Consider a 2 × 2 square matrix.

\({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\rm{\sigma }}&{\rm{x}}\\ {\rm{\omega }}&{\rm{\sigma }} \end{array}} \right]\)

Consider the first order initial value problem

y' = y + 2x − x², y(0) = 1, (0 ≤ x < ∞)

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

The I-V characteristics of three types of diodes at room temperature made of semiconductors X, Y, and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If E_gX, E_gY, and E_gZ are the band gaps of X, Y, and Z, respectively, then

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

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 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 V_O (in volt) at the steady-state is ______.

Consider the circuit shown in the figure. Assuming V_BE1 = V_EB2 = 0.7 volt, the 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 __________

The logic functionality realized by the circuit shown below is

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

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as

\({\rm{G}}\left( {\rm{s}} \right) = \frac{2}{{{\rm{s}}\left( {{\rm{s}} + 1} \right)}}\)

The steady-state error e_ss due to a unit step input is

A binary baseband digital communication system employs the signal

\({\rm{p}}\left( {\rm{t}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt {{{\rm{T}}_{\rm{s}}}} }},}&{0 \le {\rm{t}} \le {{\rm{T}}_{\rm{s}}}}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right.{\rm{\;}}\)

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

The particular solution of the initial value problem given below is:

\(\frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y=0\), with y = 3 and \(\frac{dy}{dx}|_{x=0}=-36\)

The values of the integral \(\frac{1}{{2{\rm{\pi j}}}}\mathop \oint \limits_{\rm{c}} \frac{{{{\rm{e}}^{\rm{z}}}}}{{{\rm{z}} - 2}}{\rm{\;}}\)along a closed contour c in anti-clockwise direction for

(i) the point z₀ = 2 inside the contour c, and

A signal \(2\cos \left( {\frac{{2{\rm{\pi }}}}{3}{\rm{t}}} \right) - {\rm{cos}}\left( {{\rm{\pi t}}} \right){\rm{\;}}\)is input to an LTI system with the transfer function

H(s) = e^s + e^-s

If c_k denotes the k^th coefficient in the exponential Fourier series of the output signal, then c₃ is equal to

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 (𝑡) (in ampere) at 𝑡 = 0⁺ is __________

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

The z-parameter matrix \(\left[ {\begin{array}{*{20}{c}} {{{\rm{z}}_{11}}}&{{{\rm{z}}_{12}}}\\ {{{\rm{z}}_{21}}}&{{{\rm{z}}_{21}}} \end{array}} \right]{\rm{}}\) for the two-port network shown 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

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, μn = 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 × 10−19 C)

Figures I and II show two MOS capacitors of the unit area. The capacitor in Figure I has insulator materials X (of thickness t₁ = 1 nm and dielectric constant ε₁ = 4) and Y (of thickness t₂ = 3 nm and dielectric constant ε₂ = 20). The capacitor in Figure II 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 __________

The I – V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown occurs in.

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

In the circuit shown in the figure, the channel length modulation of all transistors is non-zero (λ ≠ 0). Also, all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain (V_o/V_in) of the circuit is

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

Following is the K-map of a Boolean function of five variables P, Q, R, S, and X. The minimum sum-of-product (SOP) expression 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 __________

For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the counter is assumed to be zero.

If the clock (Clk) frequency is 1 GHz, then the counter behaves as a

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

\(\frac{{\rm{d}}}{{{\rm{dt}}}}{{\rm{x}}_1}\left( {\rm{t}} \right) + 2{{\rm{x}}_1}\left( {\rm{t}} \right) = 3{\rm{u}}\left( {\rm{t}} \right)\)

\( \frac{{\rm{d}}}{{{\rm{dt}}}}{{\rm{x}}_2}\left( {\rm{t}} \right) + {{\rm{x}}_2}\left( {\rm{t}} \right) = {\rm{u}}\left( {\rm{t}} \right) \)

where x1(t) and x2(t) are the two-state variables and u(t) denotes the input. If the output c(t) = x₁(t), then the system is:

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as

\({\rm{G}}\left( {\rm{s}} \right) = \frac{{{\rm{K}}\left( {{\rm{s}} + 2} \right)}}{{{{\rm{s}}^2} + 2{\rm{s}} + 2}}{~\rm{and\;H}}\left( {\rm{s}} \right) = 1\)

A wide sense stationary random process (𝑡) passes through the LTI system shown in the figure. If the autocorrelation function of (𝑡) is (𝜏), then the autocorrelation function (𝜏) of the output (𝑡) is equal to

The bit error probability of a memory less binary symmetric channel is 10⁻⁵. If 10⁵ bits are sent over this channel, then the probability that not more than one bit will be in error is __________

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