A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain A_v0, input resistance R_in, and output resistance R₀ for A1 and A2 are as follows:
A1: A_v0 = 10,R_in = 10 kΩ ,R₀ =1 kΩ
A2 : A_v0 = 5,R_in = 5 kΩ , R₀ = 200 Ω
The approximate overall voltage gain $$\frac{{\mathrm V}_\mathrm{out}}{{\mathrm V}_\mathrm{in}}$$ is ______.

In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are 𝐴_cm and 𝐴_d, respectively. If the resistance R_E is increased, then

The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is

The power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f \right| \le W} \cr {0,\left| f \right| > W} \cr } } \right.$$$

The value of the expectation $$$E\left[ {\pi X\left( t \right)X\left( {t - {1 \over {4W}}} \right)} \right]$$$
is ---------------.

The input to a 1-bit quantizer is a random variable X with pdf $${f_x}(x) = 2{e^{ - 2x}}\,\,for\,\,x \ge 0$$ and $${f_x}(x) = 0\,\,for\,\,x\, < \,0$$. For outputs to be of equal probability, the quantizer threshold should be _______________.

The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 + {P \over {{\sigma ^2}\,W}}} \right)$$ bits per second (bps), where W is the channel bandwidth, P is the average power received and $${{\sigma ^2}}$$ is the one-sided power spectral density of the AWGN.
For a Fixed $${{P \over {{\sigma ^2}\,}} = 1000}$$, the channel capacity (in kbps) with infinite band width $$(W \to \infty )$$ is approximately

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $${s_1}\,(t)\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_1}\,t\,and\,\,{s_{2\,}}(t)\,\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_2}\,t$$, where $$\,\alpha = 4\,\,\,mV$$. Assume an AWGN channel with two-sided noise power spectral density $$\,{{{N_0}} \over 2} = 0.5\,\, \times \,{10^{ - 12}}$$ W/Hz. Using an optimal receiver and the relation $$Q(v) = {1 \over {\sqrt {2\,\pi } }}\,\int\limits_v^\infty {e{\,^{ - {u^2}/2}}} \,du$$, the bit error probability for a data rate of 500 kbps is

For the following system, When X₁(s) = 0 , the transfer function $$\frac{\mathrm Y\left(\mathrm s\right)}{{\mathrm X}_2\left(\mathrm s\right)}$$ is

The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.

If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is

An unforced linear time invariant (LTI) system is represented by $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right].$$$

If the initial conditions are x₁(0)= 1 and x₂(0)=-1, the solution of the state equation is

Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

The outputs of the two flip-flops Q₁, Q₂ in the figure shown are initialized to 0, 0. The sequence generated at Q₁ upon application of clock signal is

In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W₁, W₂, W₃ and W₄.

The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is __________ .

For an n - variable Boolean function maximum number of prime implicants is

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by

In the transmission line shown, the impedance $${Z_{in}}$$ (in ohms) between node A and the ground is

To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $$\lambda /4$$ transformer as shown.

Which one of the following field patterns represents a TEM wave traveling in the positive $$x$$ direction?

If the electric field of a plane wave is $$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) - \widehat y4\sin \left( {\omega t - kz + {{45}^ \circ }} \right)\left( {mV/m} \right)$$$

The polarization state of the plane wave is

For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencies for $$T{E_{10}}$$ mode and $$T{E_{20}}$$ mode. If a $$ = \sqrt 5 \,cm$$, the value of b (in cm) is

Assume electronic charge q = 1.6×10^-19 C, kT/q = 25 mV and electron mobility μ_n = 1000 cm²/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1×10²¹/cm⁴, the magnitude of electron diffusion current density (in A/cm²) is _________.

Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width X_n on the N-side of the junction is 0.2 µm and the permittivity of silicon (ε_si) is 1.044×10^-12 F/cm. At the junction, the approximate value of the peak electric field (in kV/cm) is _________.

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

For the n-channel MOS transistor shown in the figure, the threshold voltage V_Th is 0.8V. Neglect channel length modulation effects. When the drain voltage V_D = 1.6 V, the drain current I_D was found to be 0.5 mA.

For the MOSFETs shown in the figure, the threshold voltage |V_t| = 2V and
K=$${1 \over 2}\mu {C_{OX}}\left( {{W \over L}} \right) = 0.1mA/{V^2}$$ . The value of I_D (in mA) is _______

The system of linear equations $$\left( {\matrix{ 2 & 1 & 3 \cr 3 & 0 & 1 \cr 1 & 2 & 5 \cr } } \right)\left( {\matrix{ a \cr b \cr c \cr } } \right) = \left( {\matrix{ 5 \cr { - 4} \cr {14} \cr } } \right)$$ has

The determinant of matrix $$A$$ is $$5$$ and the determinant of matrix $$B$$ is $$40.$$ The determinant of matrix $$AB$$ is _______.

The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______.

For $$0 \le t < \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occurs at

The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is

If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarrow r } \right| = r,$$ then div $$\left( {{r^2}\nabla \left( {\ln \,r} \right)} \right) $$ = ________.

Let $$X$$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $$100.$$ The expectation, $$E\left[ X \right],$$ is __________.

If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + y = 0\,\,$$ has two equal roots, then the values of $$\alpha $$ are

The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The imaginary part of $$f(z)$$ is

For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI₀ – DI₇) from an external device is shown in the figure. The instruction for correct data transfer is

Norton's theorem states that a complex network connected to a load can be replaced with an equivalent impedance

In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then the magnitude of the current (in mA) through the $$4k\Omega$$ resistor at t = 0⁺ is _______.

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1Ω , respectively, the operating angular frequency (in rad/s) is ________.

In the h-parameter model of the 2-port network given in the figure shown, the value of h₂₂ (in S) is _____ .

In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I(t) (in mA) for t > 0?

In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ______ .

An FIR system is described by the system function $$$H(z) = 1 + {7 \over 2}{z^{ - 1}} + {3 \over 2}{z^{ - 2}}$$$

Let x$$\left[ n \right]$$ = x$$\left[- n \right]$$ . Let X(z) be the z-transform of x$$\left[ n \right]$$. if 0.5 +j 0.25 is a zero of X(z), which one of the folowing must also be a zero of X (z)

The input-output relationship of a causal stable LTI system is given as
𝑦[𝑛] = 𝛼 𝑦[𝑛 − 1] + $$\beta $$ x[n].
If the impulse response h[n] of this system satisfies the condition $$\sum\limits_{n = 0}^\infty h $$[n] = 2, the relationship between α and is $$\alpha $$ and $$\beta $$ is

The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}} $$ (5t) dt is

Consider a discrete-time signal
$$x\left[ n \right] = \left\{ {\matrix{ {n\,\,for\,\,0 \le n \le 10} \cr {0\,\,otherwise} \cr } } \right.$$

If $$y\left[ n \right]$$ is the convolution of $$x\left[ n \right]$$ with itself, the value of $$y\left[ 4 \right]$$ is

Consider the periodic square wave in the figure shown. The ratio of the power in the 7^th harmonic to the power in the 5^th harmonic for this waveform is closest in value to _______.