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1
GATE ECE 2024 | GA Question: 5
The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is $13$ $17$ $3$ $11$
The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is$13$$17$$3$$11$
1 votes
2 answers
2
GATE ECE 2008 | Question: 28
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is $\exp (\pi)$ $0.5 \exp (\pi)$ $\exp (\pi)+1$ $\exp (\pi)-1$
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is$\exp (\pi)$$0.5 \exp (\pi)$$\exp (\pi)+1$$\exp (\pi)-1$...
0 votes
1 answer
4
GATE ECE 2024 | Question: 46
​​​​​The radian frequency value(s) for which the discrete time sinusoidal signal $x[n]=A \cos (\Omega n+\pi / 3)$ has a period of $40$ is/are $\_\_\_\_\_\_$. $0.15 \pi$ $0.225 \pi$ $0.3 \pi$ $0.45 \pi$
​​​​​The radian frequency value(s) for which the discrete time sinusoidal signal $x[n]=A \cos (\Omega n+\pi / 3)$ has a period of $40$ is/are $\_\_\_\_\_\_$.$0....
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5
GATE ECE 2023 | Question: 3
Let $w^4=16 j$. Which of the following cannot be a value of $w$ ? $2 e^{\frac{j 2 \pi}{8}}$ $2 e^{\frac{j \pi}{8}}$ $2 e^{\frac{j5 \pi}{8}}$ $2 e^{\frac{j9 \pi}{8}}$
Let $w^4=16 j$. Which of the following cannot be a value of $w$ ?$2 e^{\frac{j 2 \pi}{8}}$$2 e^{\frac{j \pi}{8}}$$2 e^{\frac{j5 \pi}{8}}$$2 e^{\frac{j9 \pi}{8}}$
0 votes
1 answer
7
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{...
0 votes
1 answer
8
GATE ECE 2023 | Question: 45
The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).
The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).
0 votes
1 answer
9
GATE ECE 2023 | Question: 53
In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of $1 \; \mathrm{MHz}$, the frequency of signal $\mathrm{Q}_2$ in $\mathrm{kHz}$, is __________ (rounded off to the nearest integer).
In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of $1 \; \mathrm{MHz}$, the frequency of signal $\mathrm{Q}_2$ in $\mathrm{kH...
0 votes
1 answer
11
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...
0 votes
1 answer
12
GATE ECE 2005 | Question: 57
The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of the counter is $Q_{2} \; Q_{1} \; Q_{0}=011$, then its next state $\left(Q_{2} \; Q_{1} \; Q_{n}\right)$ will be $010$ $100$ $111$ $101$
The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of the counter is $Q_{2} \; Q_{1} \; Q_{0}=011$, then its next stat...
1 votes
1 answer
15
GATE ECE 2007 | Question: 44
The following binary values were applied to the $\mathrm{X}$ and $\mathrm{Y}$ inputs of the NAND latch shown in the figure in the sequence indicated below: \[ \mathrm{X}=0, \mathrm{Y}=1 ; \quad \mathrm{X}=0, \mathrm{Y}=0 ; \quad \mathrm{X}=1, \mathrm{Y}=1 \ ...
The following binary values were applied to the $\mathrm{X}$ and $\mathrm{Y}$ inputs of the NAND latch shown in the figure in the sequence indicated below:\[ \mathrm{X}=0...
1 votes
1 answer
16
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...
0 votes
1 answer
17
GATE ECE 1992 | Question 1.29
Which of the following signals is/are periodic? $\mathrm{S}(t)=\cos 2 t+\cos 3 t+\cos 5 t$ $\mathrm{S}(t)=\exp (j 8 \pi t)$ $S(t)=\exp (-7 t) \sin 10 \pi t$ $S(t)=\cos 2 t \cos 4 t$
Which of the following signals is/are periodic?$\mathrm{S}(t)=\cos 2 t+\cos 3 t+\cos 5 t$$\mathrm{S}(t)=\exp (j 8 \pi t)$$S(t)=\exp (-7 t) \sin 10 \pi t$$S(t)=\cos 2 t \c...
1 votes
1 answer
18
GATE ECE 2011 | Question: 16
The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by $G(s) H(s)=k \frac{s(s+1)}{(s+2)(s+3)}$ $G(s) H(s)=k \frac{(s+1)}{s(s+2)(s+3)^2}$ $G(s) H(s)=k \frac{1}{s(s-1)(s+2)(s+3)}$ $G(s) H(s)=k \frac{(s+1)}{s(s+2)(s+3)}$
The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by$G(s) H(s)=k \frac{s(s+1)}{(s+2)(s+3)}$$G(s) H(s)=k...
1 votes
1 answer
19
GATE ECE 2011 | Question: 18
If the unit step response of a network is $\left(1-e^{-\alpha t}\right)$, then its unit impulse response is $\alpha e^{-\alpha t}$ $\alpha^{-1} e^{-\alpha t}$ $\left(1-\alpha^{-1}\right) e^{-\alpha t}$ $(1-\alpha) e^{-\alpha t}$
If the unit step response of a network is $\left(1-e^{-\alpha t}\right)$, then its unit impulse response is$\alpha e^{-\alpha t}$$\alpha^{-1} e^{-\alpha t}$$\left(1-\alph...
2 votes
1 answer
21
GATE ECE 2022 | Question: 17
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation. $x + z + xy$ $(x + y)(x + z)$ $x + xy + yz$ $x + xz + xy$
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation.$x + z + xy$$(x + y)(x + z...
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25
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 ...
0 votes
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26
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$$36$
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30
GATE ECE 2024 | GA Question: 9
Examples of mirror and water reflections are shown in the figures below: An object appears as the following image after first reflecting in a mirror and then reflecting on water. The original object is
Examples of mirror and water reflections are shown in the figures below: An object appears as the following image after first reflecting in a mirror and then reflecting o...
0 votes
0 answers
32
GATE ECE 2024 | Question: 1
The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ ...
The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ are real constants determined by the init...
0 votes
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33
GATE ECE 2024 | Question: 2
​​​​​In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$ $12 \mathrm{~dB} /$ octave $6 \mathrm{~dB} /$ octave $20 \mathrm{~dB} /$ octave $10 \mathrm{~dB} /$ octave
​​​​​In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$$12 \mathrm{~dB} /$ octave$6 \mathrm{~dB} /$ octave$20 \ma...
0 votes
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38
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 $...
0 votes
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40
GATE ECE 2024 | Question: 9
​​​​For the Boolean function \[ F(A, B, C, D)=\sum m(0,2,5,7,8,10,12,13,14,15) \text {, } \] the essential prime implicants are $\_\_\_\_\_\_$. $B D, \bar{B} \bar{D}$ $B D, A B$ $A B, \bar{B} \bar{D}$ $B D, \bar{B} \bar{D}, A B$
​​​​For the Boolean function\[F(A, B, C, D)=\sum m(0,2,5,7,8,10,12,13,14,15) \text {, }\]the essential prime implicants are $\_\_\_\_\_\_$.$B D, \bar{B} \bar{D}$$...
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