The circuit below implements a filter between the input current i_i and the output voltage v₀. Assume that the op-amp- is ideal, The filter implemented is a

In the circuit shown below, assume that the voltage drop across a forward biased diode is 0.7V. The thermal voltage V_t = kT/q = 25mV. The small signal input v_i = V_P cos ($$\omega t$$) where V_P = 100mV. The ac output voltage v_ac is

In the circuit shown below, assume that the voltage drop across a forward biased diode is 0.7V. The thermal voltage V_t = kT/q = 25mV. The small signal input v_i = V_P cos ($$\omega t$$) where V_P = 100mV. The bias current I_DC through the diodes is

In the circuit shown below, capacitors C₁ and C₂ are very large and are shorts at the input frequency. V_i is a small signal input. The gain magnitude $$\left|\frac{{\mathrm V}_0}{{\mathrm V}_\mathrm i}\right|$$ at 10 Mrad/s is

For a BJT, the common-base current gain $$\alpha = \,\,0.98$$ and the colector base junction reverse bias saturation current I_co = 0.6 $$\mu {\rm A}$$. This BJT is connected in the common emitter mode and operated in the active region with a base drive current I_B = 20$$\mu {\rm A}$$. The collector current I_c for this mode of operation is

For the BJT Q₁ in the circuit shown below, $$\beta = \infty ,\,\,\,\,{V_{BEon\,}}\, = \,0.7V,\,\,\,{V_{CEsat}}\, = \,0.7V.$$. The switch is initially closed. at time t = 0, the switch is opened. The time t at which q₁ leaves the active region is

An analog signal is band-limited to 4kHz. sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable, bit rate is

A four phase and an eight-phase signal constellation are shown in the figure below.

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

X(t) is a stationary random process with autocorrelation function R_x$$\left( \tau \right)$$= exp$$\left( { - \pi {\tau ^2}} \right)$$. This process is passed through the system shown below. The power spectral density of the output process Y(t) is

A four phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii r₁, and r² of the circles are

The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by

The differential equation $$$100\frac{\mathrm d^2\mathrm y}{\mathrm{dt}^2}-20\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm y=\mathrm x\left(\mathrm t\right)$$$ describes a system with an input x(t) and an output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

The input-output transfer function of a plant is h(s)=$${{100} \over {s{{\left( {s + 10} \right)}^2}}}$$. The plant is placed in a unity negative feedback configuration as shown in the figure below. The gain margin of the system under closed loop unity negative feedback is

For the transfer function G$$\left( {j\omega } \right) = 5 + j\omega ,$$ the corresponding Nyquist plot for positive frequency has the form

The input-output transfer function of a plant is h(s)=$${{100} \over {s{{\left( {s + 10} \right)}^2}}}$$. The plant is placed in a unity negative feedback configuration as shown in the figure below. The signal flow graph that DOES NOT model the plant transfer function H(s) is

The block diagram of a system with one input u and two outputs y₁ and y₂ is given below

A state space model of the above system in terms of the state vector $$\underline x $$ and the output vector $$\underline y = {\left[ {\matrix{ {{y_1}} & {{y_2}} \cr } } \right]^\tau }$$ is

Two D flip-flops are connected as a synchronous counter that goes through the following Q_B Q_A sequence $$00 \to 11 \to 01 \to 10 \to 00 \to ......$$

When the output Y in the circuit below is ‘1’, it implies that data has

The output of a 3-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all the states of the counter to be unset initially. The waveform which represents the D/A converter output V_o is

The output Y in the circuit below is always ‘1’ when

The logic function implemented by the circuit below is (ground implies a logic "0"

A transmission line of characteristic impedance 50 $$\Omega $$ is terminated by a 50 $$\Omega $$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be $$\pi /4$$ radians. The phase velocity of the wave along the line is

The modes in a rectangular waveguide are denoted by $$T{E_{mn}}\,$$/$$T{M_{mn}}\,$$ where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following satements is TRUE?

A transmission line of characteristic impedance 50 $$\Omega $$ is terminated in a load impedance $$Z_L$$. The VSWR of the line is measured as 5 and the first of the voltage naxima in the line is observed at a distance of $$\lambda /4$$ from the load. The value of $$Z_L$$ is

The electric and magnetic fields for a TEM wave of frequency $$14 GHz$$ in a homogeneous medium of relative permittivity $${\varepsilon _r}$$ and relative permeability $${\mu _r} = 1$$ are given by $$$\overrightarrow E = {E_p}\,\,{e^{j\left( {\omega t - 280\pi y} \right)}}\,\,{\widehat u_z}\,\,V/m$$$ $$$\overrightarrow H = \,\,3\,\,{e^{j\left( {\omega \,t - 280\,\,\pi \,y} \right)}}\,\,\widehat u{\,_x}\,\,A/m$$$

Assuming the speed of light in free space to be $$3\,\, \times {10^8}\,\,\,m/s,$$ the intrinsic impedance of free space to be $$120\,\,\,\pi $$, the relative permittivity $${\varepsilon _r}$$ of the medium and the electric field amplitude $${E_p}$$ are

Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$ is the position vector of a point inside S, with $$\widehat n$$ the unit normal on S, the value of the integral is

