In the following transistor circuit, V_BE = 0.7V, r_e = 25m/I_E, $$\beta $$ and all the capacitances are very large.

The mid-band voltage gain of the amplifier is approximately

The Op-Amp circuit shown above represents a

Consider the following circuit using an ideal Op-Amp. The I-V characteristics of the diode is described by the relation $$$I = {I_0}\left[ {{e^{{V \over {VT}}}} - 1} \right], where \,{V_T}\,\, = \,\,25mV,{I_0}\,\, = 1 \mu {\rm A}$$$

and V is the voltage across the diode (taken as positive for forward bias). For an input voltage $${V_i}\,\, = \,\, - 1V,$$ the output voltage V₀ is

Consider the Schmitt trigger circuit shown below.

A triangular wave which goes from -12V to 12V is applied to the inverting input of the OP-AMP. Assume that the output of the OP-AMP swings from +15V to -15V. The voltage at the non-inverting input switches between.

In the following transistor circuit, V_BE = 0.7V, r_e = 25m/I_E, $$\beta $$ and all the capacitances are very large.

The Value of DC current I_E is

Four messages band limited to W, W, 2 W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this TDM signal is

Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-dB cut-off frequency of f_c. The noise power at the filter output is

Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a sequence of three 1s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is

A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

The number of quantitization levels required to reduce the quantization noise by a factor of 4 would be

A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

Assuming the signal to be uniformly distributed between its peak values, the signal to noise ratio at the quantizer output is

A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n

A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is

Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For demodulating the signal using envelope detector, the minimum value of A_c should be

The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {\sqrt 3 }}$$ at 5 $$\sqrt 2 $$ rad/sec. The transfer function of the system is

A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter. Consider the standard negative unity feedback configuration as shown below Which of the following statements is true?

Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions

Group I $$$P=\frac{25}{s^2+25}\;\;\;\;\;Q=\frac{36}{s^2+20s+36}$$$ $$$R=\frac{36}{s^2+12s+36}\;\;\;\;\;S=\frac{49}{s^2+7s+49}$$$

Group II

The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

A signal flow graph of a system is given below.

The set of equations that correspond to this signal flow graph is

The pole-zero plot given below corresponds to a

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function.

The output of this system to the sinusoidal input x(t) = 2cos(t) for all time 't' is

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function.

The frequency response H(ω) of the system in terms of angular frequency 'ω' is given by h( ω)

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition $${R_2}{C_2} > {R_1}{C_{1.}}$$ The transfer $${\textstyle{{{V_0}} \over {{V_1}}}}$$ function represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II. Group - I

Group - II
1. PID controller
2. Lead compensator
3. Lag compensator

In the following circuit, the comparator output is logic “I” if V₁ > V₂ and is logic “0” otherwise. The D/A conversion is done as per the relation $$${V_{DAC}} = \sum\limits_{n = 0}^3 {{2^{n - 1}}{b_n}\,\,} Volts,$$$ where b₃(MSB), b₂, b₁ and b₀ (LSB) are the counter outputs.

The counter starts from the clear state.

The magnitude of the error between V_DAC and V_in at steady state in volts is

The logic function implemented by the following circuit at the terminal OUT is

For each of the positive edge-triggered J-K flip flop used in the following future, the propagation delay is $$\Delta $$T

Which of the following waveforms correctly represents the output at Q₁?

In the following circuit, the comparator output is logic “I” if V₁ > V₂ and is logic “0” otherwise. The D/A conversion is done as per the relation $$${V_{DAC}} = \sum\limits_{n = 0}^3 {{2^{n - 1}}{b_n}\,\,} Volts,$$$ where b₃(MSB), b₂, b₁ and b₀ (LSB) are the counter outputs.

The counter starts from the clear state.

The stable reading of the LED display is

Which of the follwing Boolean expression correctly represents the relation between P, Q, R and M₁?

For the circuit shown in the following figure $${I_0}$$ - $${I_3}$$ are inputs to the 4:1 multiplexer R(MSB) and S are control bits. tHE OUTPUT Zcan be represented by

For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is

At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is

One end of loss-less transmission line having the characteristic impedance of 75 $$\Omega $$ and length of 1 cm is short-ciruited. At 3 GHz, the input impedance at the other end of the transmission line is

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $${\varepsilon _r} = 9$$ ). The magnitude of the reflection coefficient is

A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in $$T{E_{11}}$$ mode. The minimum operating frequency is

The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ along the straight line segment from the point (0, 0) to the point (1, 2) in the x-y plane is

Which of the following is true?

The measured transconductance g_m of an NMOS transistor operating in the linear region is plotted against the gate voltage V_G at constant drain voltage V_D. Which of the following figures represents the expected dependence of g_m on V_G?

Which of the following is NOT associated with a P-N junction?

In the following limiter circuit, an input voltage $${\mathrm V}_\mathrm i\;=\;10\sin\left(100\mathrm{πt}\right)$$ applied. Assume that the diode drop is 0.7V when it is forward biased. The Zener breakdown voltage is 6.8V.

