Recent questions tagged numerical-answers

Which one of the following options is correct for the given data in the table?$\begin{array}{|c|c|c|c|c|}\hline\text{Iteration (i)} & 0 & 1 & 2 & 3 \\ \hline\text{Input (...

In the given figure, $PQRS$ is a square of side $2 \: \mathrm{cm}$ and $PLMN$ is a rectangle. The corner $L$ of the rectangle is on the side $QR$. Side $MN$ of the rectan...

The primary coil of a linear variable differential transformer (LVDT) is supplied with AC voltage as shown in the figure. The secondary coils are connected in series oppo...

Let a continuous-time signal be $x(t)=e^{j 9 t}+e^{j 5 t}$, where $j=\sqrt{-1}$ and $t$ is in seconds. The fundamental period of magnitude of $x(t)$, in seconds, is$\pi$$...

The $4$-bit signed $2$'s complement form of $(5)_{10}+(5)_{10}$ is$(-6)_{10}$$(-7)_{10}$$(-5)_{10}$$(-8)_{10}$

An infinite sheet of uniform charge $\rho_{s}=10 \mathrm{C} / \mathrm{m}^{2}$ is placed on $z=0$ plane. The medium surrounding the sheet has a relative permittivity of $1...

For the ideal opamp based circuit shown in the figure, the ratio $\frac{V}{I}$ is$\left(\frac{R_{3}+R_{4}}{R_{1}+R_{3}}\right) R_{1}$$\left(\frac{R_{2}+R_{4}}{R_{1}+R_{3}...

A $3\frac{1}{ 2}$ digit digital voltmeter has a specified accuracy of $\pm(0.5 \%+1)$. If it is used to measure $10 \:\mathrm{V}$ DC voltage, the error in the measurement...

The circuit shown in Figure (a) can be represented using its equivalent T-model as shown in Figure (b). The values of the inductances $L_{1}, L_{2}$, and $L_{3}$ in the e...

Three parallel admittances $Y_{a}=-j 0.2 \mathrm{~S}, Y_{b}=0.3 \mathrm{~S}$, and $\quad Y_{c}=j 0.4 \mathrm{~S}$ connected in parallel with a voltage source $V_{s}=10 \a...

For the transfer function $G(s)=1+\frac{2 s-1}{s^{3}+5 s^{2}+3 s+22}$, the number of zeros lying in the left half of the $s$-plane is$0$$1$$2$$3$

A $60 \: \mathrm{V}$ DC source with an internal resistance $R_{\text{i n t}}=0.5 \: \Omega$ is connected through a switch to a pair of infinitely long rails separated by ...

If one of the eigenvectors of the matrix $A=\left[\begin{array}{cc}-1 & -1 \\ x & -4\end{array}\right]$ is along the direction of $\left[\begin{array}{c}\alpha \\ 2 \alph...

Consider the function $f(z)=\frac{2 z+1}{z^{2}-z}$, where $z$ is a complex variable. The sum of the residues at singular points of $f(z)$ is ______________ (in integer).

A dual-slope ADC has a fixed integration time of $100 \: \mathrm{ms}$. The reference voltage of the ADC is $-5 \: \mathrm{V}$. The time taken by the ADC to measure an inp...

In the circuit shown, assume that the BJT in the circuit has very high $\beta$ and $V_{B E}=0.7 \mathrm{~V}$, and the Zener diode has $V_{Z}=4.7 \mathrm{~V}$. The current...

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 ...

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...

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 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).

​​​​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...

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...