Recent questions without answers

The value of the surface integral $\iint_{S}(2 x+z) \mathrm{d} y \mathrm{~d} z+(2 x+z) \mathrm{d} x \mathrm{~d} z+(2 z+y) \mathrm{d} x \mathrm{~d} y$ over the sphere $S: ...

Newton-Raphson method is used to compute the inverse of the number $1.6$. Among the following options, the initial guess of the solution that results in non-convergence o...

The value of the integral $\int_{-\pi}^{\pi}\left(\cos ^{6} x+\cos ^{4} x\right) \mathrm{d} x$ is$\frac{\pi}{2}$$\frac{5 \pi}{8}$$\frac{11 \pi}{8}$$\frac{9 \pi}{8}$

Let $y[n]=\frac{1}{\alpha} y[n-1]+x[n]$, where $\alpha>1$ and real, represent a difference equation of a causal discrete-time linear time invariant system. The system is ...

A chopper amplifier shown in the figure is designed to process a biomedical signal $v_{\text {in }}(t)$ to generate conditioned output $v_{\text {out }}(t)$. The signals ...

An $8$-bit microprocessor has $16$ -bit address bus $\left(\mathrm{A}_{15}-\mathrm{A}_{0}\right)$ where $\mathrm{A}_{0}$ is the LSB. As shown in Figure (a), it has a pre-...

A $3$-bit DAC is implemented using ideal opamp and switches as shown in the figure. Each of the switches gets closed when its corresponding digital input is at logic $1$....

Power consumed by a three-phase balanced load is measured using two-wattmeter method. The per-phase average power drawn by the load is $30 \: \mathrm{kW}$ at $\frac{\sqr...

The bridge circuit, shown in Figure (a), can be equivalently represented using the circuit shown in Figure (b). The values of $R_{1}, R_{2}$, and $V_{\mathrm{C}}$ in the ...

A $2$-pole, $50 \mathrm{~Hz}, 3$-phase induction motor supplies power to a certain load at $2970 \: \mathrm{rpm}$ . The torque-speed curve of this machine follows a linea...

The figure shows a closed-loop system with a plant $G(s)=\frac{1}{s^{2}}$ and a lead compensator $C(s)$. The compensator is designed to place the dominant closed-loop pol...

Let $f(t)$ and $g(t)$ represent continuous-time real-valued signals. If $h(t)$ denotes cross-correlation between $f(t)$ and $g(-t)$, its continuous-time Fourier transform...

Choose the correct statement(s) from the following options, regarding Cauchy's theorem on complex integration $\oint_{C} f(z) \mathrm{d} z$ where $C$ is a simple closed p...

The plant in the feedback control system shown in the figure is $P(s)=\frac{a}{s^{2}-b^{2}}$, where $a>0$ and $b>0$. The type(s) of controller $C(s)$ that CANNOT stabiliz...

Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems from the following options.$e^{j \frac{2 \pi}{3} t}$$\cos \left(\frac{2 \pi}{3} t\righ...

The probability of a student missing a class is $0.1$. In a total number of $10$ classes, the probability that the student will not miss more than one class is __________...

A metallic strain-gauge $(\mathrm{SG})$ with resistance $R_{\mathrm{SG}}$ is connected as shown in the figure, where $R_{\mathrm{L} 1}, R_{\mathrm{L} 2}, R_{\mathrm{L} 3}...

Let $X\left(e^{j \omega}\right)$ represent the discrete time Fourier transform of a $4$-length sequence $x[n]$, where $x[0]=1, x =2, x =2$, and $x[3]=4 . X\left(e^{j \ome...

A schematic of a Michelson interferometer, used for the measurement of refractive index of gas, is shown in the figure. The transparent chamber is filled with a gas of re...

Consider an AC bridge shown in the figure with $\mathrm{R}=300 \: \Omega, \mathrm{R} 1=1000 \: \Omega$, $\mathrm{R} 2=500 \: \Omega, \mathrm{~L}=30 \mathrm{mH}$, and a de...

An air filled parallel plate electrostatic actuator is shown in the figure. The area of each capacitor plate is $100 \: \mu \mathrm{m} \times 100 \: \mu \mathrm{m}$. The ...

The resistance of a thermistor is measured to be $2.25 \: \mathrm{k} \Omega$ at $30^{\circ} \mathrm{C}$ and $1.17 \: \mathrm{k} \Omega$ at $60^{\circ} \mathrm{C}$. Its ma...

A feedback control system is shown in the figure.The maximum allowable value of $n$ such that the output $y(t)$, due to any step disturbance signal $d(t)$, becomes zero a...

The circuit given in the figure is driven by a voltage source $V_{S}=25 \sqrt{2} \angle 30^{\circ} \: \mathrm{V}$. The system is operating at a frequency of $50 \: \mathr...

In the circuit shown, the galvanometer $(G)$ has an internal resistance of $100 \: \Omega$. The galvanometer current $I_{G}$ is ____________ $\mu \mathrm{A}$ (rounded off...

A series RLC circuit resonates at $7500 \: \mathrm{rad} / \mathrm{s}$ for inductance $L=20 \: \mathrm{mH}$ and resistance $R=10\: \Omega$. The uncertainties in the measur...

In the circuit shown, the switch is opened at $t=0 \mathrm{~s}$. The current $i(t)$ at $t=2 \mathrm{~ms}$ is __________ $\mathrm{mA}$ (rounded off to two decimal places).

A signal $V_{M}=5 \sin (\pi t / 3) \mathrm{V}$ is applied to the circuit consisting of a switch $S$ and capacitor $C=0.1 \mu \mathrm{~F}$, as shown in the figure. The out...

For the circuit shown in the figure, the active power supplied by the source is ___________ $W$ (rounded off to one decimal place).

​​​​If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words[drizzle $\rightarrow$ rain $\rightarrow$ downpour] is analogous to [ $\right...

​​​​Statements:All heroes are winners.All winners are lucky people.Inferences:All lucky people are heroes.Some lucky people are heroes.Some winners are heroes.Which of th...

​​​​​If the sum of the first $20$ consecutive positive odd numbers is divided by $20^{2}$, the result is$1$$20$$2$$1 / 2$

​​​​The ratio of the number of girls to boys in class $\text{VIII}$ is the same as the ratio of the number of boys to girls in class $\text{IX}$. The total number of stud...

In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.Yoko Roi stands _$\text{(i)}$_ as an author for standing _$\text{(i...

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.The...

​​​​The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which on...

​​​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} \\ \...