The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage V₀ (in volt) at the steady state is__________.

Consider the circuit shown in the figure. Assuming V_BE1 = V_EB2 = 0.7 volt, value of the dc voltage V_c2 (in volt) is _______

In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin 3 is

For the circuit shown in the figure, R₁ = R₂ = R₃ = 1 Ω, L = 1 µH and C = 1 µF. If the input V_in = cos(10⁶t) , then the overall voltage gain (V_out /V_in) of the circuit is __________.

A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrelation function of $$X(t)$$ is $${R_x}\left( \tau \right),$$ then the autocorrelation function $${R_x}\left( \tau \right),$$ of the output $$Y(t)$$ is equal to

The bit error probability of a memoryless binary symmetric channel is $${10^{ - 5}}$$. If $${10^{ - 5}}$$ bits are sent over this channel, then the probability that not more than one bit will be in error is ________________

An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $${p_1}$$ = $${p_4}$$ = 0.125 and $${p_2}$$ =$${p_3}$$. The information rate (bits/sec) of the message source is ____________________

A binary baseband digital communication system employs the signal $$$p\left( t \right) = \left\{ {\matrix{ {{1 \over {\sqrt {{T_s}} }},} & {0 \le t \le {T_s}} \cr {0,} & {otherwise} \cr } ,} \right.$$$

for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density $${\eta \over 2} = 2.5\, \times \,{10^{ - 5}}$$ Watt per Hz. If information at the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit energy $${E_b}$$ (in mJ/bit) necessary is ________________

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in MHz) is _________.

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as $$G\left(s\right)\;=\;\frac2{s\left(s\;+\;1\right)}$$ .The steady state error e_ss due to a unit step input is

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G\left(s\right)=\frac{K\left(s+2\right)}{s^2+2s+2}$$ and H(s) = 1 respectively.If the variable parameter K is real positive, then the location of the breakaway point on the root locus diagram of the system is_____________.

The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which the system is stable is

A second-order linear time-invariant system is described by the following state equations $$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \right) \cr & {d \over {dt}}{x_2}\left( t \right) + {x_2}\left( t \right) = u\left( t \right) \cr} $$$

Where x₁(t), then the system is

Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is

For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns, 1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is ___________.

The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

Consider an air-filled rectangular waveguide with dimensions a = 2.286cm and b = 1.016cm. At 10GHz operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _____________________

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the cut-off frequencies for different modes is

A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and reception to a target 1 km away having radar cross-section of 3m². If it transmits 100 kW, then the received power (in $$\mu W$$) is ______ .

The injected excess electron concentration profile in the base region of an npn BJT, biased in the active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm², µ_n = 800 cm²/(V-s) in the base region and depletion layer widths are negligible, then the collector current I_c (in mA) at room temperature is __________. (Given: thermal voltage V_T = 26 mV at room temperature, electronic charge q = $$1.6\times10^{-19}\;C$$ )

Consider the charge profile shown in the figure. The resultant potential distribution is best described by

The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of power 100 mW/cm². The solar cell has an area of 3 cm² and a fill factor of 0.7. The maximum efficiency (in %) of the device is __________.

The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in

Figures $${\rm I}$$ and $${\rm I}{\rm I}$$ show two MOS capacitor of unit area. The capacitor in Figure I has insulator materials X (of thickness t₁ = 1 nm and dielectric constant $${\varepsilon _1}$$ = 4) and Y (of thickness t₂ =3 nm and dielectric constant $${\varepsilon _2}$$ = 200). The capacitor in Figure $${\rm I}{\rm I}$$ has only insulator material X of thickness t_eq. If the capacitors are of equal capacitance, then the value of t_eq (in nm) is ______

In the circuit shown in the figure, the channel length modulation of all transistors is non-zero $$\left( {\lambda \ne 0} \right)$$. Also all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain $$\left( {{V_0}/{V_{in}}} \right)$$ of the circuit is

In the circuit shown in the figure, transistor M1 is in saturation and has transconductance g_m = 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation $$\lambda $$ to be zero, the small signal input pole frequency (in kHz) is _____

Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \right]$$
Where $$x$$ is unknown. If the eigenvalues of the matrix $$A$$ are $$\left( {\sigma + j\omega } \right)$$ and $$\left( {\sigma - j\omega } \right)$$, then $$x$$ is equal to

If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \right)$$ form an orthogonal basis of the three dimensional real space $${R^3},$$ then the vectors $$u = \left( {4,3, - 3} \right) \in {R^3}$$ can be expressed as

The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}} $$ is equal ________.

A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangle and under the plane $$x+y+z=6Z$$ is ________.

The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a ''head'' is obtained. If the tosses are independent, then the probability of getting ''head'' for the first time in the fifth toss is ________.

The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}} + 36y = 0\,\,$$ with $$\,y\left( 0 \right) = 3\,\,$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = - 36\,\,$$

Consider the first order initial value problem $$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x < \infty } \right)$$ With exact solution $$y\left( x \right)\,\, = \,\,{x^2} + {e^x}.\,\,$$ For $$x=0.1,$$ the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size $$h=0.1$$ is __________.

The value of the integral $${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz} $$ along a closed contour $$c$$ in anti-clockwise direction for
(i) the point $${z_0} = 2$$ inside the contour $$c,$$ and
(ii) the point $${z_0} = 2$$ outside the contour $$c,$$ respectively, are

For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.

In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be

In the $$RLC$$ circuit shown in the figure, the input voltage is given by v_i(t) = 2 cos(200t)+4 sin(500t). The output voltage v₀(t) is

The z-parameter matrix for the two-port network shown is $$$\left[ {\matrix{ {2\,j\,\omega } & {j\,\omega } \cr {j\,\omega } & {3\, + \,2\,j\,\omega } \cr } } \right]$$$ Where the entries are in $$\Omega $$. Suppose $$\,{Z_b}\,\left( {j\,\omega } \right) = {R_b} + j\,\omega $$ Then the value of $${R_b}$$ (in $$\Omega $$) equals _______________________3

The z-parameter matrix $$\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}$$ for the two-port network shown is

Assume that the circuit in the figure has reached the steady state before time t = 0 when the 3 Ω resistor suddenly burns out, resulting in an open circuit. The current i(t) (in ampere) at t = 0⁺ is ____________.

In the figure shown, the current i (in ampere) is ______.

A continuous-time speech signal $${x_a}(t)$$ is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all operations sequentially, and takes 20 µs for computing each complex multiplication (including multiplications by 1 and −1) and the time required for addition/ subtraction is negligible, then the maximum value of N is __________.

A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z) is the z-transform of another signal y$$\left[ n \right]$$, then

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal $$x\left[ n \right] = \,{\left( {2.0} \right)^{\left| n \right|}}$$ , $$ - \infty < n < + \infty $$ then the ROC of its z-transform is represented by

Consider the signal $$\,x\left( t \right)$$ $$\,\,\, = \,\,\,\cos \left( {6\pi t} \right)\,\, + \,\,\sin \left( {8\pi t} \right),$$ where $$\,t$$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $$y\left( t \right)\, = x\,\,\left( {2t + 5} \right)$$ is

The direct form structure of an FIR (finite impulse response) filter is shown in the figure.

The filter can be used to approximate a

If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation, then x(t) is equal to

The number that least fits this set: (324, 441, 97 and 64) is ________.

It takes 10 s and 15 s, respectively, for two trains traveling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.