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Consider a low-pass filter module with a pass-band ripple of $\delta$ in the gain magnitude. If $M$ such identical modules are cascaded, ignoring the loading effects, the...
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The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
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If the deflection of the galvanometer in the bridge circuit shown in the figure is zero, then the value of $R_X$ in ohms is _______________ $\Omega.$
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In the potentiometer circuit shown in the figure, the expression for $V_X$ is ____________.$(1-2\alpha)V$$(1-\alpha)V$$(\alpha-1)V$$\alpha V$
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The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are$\pm \frac{\pi}{4}$$\pm \frac{\pi}{3}$$\pm \fr...
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A system is represented in state-space as $\dot{X}=AX+BU,$ where $A=\begin{bmatrix} 1 & 2 \\ \alpha & 6\end{bmatrix}$ and $B=\begin{bmatrix} 1 \\ 1\end{bmatrix}$. The val...
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A liquid level measurement system employing a radio-isotope is mounted on a tank as shown in the figure. The absorption coefficient of water for the radiation is $7.7 \;m...
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The figure shows a spot of light of uniform intensity $50\;W/m^2$ and size $10\;mm\times10\;mm$ incident at the exact center of a photo-detector, comprising two identical...
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A beam of monochromatic light passes through two glass slabs of the same geometrical thickness at normal incidence. The refractive index of the first slab is $1.5$ and th...
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The resolving power of a spectrometer consisting of a collimator, a grating and a telescope can be increased byincreasing the angular magnification of the telescopeincrea...
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Choose the most appropriate word from the options given below to complete the following sentence.A person suffering from Alzheimer’s disease ___________ short-term memory...
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Choose the most appropriate word from the options given below to complete the following sentence.____________is the key to their happiness; they are satisfied with what t...
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Which of the following options is the closest in meaning to the sentence below? $\text{“As a woman. I have no country.”}$Women have no country.Women are not cit...
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In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$.The average time between successive occurrence...
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The population of a new city is $5$ million and is growing at $20\%$ annually. How many years would it take to double at its growth rate?$3-4$ years$4-5$ years$5-6$ years...
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In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the e...
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Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, co...
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The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item as a percent...
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$X$ is $1$ km northeast of $Y$. $Y$ is $1$ km southeast of $Z$. $W$ is $1$ km west of $Z$. $P$ is $1$ km south of $W$. $Q$ is $1$ km east of $P$. What is the distance bet...
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$10\%$ of the population in a town is $HIV^+$. A new diagnostic kit for $HIV$ detection is available; this kit correctly identifies $HIV^+$ individuals $95\%$ of the time...
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Given $x(t)=3\sin (1000\; \pi t)\; and\;y(t)=5\cos (1000\;\pi t+\frac{\pi}{4})$The $x-y$ plot will bea circlea multi-loop closed curvea hyperbolaan ellipse
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Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________.
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The figure shows the plot of $y$ as a function of $x$The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is :$\fr...
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A vector is defined as $$f=y\hat{i}+x\hat{j}+z\hat{k}$$where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system.The surface integral $f....
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The figure shows the schematic of a production process with machines $A, B$ and $C$. An input job needs to be pre-processed either by $A$ or by $B$ before it is fed to $C...
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The circuit shown in figure was at steady state for $t < 0$ with the switch at position $‘A’$. The switch is thrown to position $‘B’$ at time $t=0$. The voltage V(volts)...
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The average real power in watts delivered to a load impedance $Z_L=(4-j2)\Omega$ by an ideal current source $i(t)=4\sin(\omega t+20^\circ)A $ is ____________.
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Time domain expressions for the voltage $v_1(t)$ and $v_2(t)$ are given as$$v_1(t)=V_m\sin(10t-130^\circ)\; and\; v_2(t)=V_m\cos(10t+10^\circ)$$Which one of the following...
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A pHelectrode obeys Nernst equation and is being operated at $25^\circ C$. The change in the open circuit voltage in millivolts across the electrode for a pH change from ...
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The pressure and velocity at the throat of a Venturi tube, measuring the flow of a liquid, are related to the upstream pressure and velocity, respectively, as follows:pre...
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Semiconductor strain gages typically have much higher gage factors than those of metallic strain gages, primarily due to:higher temperature sensitivityhigher Poisson’s ra...
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For a rotameter, which one of the following statements is $TRUE$?the weight of the float is balanced by the buoyancy and the drag force acting on the floatthe velocity of...
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For the op-amp shown in the figure, the bias currents are $I_{b1}=450\;nA$ and $I_{b2}=350\;nA$. The values of the input bias current $(I_B)$ and the input offset current...
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The amplifier in the figure has gain of $-10$ and input resistance of $50\;k\Omega$. The values of $R_i$ and $R_f$ are:$R_i=500\;k\Omega, R_f=50\;k\Omega$$R_i=50\;k\Omega...
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For the circuit shown in the figure assume ideal diodes with zero forward resistance and zero forward voltage drop. The current through the diode $D_2$ in $mA$ is _______...
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The system function of an LTI system is given by$$H(Z)=\frac{1-\frac{1}{3}Z^{-1}}{1-\frac{1}{4}Z^{-1}}$$The above system can have stable inverse if the region of converge...
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The figure is a logic circuit with inputs $A$ and $B$ and output $Y.V_{95}=+5\;V$. The circuit is of type$NOR$$AND$$OR$$NAND$
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The impulse response of an LTI system is given as:$h[n]=\left\{ \begin{array}{rcl} \frac{\omega_c}{\pi} & n=0\\ \frac{\sin \omega_cn}{\pi n} & n\neq 0 \end{array}\right.$...
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A discrete-time signal $x[n]$ is obtained by sampling an analog signal at $10\;kHz$. The signal $x[n]$ is filtered by a system with impulse response $h[n]=0.5${$ \delta [...
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A full duplex binary $FSK$ transmission is made through a channel of bandwidth $10\;kHz$. In each direction of transmission the two carriers used for the two states are s...