?

In the circuit below, the diode is ideal. The voltage V is given by

Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased from zero, while the gate voltage of the p-MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the transconductance parameter and the $$\left(\frac WL\right)$$ ratio, i.e. the quantity $$\mu C_{ox}\left(\frac WL\right)$$ , is 1 mAV^-2.
For small increase in V_G beyond 1 V, which of the following gives the correct description of the region of operation of each MOSFET?

Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased from zero, while the gate voltage of the p-MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the transconductance parameter and the $$\left(\frac WL\right)$$ ratio, i.e. the quantity $$\mu C_{ox}\left(\frac WL\right)$$ , is 1 mAV^-2.
Estimate the output voltage V₀ for V_G =1.5 V. [Hints: Use the appropriate current-voltage equation for each MOSFET, based on the answer]

The eigen values of the following matrix $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & 0 & 3 \cr } } \right]$$ are

The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi $$ is given by

If a vector field$$\overrightarrow V $$ is related to another field $$\overrightarrow A $$ through $$\,\overrightarrow V = \nabla \times \overrightarrow A ,$$ which of the following is true?

Note: $$C$$ and $${S_C}$$ refer to any closed contour and any surface whose boundary is $$C.$$

A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?

Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ with probability $$1/2,$$ $$1/4$$ and $$1/4$$ respectively. What is the conditional probability $$P(X+Y=2/X-Y=0)?$$

A discrete random variable $$X$$ takes value from $$1$$ to $$5$$ with probabilities as shown in the table. A student calculates the mean of $$X$$ as $$3.5$$ and her teacher calculates the variance to $$X$$ as $$1.5.$$ Which of the following statements is true?

Match each differential equation in Group $$I$$ to its family of solution curves from Group $$II.$$

Group $$I$$
$$P:$$$$\,\,\,$$ $${{dy} \over {dx}} = {y \over x}$$
$$Q:$$$$\,\,\,$$ $${{dy} \over {dx}} = {{ - y} \over x}$$
$$R:$$$$\,\,\,$$ $${{dy} \over {dx}} = {x \over y}$$
$$S:$$$$\,\,\,$$ $${{dy} \over {dx}} = {{ - x} \over y}$$

Group $$II$$
$$(1)$$$$\,\,\,$$ Circle
$$(2)$$$$\,\,\,$$ straight lines
$$(3)$$$$\,\,\,$$ Hyperbola

The order of differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e^{ - t}}\,\,$$ is

Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is

If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} \,\,dz$$ is given

If the transfer function of the following network is $$\,{{{V_0}(s)} \over {{V_i}(s)}} = {1 \over {2\, + \,sCR}}$$

The value of the load resistance $${R_L}$$ is

A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-time. Assume that, during the talk-time, the battery delivers a constant current of 2 A and its voltage drops linearly from 12 V to 10 V as shown in the figure. How much energy does the battery deliver during this talk-time?

An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega $$ feeds a load of impedance $${Z_L} = \left( {7 + 4j} \right)\Omega $$ in the figure below. The reactive power consumed by the load is

In the circuit shown, what value of R_L maximizes the power delivered to R_L?

The switch in the circuit shown was on position ‘a’ for a long time and is moved to position ‘b’ at time t = 0. The current i(t) for t > 0 is given by

The time domain behavior of an RL circuit is represented by $$$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm{dt}}+\mathrm{Ri}\;=\;{\mathrm V}_0\left(1\;+\;\mathrm{Be}^{-\mathrm{Rt}/\mathrm L}\;\sin\;\mathrm t\right)\mathrm u\left(\mathrm t\right)$$$ For an initial current of i(0) = $$\frac{{\mathrm V}_0}{\mathrm R}$$, the steady state value of the current is given by

In the interconnection of ideal sources shown in the figure, it is known that the 60V source is absorbing power.

Which of the following can be the value of the current source I?

Consider a system whose input x and output y are related by the equation $$$y(t) = \int\limits_{ - \infty }^\infty {x(t - \tau )\,h(2\tau )\,d\tau } $$$

Where h(t) is shown in the graph.

Which of the following four properties are possessed by the system?

BIBO: Bounded input gives a bounded output.
Causal: The system is casual.
LP: The system is low pass.
LTI: The system is linear and time- invariant.

A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise. Consider the following statements.
S1: H(z) is a low-pass filter.
S2: H(z) is an FIR filter.

Which of the following is correct?

An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in steady state. The output is sampled at a rate $${\omega _s}\,\,rad/s$$ to obtain the final output {y(k)}. Which of the following is true?

The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1)$$ is

The Fourier series of a real periodic function has only

P. Cosine terms if it is even

Q. Sine terms if it is even

R. Cosine terms if it odd

S. Sine terms if it is odd

Which of the above statement are correct?

A function is given by f(t) = sin²t +cos2t . Which of the following is true?

Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau } $$ is

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is