Recent questions without answers

In the given figure angle $Q$ is a right angle, $PS:QS=3:1, RT:QT=5:2$ and $PU:UR=1:1$. If area of triangle $QTS$ is $20\; cm^2$, then the area of triangle $PQR$ in $cm^2...

Right triangle $PQR$ is to be constructed in the xy-plane so that the right angle is at $P$ and line $PR$ is parallel to the x-axis. The $x$ and $y$ coordinates of $P, Q$...

A coin is tossed thrice. Let $X$ be the event that head occurs in each of the first two tosses. Let $Y$ be the event that a tail occurs on the third toss. Let $Z$ be the ...

Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is$r$$n$$n-r$$n+r$

The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is$-2\pi i$$0$$2\pi i$$4\pi i$

The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to$\int_0^x\int_0^y f(x,y) dx\;dy$$\int_0^a \int_x^y f(x,y) dx\;dy$$\int_0^a \int_x^a f(x,y) dy\;dx$$\...

The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is$4\sqrt{2}$$5\sqrt{...

The figure shows a half-wave rectifier circuit with input voltage $V(t)=10\sin(100\;\pi t)$ volts. Assuming ideal diode characteristics with zero forward voltage drop and...

The capacitor shown in the figure is initially charged to $\text{+10 V}$. The switch closes at time $t=0$. Then the value of $V_C(t)$ in volts at time $\text{t=0 ms}$ is ...

The torque transmitted by a cylindrical shaft is to be measured by using two strain gauges. The angles for mounting the strain gauges relative to the axis of the shaft fo...

A p-type semiconductor strain gauge has a nominal resistance of $1000\;\Omega$ and a gauge factor of $+200$ at $25\;^\circ C$. The resistance of the strain gauge in ohms ...

Liquid flow rate is measured usinga Pirani gaugea pyrometeran orifice platea Bourdon tube

The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by$NV_i\sin \omega t$$-NV_i\sin \omega t$$\frac{1}{N}V_i\sin \omega ...

A load resistor $R_L$ is connected to a battery of voltage $E$ with internal resistance $R_i$ through a resistance $R_s$ as shown in the figure. For fixed values of $R_L$...

Consider the logic circuit with input signal $\text{TEST}$ shown in the figure. All gates in the figure shown have identical non-zero delay. The signal $\text{TEST}$ whic...

The logic evaluated by the circuit at the output is $X\overline{Y}+Y\overline{X}$$(\overline{X+Y})XY$$\overline{XY}+XY$$\overline{X}Y+X\overline{Y}+X+Y$

In the circuit shown, the switch is momentarily closed and then opened. Assuming the logic gates to have equal non-zero delay, at steady state, the logic states of X and ...

The highest frequency present in the signal $x(t)$ is $f_{max}$. The highest frequency present in the signal $y(t)=x^2(t)$ is$\frac{1}{2}f_{max}$$f_{max}$$2f_{max}$$4f_{m...

The filter whose transfer function is of the form $G(s)=\frac{s^2-bs+c}{s^2+bs+c}$ isa high-pass filtera low-pass filteran all-pass filtera band-reject filter

Let 3+4j be a zero of a fourth order linear-phase $FIR$ filter. The complex number which is $NOT$ a zero of this filter is$3-4j$$\frac{3}{25}+\frac{4}{25}j$$\frac{3}{25}-...

Consider the ammeter-voltmeter method of determining the value of the resistance $R$ using the circuit shown in the figure. The maximum possible errors of the voltmeter a...

The bridge most suited for measurement of a four-terminal resistance in the range of $0.001\;\Omega$ to $0.1\;\Omega$ isWien’s bridgeKelvin double bridgeMaxwell’s bridgeS...

A power line is coupled capacitively through various parasitic capacitances to a shielded signal line as shown in the figure. The conductive shield is grounded solidly at...

A mass-spring-damper system with force as input and displacement of the mass as output has a transfer function $G(s)=1/(s^2+24s+900)$. A force input $F(t)=10\sin(70t)$ ne...

A system with transfer function $G(S)=\frac{1}{s^2+1} $ has zero initial conditions. The percentage overshoot in its step response is ______________ $\%$.

The voltage $(E_0)$ developed across a glass electrode for $pH$ measurement is related to the temperature $(T)$ by the relation$E_0 \varpropto \frac{1}{T^2}$$E_0 \varprop...

A light detector circuit using an ideal photo-diode is shown in the figure. The sensitivity of the photo-diode is $0.5\:\mu A/\mu W$. With $V_r=6\:V$, the output voltage ...

An apparatus to capture $ECG$ signals has a filter followed by a data acquisition system. The filter best suited for this application islow pass with cutoff frequency $20...

The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ ar...

The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}...

The $z-$transform of $x[n]=\alpha ^{|n|}, 0<|\alpha|<1,$ is $X(z).$ The region of convergence of $X(z)$ is$|\alpha|<|z|<\frac{1}{|\alpha|}$$|z|>\alpha$$|z|>\frac{1}{|\alp...

The current in amperes through the resistor $R$ in the circuit shown in the figure is ______________ $A$.

The linear $I-V$ characteristics of 2-terminal non-ideal dc sources $X$ and $Y$ are shown in the figure. If the sources are connected to a $1\Omega$ resistor as shown, th...

Consider the circuits shown in the figure. The magnitude of the ratio of the currents, i.e., $|I_1/I_2|$, is ___________.

The circuit shown in the figure is in series resonance at frequency $f_c\;Hz$. The value of $V_c$ in volts is _____________ $V$.

The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $1...

The Seebeck coefficients, in $\mu V/^\circ C,$ for copper, constant an and iron, with respect to platinum, are $1.9, \:-38.3$ and $13.3$, respectively. The magnitude of t...

In the figure shown, $R_T$ represents a resistance temperature device $(RTD)$, whose characteristic is given by $R_T=R_\circ(1+\alpha T),$ where $R_\circ=100\: \Omega, \:...

In the circuit shown in the figure, it is found that $V_{BE}=0.7\:V$ and $V_E=0\:V$. If $\beta_{dc}=99$ for the transistor, then the value of $R_B$ in kilo ohms is ______...

An opamp has ideal characteristics except that its open loop gain is given by the expression $Av(S)=10^4/(1+10^{-3}\;s).$ This op-amp is used in the circuit shown in the ...