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Recent questions tagged numerical-answers

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GATE IN 2024 | GA | Question: 4
​​​​​If the sum of the first $20$ consecutive positive odd numbers is divided by $20^{2}$, the result is$1$$20$$2$$1 / 2$
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GATE IN 2024 | GA | Question: 10
​​​​Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. ...
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GATE IN 2024 | Question: 3
A discrete-time sequence is given by $x[n]=[1,2,3,4]$ for $0 \leq n \leq 3$. The zero lag auto-correlation value of $x[n]$ is$1$$10$$20$$30$
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GATE IN 2024 | Question: 5
The capacitor shown in the figure has parallel plates, with each plate having an area $A$. The thickness of the dielectric materials are $d_{1}$ and $d_{2}$ and their rel...
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GATE IN 2024 | Question: 11
A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is $\_\_\_\_\_$ $\mathrm{mA} /{ }^{\circ} \mathrm{C}$ (rounded off to two...
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GATE IN 2024 | Question: 12
Consider a filter defined by the difference equation$$ y[n]-0.5 y[n-2]=a x[n-4] $$where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude r...
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GATE IN 2024 | Question: 13
Consider the circuit shown in the figure.The CMOS digital logic circuit has infinite input impedance. Assume the opamp is ideal. A $1.8 \mathrm{~V}$ Zener diode with a mi...
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GATE IN 2024 | Question: 14
Figure shows an amplifier using an NMOS transistor. Assume that the transistor is in saturation with device parameters, $\mu_{n} C_{\text{o x}}=250 \mu \mathrm{A} / \math...
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GATE IN 2024 | Question: 15
The number of complex multiplications required for computing a $16$-point DFT using the decimation-in-time radix-$2$ FFT is $\_\_\_\_\_\_\_$ (in integer).
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GATE IN 2024 | Question: 16
A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\dfrac{1}{4}, 1$, and $-2$. The value of $\mid P^{-1}\mid$ is $\_\_\_\_\_\_$ (rounded off to nearest int...
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GATE IN 2024 | Question: 17
The Nyquist sampling frequency for $x(t)=10 \sin ^{2}(200 \pi t)$ is $\_\_\_\_\_\_\_ \mathrm{~Hz}$ (rounded off to nearest integer).
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GATE IN 2024 | Question: 18
The resistance of a $20 \mathrm{~k} \Omega$ resistor is measured six consecutive times using an LCR meter. The first five readings are $19 \mathrm{~k} \Omega, 18 \mathrm{...
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GATE IN 2024 | Question: 19
Consider the readout circuit of a piezoelectric sensor shown in the figure.When the piezoelectric sensor generates a charge $q_{p}$, the resulting change in voltage $\mat...
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GATE IN 2024 | Question: 20
The voltage applied and the current drawn by a circuit are$$ \begin{array}{c} v(t)=95+200 \cos (120 \pi t)+90 \cos \left(360 \pi t-60^{\circ}\right) \mathrm{V} \\i(t)=4 \...
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GATE IN 2024 | Question: 21
The current $i(t)$ drawn by a circuit is given as$$i(t)=4+30 \cos (t)-20 \sin (t)+15 \cos (3 t)-10 \sin (3 t) \mathrm{A}$$The root-mean-square value of $i(t)$ is $\_\_\_\...
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GATE IN 2024 | Question: 22
A linear potentiometer $(0-10 \mathrm{k} \Omega)$ is used to measure the water level as shown in the figure. The resistance between $\mathrm{A}$ and $\mathrm{C}$ varies l...
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GATE IN 2024 | Question: 23
The switch in the following figure has been closed for a long time $(t<0)$. It is opened at $t=0$ seconds. The value of $d v_{0} / d t$ at $t=0^{+}$is $\_\_\_\_\_\_ ~ \ma...
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GATE IN 2024 | Question: 24
Consider a system given by the following first order differential equation:$$ \frac{d y}{d t}=y+2 t-t^{2} $$where, $y(0)=1$ and $0 \leq t<\infty$. Using a step size $h=0....
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GATE IN 2024 | Question: 25
Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...
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GATE IN 2024 | Question: 26
​A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $\mathbf{J}=k s^{2}$, where $k$ is a constant, $s$ is the radial...
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GATE IN 2024 | Question: 29
​​​​​In the bridge circuit shown in the figure, under balanced condition, the values of $R$ and $C$ respectively, are$1.010 ~\Omega$ and $19.802 ~\mu \mathrm{F}$$9.901 ~\...
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GATE IN 2024 | Question: 33
​​​In the figure shown, $R=1 \mathrm{~k} \Omega$ and $C=0.1 ~\mu \mathrm{F}$. For a dc gain of $-10$, the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal p...
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GATE IN 2024 | Question: 34
​​​​Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ i...
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GATE IN 2024 | Question: 40
The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient ...
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GATE IN 2024 | Question: 41
In the figure shown, $\mathrm{R}=4.5 \mathrm{~k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{~k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance b...
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GATE IN 2024 | Question: 42
Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal...
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GATE IN 2024 | Question: 43
The $4$-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the $4$ -point circular...
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GATE IN 2024 | Question: 44
Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\_\_\_\_\_ ~\Omega$ (rounded off to nearest integer).
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GATE IN 2024 | Question: 45
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value ...
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GATE IN 2024 | Question: 46
A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{~pF}$ and $\mathrm{R}_{\text {wire }}=10 ~\Omega$ is used to connect the inductive sensors as shown in the f...
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GATE IN 2024 | Question: 47
In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in ...
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GATE IN 2024 | Question: 48
An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 ~\mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $5...
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GATE IN 2024 | Question: 49
In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\_\_\_\_\_~\mathrm{V}$ ...
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GATE IN 2024 | Question: 50
In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the p...
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GATE IN 2024 | Question: 51
A $50 \mathrm{~kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transforme...
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GATE IN 2024 | Question: 52
A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting...
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GATE IN 2024 | Question: 53
Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{~mH}$. When connected in series-opposing configurat...
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GATE IN 2024 | Question: 54
The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is$$y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...
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GATE IN 2024 | Question: 55
A random variable $X$ has a probability density function$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$The probability of $X>2$ is $...
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GATE IN 2023 | Question: 5
Capacitance ' $\text{C}$ ' of a parallel plate structure is calculated as $20 ~ \mathrm{pF}$ using $C=\frac{\varepsilon_0 \varepsilon_r A}{d}$, where $\varepsilon_o$ is t...
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