The state equation and the output equation of a control system are given below: $$\mathop x\limits^. = \left[ {\matrix{

The figure below shows the Bode magnitude and phase plots of a stable transfer function $$G(s) = {{{n_0}} \over {{s^3} +

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability o

Consider p(s) = s3 + $${a_2}$$s2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p

For a unity feedback control system with the forward path transfer function $$G(s) = {K \over {s\left( {s + 2} \right)}}

The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for LOW logic level at the outp

A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 s

In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data Din using clock CK. Th

A 2 $$ \times $$ 2 ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals

A four-variable Boolean function is realized using 4 $$ \times $$ 1 multiplexers as shown in the figure. The minimized

A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F = $

Consider matrix $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and vect

Let M be a real 4 $$ \times $$ 4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvecto

The position of a particle y(t) is described by the differential equation : $${{{d^2}y} \over {d{t^2}}} = - {{dy} \over

Let r = x2 + y - z and z3 - xy + yz + y3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1),

A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{

Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f}

The contour C given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1} $$. The value of the integra

Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ arou

Let X1 , X2 , X3 and X4 be independent normal random variables with zero mean and unit variance. The probability that X4

Consider the network shown below with R1 = 1 $$\Omega $$, R2 = 2 $$\Omega $$ and R3 = 3 $$\Omega $$. The network is conn

The ABCD matrix for a two-port network is defined by : $$\left[ {\matrix{ {{V_1}} \cr {{I_1}} \cr } } \right

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5

For the circuit given in the figure, the voltage VC (in volts) across the capacitor is :

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among th

Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎

Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n], where X[k] = $$\sum\limits_{n = 0}^{N - 1} {x\left[ n \ri

A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of t

A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and t

If the number 715 ■ 423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the smallest whol

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post ca

"Even though there is a vast scope for its __________, tourism has remained a/an _________ area." The words that best fi

What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?

"By giving him the last __________ of the cake, you will ensure lasting ________ in our house today." The words that bes

A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloy

The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should depos