Drift current in the semiconductors depends upon

For a BJT the common base current gain $$\alpha$$ = 0.98 and the collector base junction reverse bias saturation current I_CO = 0.6μA. This BJT is connected in the common emitter mode and operated in the active region with a base drive current I_B=20μA. The collector current IC for this mode of operation is

The channel resistance of an N-channel JFET shown in the figure below is 600 W when the full channel thickness (t_ch) of 10 μm is available for conduction. The built-in voltage of the gate P⁺N junction (V_bi) is -1 V. When the gate to source voltage (V_GS) is 0 V, the channel is depleted by 1 μm on each side due to the built in voltage and hence the thickness available for conduction is only 8 μm The channel resistance when V_GS = -3 V is

The channel resistance of an N-channel JFET shown in the figure below is 600 W when the full channel thickness (t_ch) of 10 μm is available for conduction. The built-in voltage of the gate P⁺N junction (V_bi) is -1 V. When the gate to source voltage (V_GS) is 0 V, the channel is depleted by 1 μm on each side due to the built in voltage and hence the thickness available for conduction is only 8 μm The channel resistance when V_GS = 0 V is

In the circuit shown below, for the MOS transistors, $$\mu_nC_{ox}\;=\;100\;\mu A/V^2$$ and the threshold voltage V_T = 1 V. The voltage V_x at the source of the upper transistor is

The system of equations $$x+y+z=6,$$ $$x+4y+6z=20,$$ $$x + 4y + \lambda z = \mu $$ has no solution for values of $$\lambda $$ and $$\mu $$ given by

Consider a closed surface $$'S'$$ surrounding a volume $$V.$$ If $$\overrightarrow r $$ is the position vector of a point inside $$S$$ with $$\overrightarrow n $$ the unit normal on $$'S',$$ the value of the integral is

A fair dice is tossed two times. The probability that the $$2$$^nd toss results in a value that is higher than the first toss is

The solution of differential equation $${{dy} \over {dx}} = ky,y\left( 0 \right) = C$$ is

A numerical solution of the equation $$f\left( x \right) = x + \sqrt x - 3 = 0$$ can be obtained using Newton $$-$$ Raphson method. If the starting values is $$x=2$$ for the iteration then the value of $$x$$ that is to be used in the next step is

The value of the integral $$\oint\limits_c {{{ - 3z + 4} \over {{z^2} + 4z + 5}}} \,\,dz,$$ when $$C$$ is the circle $$|z| = 1$$ is given by

An 8085 assembly language program is given below. Assume that the carry flag is initially unset. The content of the accumulator after the execution of the program is
MVI A,07H
RLC
MOV B,A
RLC
RLC
ADD B
RRC

In the circuit shown below the value of R_L such that the power transferred to R_L is maximum

In the circuit shown below, the Norton equivalent current in amperes with respect to terminals P and Q is

If the unit step response of a network is $$(1-e^{-\alpha t})$$, then its unit impulse response is

In the circuit shown below, the network N is described by the following Y matrix: $$$Y\;=\;\begin{bmatrix}0.1S&-0.01S\\0.01S&0.1S\end{bmatrix}$$$ The voltage gain $$\frac{V_2}{V_1}$$ is

In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t=0. The current i(t) at a time t after the switch is closed is

In the circuit shown below, the current I is equal to

If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of f(t) are respectively

The differential equation $$100{{{d^2}y} \over {dt}} - 20{{dy} \over {dt}} + y = x\left( t \right)$$ describes a system with an input x(t) and output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

An input x(t) = exp( -2t) u(t) + $$\delta $$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The output is

The first six points of the 8-point DFT of a real valued sequence are 5, 1 - j3, 0, 3- j4, 0 and 3+ j4. The last two points of the DFT are respectively

A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is

Two system $${H_1}\left( z \right)$$ and $${H_2}\left( z \right)$$ are connected in cascade as shown below. The overall output $$y\left( n \right)$$ is the same as the input $$x\left( n \right)$$ with a one unit delay. The transfer function of the second system $${H_2}\left( z \right)$$ is

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair:

Gladiator : Arena

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

Under ethical guidelines recently adopted by the Indian Medical Association, human genes are to be manipulated only to correct diseases for which ______________ treatments are unsatisfactory.

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

It was her view that the country's problems had been_________ by foreign technocrats, so that to invite them to come back would be counter-productive.

Choose the word from the options given below that is most nearly opposite in meaning to the given word:

Frequency

There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?

The sum of n terms of the series 4 + 44 + 444 +.... is

The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with diphtheria and tetanus were developed this way. It can be inferred from the passage that horses were

Three friends, R, S and T shared toffee from a bowl. R took 1/3^rd of the toffees, but returned four to the bowl. S took 1/4^rd of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees-were originally there in the bowl?

Given that f(y) = |y| / y, and q is any non-zero real number, the value of | f(q) - f(-q) | is

The fuel consumed by a motorcycle during a journey while traveling at various speeds is indicated in the graph below.

The distances covered during four laps of the journey are listed in the table below

From the given data, we can conclude that the fuel consumed per kilometre was least during the lap