The maximum and minimum values of the output voltage respectively are

Two identical NMOS transistors M₁ and M₂ are connected as shown below. V_bias is chosen so that both transistors are in saturation. The equivalent g_m of the pair is defined to be $$\frac{\partial I_{out}}{\partial v_i}$$ at constant V_out. The equivalent g_m of the pair is

A silicon wafer has 100 mm of oxide on it and is inserted in a furnace at a temperature above 1000ºC for further oxidation in dry oxygen. The oxidation rate

For the circuit shown in the following figure, transistors M1 and M2 are identical NMOS transistors. Assume that M2 is in saturation and the output is unloaded The current I_x is related to I_bias as

The drain current of a MOSFET in saturation is given by $$I_D\;=\;K\left(V_{GS}\;-V_T\right)^2$$ where 'K' is a constant. The magnitude of the transconductance g_m is

The system of linear equations $$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$ has

The equation sin(z) = 10 has

The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is

The residue of the function
$$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is

Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right) = 0,\,\,x\left( 0 \right) = 2?$$

Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q {\left( {x\,dx + y\,dy} \right)\,\,} $$ along the semicircle with the line segment $$PQ$$ as its diameter

The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line segment from the point $$(0,0)$$ to the point $$(1,2)$$ in the $$xy$$ -plane is

In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \pi } \right)^2}$$ is

For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is

Which of the following function would have only odd powers of $$x$$ in its Taylor series expansion about the point $$x=0$$ ?

All the four entries of $$2$$ $$x$$ $$2$$ matrix
$$P = \left[ {\matrix{ {{p_{11}}} & {{p_{12}}} \cr {{p_{21}}} & {{p_{22}}} \cr } } \right]$$ are non-zero and one of the eigen values is zero. Which of the following statement is true?

An 8085 executes the following instructions
2710 LXI H, 30A0H
DAD H
PCHL

All addresses and constants are in Hex. Let PC be the contents of the program counter and HL be the contents of the HL register pair just after executing PCHL.

Which of the following statements is correct.

A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters $${V_1}$$, $${V_2}$$ and ammeter $${A_1}$$, $${A_2}$$ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

(i) $${S_1} - open,\,\,\,\,{S_2} - closed$$
$${A_1} = 0\,A,\,\,\,\,\,\,{V_1} = \,4.5\,\,V,$$
$${V_2}\, = \,1.5\,V,\,\,\,\,{A_2}\, = \,1\,A$$

(ii) $${S_1} - Closed,\,\,\,\,{S_2} - Open$$
$${A_1} = 4\,A,\,\,\,\,\,\,{V_1} = \,6\,\,V,$$
$${V_2}\, = \,6\,V,\,\,\,\,{A_2}\, = \,0\,A$$

The h-parameter matrix for this network is

A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters $${V_1}$$, $${V_2}$$ and ammeter $${A_1}$$, $${A_2}$$ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

(i) $${S_1} - open,\,\,\,\,{S_2} - closed$$
$${A_1} = 0\,A,\,\,\,\,\,\,{V_1} = \,4.5\,\,V,$$
$${V_2}\, = \,1.5\,V,\,\,\,\,{A_2}\, = \,1\,A$$

(ii) $${S_1} - Closed,\,\,\,\,{S_2} - Open$$
$${A_1} = 4\,A,\,\,\,\,\,\,{V_1} = \,6\,\,V,$$
$${V_2}\, = \,6\,V,\,\,\,\,{A_2}\, = \,0\,A$$

The z-parameter matrix for this network is

The driving point impedance of the following network is given by $$Z(s) = {{0.2\,s} \over {{s^2}\, + \,0.1\,s\, + \,2}}$$. The component values are

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage V_c(t) across the capacitor is given by

In the following graph, the number of trees (P) and the number of cut-sets (Q) are

The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the output voltage V_c(t) is

The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the voltage across the resistor is

In the following circuit, the switch S is closed at t=0. The rate of change of current $$\frac{di}{dt}(0^+)$$ is given by

The Thevenin equivalent impedance Z_th between the nodes P and Q in the following circuit is

In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency is 10 Hz.

The samples x (n) (n=0, 1, 2,...........) are given by

A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$ $$ = 1,\,\,h\left[ 1 \right]\,\, = - 1,\,\,h\left[ 2 \right]\,\, = \,2$$, and zero otherwise. The system is given an input sequence $$x\left[ n \right]$$ with $$x\left[ 0 \right]$$ $$ = \,x\left[ 2 \right]\, = \,1,$$ and zero otherwise. The number of nonzero samples in the output sequence $$y\left[ n \right]$$, and the value of $$y\left[ 2 \right]$$ are, respectively

The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise} \cr } } \right.$$

Two of the angular frequencies at which its Fourier transform becomes zero are

The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\left( t \right)\,\,\, + \,\,\exp \left( {\beta t} \right)u\left( { - t} \right),$$ where u(t) denotes the unit step function, and $$\alpha $$ and $$\beta $$ are real constants. This system is stable if

The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?

{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence
y (n) = $${1 \over N}\,\sum\limits_{r = 0}^{N - 1} x \,\left( r \right)x\,(n + r\,)$$ is

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4.

Properties

P1 : Linear but NOT time-invariant
P2: Time-invariant but NOT linear
P3: Linear and time-invariant

Relations

R1: y(t) = $${t^2}$$ x(t)
R2: y(t) = t$$\left| {x(t)} \right|$$
R3: y(t) = $$\left| {x(t)} \right|$$
R4: y(t) = x(t-5)

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4, and one simple zero at s = - 1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.
The expression and the region of convergence of the z-transform of the sampled signal are