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Recent questions tagged numerical-answers

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GATE ECE 2024 | GA Question: 4
​​​​For a real number $x>1$, \[ \frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1 \] The value of $x$ is $4$ $12$ $24$ $36$
​​​​For a real number $x>1$,\[\frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1\]The value of $x$ is$4$$12$$24$$36$
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GATE ECE 2024 | Question: 19
In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.
In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.
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GATE ECE 2024 | Question: 21
In the given circuit, the current $I_{x}$ (in $m A$ ) is $\_\_\_\_\_\_\_\_$.
In the given circuit, the current $I_{x}$ (in $m A$ ) is $\_\_\_\_\_\_\_\_$.
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GATE ECE 2024 | Question: 22
In the circuit given below, the switch $\text{S}$ was kept open for a sufficiently long time and is closed at time $t=0$. The time constant (in seconds) of the circuit for $t>0$ is $\_\_\_\_\_\_$.
In the circuit given below, the switch $\text{S}$ was kept open for a sufficiently long time and is closed at time $t=0$. The time constant (in seconds) of the circuit fo...
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GATE ECE 2024 | Question: 23
Suppose $\text{X}$ and $\text{Y}$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$. The probability that $\text{X} \geq \text{Y}$ is $\_\_\_\_\_\_$.
Suppose $\text{X}$ and $\text{Y}$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$. The probability tha...
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GATE ECE 2024 | Question: 24
A source transmits symbols from an alphabet of size $16$. The value of maximum achievable entropy (in bits) is $\_\_\_\_\_\_$.
A source transmits symbols from an alphabet of size $16$. The value of maximum achievable entropy (in bits) is $\_\_\_\_\_\_$.
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GATE ECE 2024 | Question: 50
For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is $\_\_\_\_\_\_$.
For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is $\_\_\_\_\_\_$.
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GATE ECE 2024 | Question: 52
In the network shown below, maximum power is to be transferred to the load $R_{L}$. The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.
In the network shown below, maximum power is to be transferred to the load $R_{L}$.The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.
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GATE ECE 2022 | Question: 22
A simple closed path $C$ in the complex plane is shown in the figure. If $\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$ where $i = \sqrt{-1},$ then the value of $A$ is _________ (rounded off to two decimal places).
A simple closed path $C$ in the complex plane is shown in the figure. If$$\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$$where $i = \sqrt{-1},$ then the value of $...
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GATE ECE 2022 | Question: 23
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}(t),$ then $\displaystyle \lim_{t \rightarrow \infty} y(t) =$ ______________ (rounded off to one decimal place).
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function.If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x...
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GATE ECE 2022 | Question: 25
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the raw (uncoded) data rate is ____________ mega-bits per second (rounded off to one decimal place).
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the ...
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GATE ECE 2022 | Question: 43
The value of the integral $ \iint_{D} 3(x^{2} + y^{2})dxdy,$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).
The value of the integral$$ \iint_{D} 3(x^{2} + y^{2})dxdy,$$where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest in...
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GATE ECE 2022 | Question: 47
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{out}}}{\partial V_{\text{in}}}$ is ____________ (rounded off to two decimal places).
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{ou...
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GATE ECE 2022 | Question: 48
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).
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GATE ECE 2022 | Question: 50
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and $d(t),$ ... $e (\infty),$ due to a unit step disturbance $d(t),$ is __________ (rounded off to two decimal places).
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and...
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GATE ECE 2021 | Question: 16
If the vectors $(1.0,\:-1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
If the vectors $(1.0,\:-1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
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