Questions by admin

​​​Let $\boldsymbol{z}=x+i y$ be a complex variable and $\overline{\boldsymbol{z}}$ be its complex conjugate. The equation $\bar{z}^{2}+z^{2}=2$ represents aparabolahyper...

The pressure drop across a control valve is constant. The control valve with inherent characteristic has decreasing sensitivity. If $x$ represents the fraction of maximum...

A discrete-time sequence is given by $x[n]=[1,2,3,4]$ for $0 \leq n \leq 3$. The zero lag auto-correlation value of $x[n]$ is$1$$10$$20$$30$

Match the following measuring devices with their principle of measurement.$$\begin{array}{|l|l|} \hline \textbf{Measuring Device} & \textbf{Principle of Measurement} \\ \...

The capacitor shown in the figure has parallel plates, with each plate having an area $A$. The thickness of the dielectric materials are $d_{1}$ and $d_{2}$ and their rel...

Among the given options, the simplified form of the Boolean function $\mathrm{F=(A+\bar{A} \cdot B)+\bar{A} \cdot(A+\bar{B}) \cdot C}$ is$\mathrm{A+B+C}$$\mathrm{A \cdot ...

Consider the state-space representation of a system$$ \dot{x}=A x+B u $$where $x$ is the state vector, $u$ is the input, $A$ is the system matrix and $B$ is the input mat...

The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T>0$, is$1-j \omega T$$\dfrac{1-j \omega T}{1+j \omega T}$$1+j \omega T$$\dfrac...

The capacitance formed between two concentric spherical metal shells having radii $x$ and $y$ with $y>x$ isNote: $\epsilon$ is the permittivity of the medium between the ...

A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is $\_\_\_\_\_$ $\mathrm{mA} /{ }^{\circ} \mathrm{C}$ (rounded off to two...

Consider a filter defined by the difference equation$$ y[n]-0.5 y[n-2]=a x[n-4] $$where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude r...

Consider the circuit shown in the figure.The CMOS digital logic circuit has infinite input impedance. Assume the opamp is ideal. A $1.8 \mathrm{~V}$ Zener diode with a mi...

Figure shows an amplifier using an NMOS transistor. Assume that the transistor is in saturation with device parameters, $\mu_{n} C_{\text{o x}}=250 \mu \mathrm{A} / \math...

The number of complex multiplications required for computing a $16$-point DFT using the decimation-in-time radix-$2$ FFT is $\_\_\_\_\_\_\_$ (in integer).

The Nyquist sampling frequency for $x(t)=10 \sin ^{2}(200 \pi t)$ is $\_\_\_\_\_\_\_ \mathrm{~Hz}$ (rounded off to nearest integer).

The resistance of a $20 \mathrm{~k} \Omega$ resistor is measured six consecutive times using an LCR meter. The first five readings are $19 \mathrm{~k} \Omega, 18 \mathrm{...

The voltage applied and the current drawn by a circuit are$$ \begin{array}{c} v(t)=95+200 \cos (120 \pi t)+90 \cos \left(360 \pi t-60^{\circ}\right) \mathrm{V} \\i(t)=4 \...

The current $i(t)$ drawn by a circuit is given as$$i(t)=4+30 \cos (t)-20 \sin (t)+15 \cos (3 t)-10 \sin (3 t) \mathrm{A}$$The root-mean-square value of $i(t)$ is $\_\_\_\...

A linear potentiometer $(0-10 \mathrm{k} \Omega)$ is used to measure the water level as shown in the figure. The resistance between $\mathrm{A}$ and $\mathrm{C}$ varies l...

The switch in the following figure has been closed for a long time $(t<0)$. It is opened at $t=0$ seconds. The value of $d v_{0} / d t$ at $t=0^{+}$is $\_\_\_\_\_\_ ~ \ma...

Consider a system given by the following first order differential equation:$$ \frac{d y}{d t}=y+2 t-t^{2} $$where, $y(0)=1$ and $0 \leq t<\infty$. Using a step size $h=0....

Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...

​A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $\mathbf{J}=k s^{2}$, where $k$ is a constant, $s$ is the radial...

​​​​The measured values from a flow instrument, whose range is between $0$ and $2$ flow units, are shown in the histogram. The systematic error (bias) and the maximum err...

​​​​Consider a discrete-time sequence$x[n]=\begin{cases} (0.2)^{n}, & 0 \leq n \leq 7 \\ 0, & \text { otherwise } \end{cases}$The region of convergence of $X(z)$, the $z$...

​​​​​In the bridge circuit shown in the figure, under balanced condition, the values of $R$ and $C$ respectively, are$1.010 ~\Omega$ and $19.802 ~\mu \mathrm{F}$$9.901 ~\...

​​​​​Laplace transform of a signal $x(t)$ is$$X(s)=\frac{1}{s^{2}+13 s+42}$$Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if t...

​​​​In the figure shown, both the opamps $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are ideal, except that the opamp $\mathrm{A}_{1}$ has an offset voltage $\left(\mathrm{V}_{...

​​​​In the figure shown, the positive edge triggered $\mathrm{D}$ flip-flops are initially reset to $Q=0$. The logic gates and the multiplexers have no propagation delay....

​​​In the figure shown, $R=1 \mathrm{~k} \Omega$ and $C=0.1 ~\mu \mathrm{F}$. For a dc gain of $-10$, the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal p...

​​​​Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ i...

​​The transfer function of a system is$$G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}}$$Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} ...

​​Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1...

​​​In the figure shown, assume$\alpha$ is the phase angle between the load current and the load voltage$\beta$ is the phase angle by which pressure coil current lags the ...

​Consider an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ vol...

​​The complex functions $f(z)=u(x, y)+i ~v(x, y)$ and $\overline{f(z)}=u(x, y)-i~ v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the foll...

The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient ...