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Recent questions tagged numerical-answers

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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 decimal places).
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 decimal plac...
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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).
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 $\frac{1}{4}, 1$, and -2 . The value of $\left|P^{-1}\right|$ is (rounded off to nearest integer).
A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\frac{1}{4}, 1$, and -2 . The value of $\left|P^{-1}\right|$ is (rounded off to nearest integer).
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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).
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: 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 A (rounded off to one decimal place).
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 A (round...
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GATE IN 2024 | Question: 23
The switch in the following figure has been closed for a long time $(t
The switch in the following figure has been closed for a long time $(t
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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
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
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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 between $\mathrm{A}$ and $\mathrm{B}$ is $\mathrm{k} \Omega$ (rounded off to nearest integer).
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 bet...
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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).
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 of $\alpha$ is (rounded off to nearest integer). Note: The poles are marked with $x$ in the figure.
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: 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 $\mathrm{V}$ (rounded off to one decimal place).
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 $\mathrm{V}$ (rounded of...
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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 transformer at $75 \%$ of the full load and 0.8 power factor is $\%$ (rounded off to one decimal place).
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 transformer...
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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 the stator impedance, the slip at the maximum torque is $\%$ (rounded off to two decimal places).
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: 55
A random variable $X$ has a probability density function \[ f_{X}(x)=\left\{\begin{array}{cc} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{array}\right. \] The probability of $X>2$ is (rounded off to three decimal places).
A random variable $X$ has a probability density function\[f_{X}(x)=\left\{\begin{array}{cc}e^{-x}, & x \geq 0 \\0, & \text { otherwise }\end{array}\right.\]The probabilit...
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GATE IN 2022 | Question: 15
An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The minimum number of bits (in integer) in the output is _________
An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The m...
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GATE IN 2022 | Question: 16
Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-bit word, the bit-duration (in microseconds) is __________ (round off to two decimal places)
Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-...
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GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
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GATE IN 2022 | Question: 19
A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one decimal place)
A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one ...
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GATE IN 2022 | Question: 22
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is ____________ (round off to two decimal places)
A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...
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GATE IN 2022 | Question: 23
In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round off to two decimal places)
In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round o...
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GATE IN 2022 | Question: 24
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value of the next approximation $x_{1}$ is ________ (round off to two decimal places)
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value...
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