Recent questions tagged gate2020-in

A sinusoid of $\text{10 kHz}$ is sampled at $\text{15 k samples/s}.$ The resulting signal is passed through an ideal low pass filter $(LPF)$ with cut-off frequency of $\t...

A $\text{200 mV}$ full-scale dual-slope analog to digital converter $\text{(DS-ADC)}$ has a reference voltage of $\text{100 mV}$. The first integration time is set as $\t...

The capacitance $C_x$ of a capacitive type sensor is $(1000x) pF,$ where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage $\text{...

Two $100\: \Omega$ resistors having tolerance $3\%$ and $4\%$ are connected in series. The effective tolerance of the series combination $\text{(in % rounded off to one d...

Consider the matrix $M=\begin {bmatrix} 1&-1&0\\1&-2&1\\0&-1&1\end{bmatrix}$. One of the eigenvectors of $M$ is$\begin {bmatrix} 1\\-1\\1\end{bmatrix}$$\begin {bmatrix} 1...

Consider the differential equation $\frac{dx}{dt}=\sin(x),$ with the initial condition $x(0)=0. $The solution to this ordinary differential equation is __________$x(t)=0$...

A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1.The equation that describes this line is __________.$\text{y=-0.5x+1}$$\text{y=x-0...

The loop transfer function of a negative feedback system is $G(s)H(s)=\frac{1}{s(s-2)}$. The Nyquist plot for the above system _________.encircles $(-1+j0)$ point once in...

$I_1,\; I_2\: and \:I_3$ in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is ____________$\begin{bmatrix} 3&-1...

Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.

Consider two identical bags $B1$ and $B2$ each containing $10$ balls of identical shapes and sizes. Bag $B1$ contains $7$ Red and $3$ Green balls, while bag $B2$ contains...

The rms value of the phasor current $\underline{I}$ in the circuit shown $\text{(in amperes)}$ is _____.

In the circuit shown, the rms value of the voltage across the $ 100 \Omega$ resistor $\text{(in volts)}$ is _________.

Let $g[n]=\left\{ \begin{array}{rcl} 1 & n=0 \\0 &n=\pm 1,\pm 2,\pm 3,\dots \end{array}\right. $ and $h[n]=\left\{ \begin{array}{rcl} 1 & n=0,3,6,9\dots \\0 & otherwise \...

The loop transfer function of a negative feedback system is given by $G(s)H(s)=\frac{K}{s(s+2)(s+6)}$, where $K>0$. The value of $K$ at the breakaway point of the root lo...

The system shown in Fig.(a) has a time response y(t) to an input $r(t)=10u(t)$ as shown in Fig. (b), $u(t)$ being the unit step input. Both $K, t$ are positive. The gain ...

Assuming that the opamp used in the circuit shown is ideal, the reading of the $1\;Hz$ bandwidth, permanent magnet moving coil $(PMMC)$ type voltmeter $\text{(in volts)}$...

If the opamps in the circuit shown are ideal and $V_x=0.5\;mV$, the steady state value of $V_\circ \; \text{(in volts, rounded off to two decimal places)}$ is ___________

Two flip-flops are interconnected as shown in the figure. The present state of the flip flops are: $A=1, B=1$. The input x is given as $1,0,1$ in the next three clock cyc...

The address lines $A_9 \dots A_2$ of a 10 bit, 1.023 V full-scale digital to analog converter $(DAC)$ is connected to the data lines $D_7$ to $D_0$ of an 8-bit microproce...

The real power drawn by a balanced load connected to a $\text{400 V, 50 Hz,}$ balanced, symmetrical 3-phase, 3-wire, $RYB$ sequence mains is measured using the two-wattme...

A $6\frac{1}{2}$ digit timer-counter is set in the ‘time period’ mode of operation and the range is set as ‘ns’. For an input signal, the timer-counter displays $1000000$...

The circuit shown uses ideal opamp powered from a supply $V_{CC}=5 V$. If the charge $q_p$ generated by the piezoelectric sensor is of the form $q_p=0.1 \sin(10000\pi t) ...

A metallic strain gauge of resistance $R_X$ with a gauge factor of 2 is bonded to a structure made of a metal with modulus of elasticity of $200\: GN/m^2$. The value of $...

A laser beam of 10 mm beam diameter is focused onto an optical fiber using a thin biconvex lens as shown in the figure. The refractive index of the lens is $1.5$. The ref...

As shown in the figure, a slab of finite thickness $t$ with refractive index $n_2=1.5$, has air $(n_1=1)$ above and below it. Light of free space wavelength $600 nm$ is i...

Consider the finite sequence $X=(1,1,1).$ The Inverse Discrete Fourier Transform (IDFT) of X is given as $\text{(x(0), x(1), x(2)).}$ The value of $x(2)$ is _______

A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G=-5 is shown in the figure. The effective capacitance across the nodes A and...

Consider the following state variable equations:$\dot{x_1}(t)=x_2(t)$$\dot{x_2}(t)=-6x_1(t)-5x_2(t)$The initial conditions are $x_1(0)=0 \:and\: x_2(0)=1.$ At $t=1$ secon...

Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is _____...

A $\text{1000/1 A, 5 VA, UPF}$ bar-primary measuring current transformer has $1000$ secondary turns. The current transformer exhibits a ratio error of $-0.1\%$ and a phas...

The mutual inductances between the primary coil and the secondary coils of linear variable differential transformer (LVDT) shown in the figure are $M_1$ and $M_2$. Assume...

In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______

The loop transfer function of a negative feedback system is $ G(s)H(s)=\frac{2(s+1)}{s^2}$. The phase margin of the system $\text{(in degrees, rounded off to one decimal ...

The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrigh...

Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solves ...

A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and ob...

A differentiator has a transfer function whosephase increases linearly with frequencymagnitude remains constantmagnitude increases linearly with frequencymagnitude decrea...

Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $The period of this signal $x[n...