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82
GATE ECE 2024 | GA Question: 3
​​​​Five years ago, the ratio of Aman's age to his father's age was $1: 4$, and five years from now, the ratio will be $2:5$. What was his father's age when Aman was born? $28$ years $30$ years $35$ years $32$ years
​​​​Five years ago, the ratio of Aman's age to his father's age was $1: 4$, and five years from now, the ratio will be $2:5$. What was his father's age when Aman ...
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1 answer
83
GATE ECE 2009 | Question: 58
Consider the CMOS circuit shown, where the gate voltage $V_{G}$ of the $\text{n-MOSFET}$ is increased from zero, while the gate voltage of the $\text{p-MOSFET}$ is kept constant at $3 \mathrm{~V}$ ... $4-\frac{\sqrt{3}}{2} \mathrm{~V}$ $4+\frac{\sqrt{3}}{2} \mathrm{~V}$
Consider the CMOS circuit shown, where the gate voltage $V_{G}$ of the $\text{n-MOSFET}$ is increased from zero, while the gate voltage of the $\text{p-MOSFET}$ is kept c...
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87
GATE ECE 2017 Set 1 | Question: 2
The rank of the matrix $\textbf{M} = \begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$ is $0$ $1$ $2$ $3$
The rank of the matrix $$\textbf{M} = \begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$$ is$0$$1$$2$$3$
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88
GATE ECE 2012 | Question: 32
The state variable description of an LTI system is given by ... $a_1\neq 0,a_2=0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3=0$ $a_1\neq 0,a_2\neq0,a_3=0$
The state variable description of an LTI system is given by$$\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \dot{x_3} \end{pmatrix}=\begin{pmatrix} 0 & a_1 & 0\\ 0 & 0 & a_2\\a_...
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91
GATE ECE 2024 | Question: 2
​​​​​In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$ $12 \mathrm{~dB} /$ octave $6 \mathrm{~dB} /$ octave $20 \mathrm{~dB} /$ octave $10 \mathrm{~dB} /$ octave
​​​​​In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$$12 \mathrm{~dB} /$ octave$6 \mathrm{~dB} /$ octave$20 \ma...
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92
GATE ECE 2017 Set 1 | Question: 14
The Miller effect in the context of a Common Emitter amplifier explains An increase in the low-frequency cutoff frequency An increase in the high-frequency cutoff frequency A decrease in the low-frequency cutoff frequency A decrease in the high -frequency cutoff frequency
The Miller effect in the context of a Common Emitter amplifier explainsAn increase in the low-frequency cutoff frequencyAn increase in the high-frequency cutoff frequency...
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93
GATE ECE 2024 | Question: 1
The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ ...
The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ are real constants determined by the init...
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95
GATE ECE 2004 | Question: 56
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops. The $2$-input gate is a NAND gate a NOR gate an OR gate an AND gate
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops.The $2$-input gate isa NAND gatea NOR gat...
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100
GATE ECE 2024 | Question: 7
In the circuit below, assume that the long channel $\text{NMOS}$ transistor is biased in saturation. The small signal trans-conductance of the transistor is $g_{m}$ ...
​​​​In the circuit below, assume that the long channel $\text{NMOS}$ transistor is biased in saturation. The small signal trans-conductance of the transistor is $...
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101
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$$36$
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104
GATE ECE 2014 Set 2 | Question: 23
Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index ($\mu$) when the maximum and minimum values of the envelope, respectively, are $3$ V and $1$ V, is ___________.
Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index ($\mu$) when the maximum and minimum values of the envelope, respectively...
1 votes
2 answers
105
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$$3$$7$$9$$11$
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107
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 $\_\_\_\_\_\_$.
0 votes
1 answer
110
GATE ECE 2023 | Question: 28
Let $\boldsymbol{x}$ be an $n \times 1$ real column vector with length $l=\sqrt{\boldsymbol{x}^{T} \boldsymbol{x}}$ The trace of the matrix $P=\boldsymbol{x} \boldsymbol{x}^{T}$ is $l^{2}$ $\frac{l^{2}}{4}$ $l$ $\frac{l^{2}}{2}$
Let $\boldsymbol{x}$ be an $n \times 1$ real column vector with length $l=\sqrt{\boldsymbol{x}^{T} \boldsymbol{x}}$ The trace of the matrix $P=\boldsymbol{x} \boldsymbol{...
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113
GATE ECE 2022 | Question: 1
Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}$ denote the unit vectors along the $x - $axis and the $y - $ ... $0$ $1$ $8 + 2 \pi$ $ - 1$
Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}...
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114
GATE ECE 2024 | Question: 27
​​​​​Consider a unity negative feedback control system with forward path gain $G(s)=\frac{K}{(s+1)(s+2)(s+3)}$ as shown. The impulse response of the closed-loop system decays faster than $e^{-t}$ if $\_\_\_\_\_\_$. $1 \leq K \leq 5$ $7 \leq K \leq 21$ $-4 \leq K \leq-1$ $-24 \leq K \leq-6$
​​​​​Consider a unity negative feedback control system with forward path gain $G(s)=\frac{K}{(s+1)(s+2)(s+3)}$ as shown.The impulse response of the closed-loop ...
2 votes
1 answer
116
GATE ECE 2018 | Question: 9
A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by $F=\overline{A}\:.\overline{B}\:.\overline{C}+\overline{A}\:.B\:.\overline{C}+A\:.\overline{B}\:.\overline{C}$ ...
A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by$$F=\overline{A}\:.\overline{B}\:.\overline{C}...
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119
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 $\_\_\_\_\_\_\_$.
3 votes
1 answer
120
GATE ECE 2023 | GA Question: 1
“I cannot support this proposal. My _________ will not permit it.” conscious consensus conscience consent
“I cannot support this proposal. My _________ will not permit it.”consciousconsensusconscienceconsent
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