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Hot questions in Engineering Mathematics
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21
GATE Electrical 2019 | Question: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are ... True and Statement $2$ is false Statement $2$ is true and Statement $1$ is false Both the Statements are true Both the statements are false
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \e...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ee
linear-algebra
matrices
eigen-values
eigen-vectors
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–
0
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0
answers
22
GATE Electrical 2019 | Question: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$ $3te^{-t}+e^{-t}$ $3e^{-t}$ $2te^{-t}+e^{-t}$ $4te^{-t}+e^{-t}$
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$$3te^{-t}+e^{-t}$$3e^{-t}$$2te^{-t}+e^{-t}$$4te^{-t}+e^{-t}$
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Transform Theory
gate2019-ee
transform-theory
laplace-transform
inverse-laplace-transform
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–
0
votes
0
answers
23
GATE Electrical 2019 | Question: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}-1}{z} \\ $ $\frac{z^{2}-1}{z+2} \\ $ $\frac{z^{2}-1}{z-0.5} \\ $ $\frac{z^{2}-1}{z+j0.5} $
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ?$\frac{z^{2}-1}{z} \\ $$\frac{z^{2}-1}{z+2} \\ $$\frac{z^{2}-1}{z-0.5} \\ $$\frac{z^...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Complex Variables
gate2019-ee
complex-variables
analytic-functions
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–
0
votes
0
answers
24
GATE Electrical 2019 | Question: 13
The output response of a system is denoted as $y(t)$, and its Laplace transform is given by $Y(s)=\frac{10}{s(s^{2}+s+100 \sqrt{2})}$ The steady state value of $y(t)$ is $\frac{1}{10 \sqrt{2}} \\ $ $10 \sqrt{2} \\ $ $\frac{1}{100 \sqrt{2}} \\ $ $100 \sqrt{2}$
The output response of a system is denoted as $y(t)$, and its Laplace transform is given by $$Y(s)=\frac{10}{s(s^{2}+s+100 \sqrt{2})}$$ The steady state value of $y(t)$ i...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Transform Theory
gate2019-ee
transform-theory
laplace-transform
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–
0
votes
0
answers
25
GATE Electrical 2019 | Question: 3
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}}- C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;$ where $c \neq 0$ is known as heat equation wave equation Poisson’s equation Laplace equation
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}}- C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Differential Equations
gate2019-ee
differential-equations
partial-differential-equation
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–
0
votes
0
answers
26
GATE Electrical 2019 | Question: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-3,2)\rightarrow(2,6,2) \rightarrow(2,6,-1) $ is___________.
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ee
numerical-answers
calculus
line-integral
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–
0
votes
0
answers
27
GATE Electrical 2019 | Question: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ee
numerical-answers
calculus
divergence
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–
0
votes
0
answers
28
GATE Electrical 2019 | Question: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $$f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin ...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ee
calculus
fourier-series
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–
0
votes
0
answers
29
GATE Electrical 2019 | Question: 27
The closed-loop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counter-clockwise, is $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$
The closed-loop line integral $$\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$$evaluated Counter-clockwise, is $+8 j \pi$$-8 j \pi$$-4 j \pi$$+4 j \pi$
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Complex Variables
gate2019-ee
complex-variables
cauchys-integral-theorem
line-integral
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–
0
votes
1
answer
30
GATE Electrical 2015 Set 1 | Question: 29
Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is $5/11$ $1/2$ $7/13$ $6/11$
Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2015-ee-1
probability-and-statistics
probability
conditional-probability
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–
0
votes
0
answers
31
GATE Electrical 2012 | Question: 1
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that $\text{max}[X,Y]$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that $\text{max}[X,Y]$ is less than $1/2$ is$3/4$$9/16$$1...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Probability & Statistics
gate2012-ee
probability-and-statistics
probability
random-variable
uniform-distribution
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–
0
votes
0
answers
32
GATE Electrical 2012 | Question: 38
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $-2$ $2$ $1$ $0$
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of ...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Calculus
gate2012-ee
differential-equations
+
–
0
votes
0
answers
33
GATE Electrical 2012 | Question: 42
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is$1/4$$1/2$$1$$2$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Transform Theory
gate2012-ee
transform-theory
fourier-transform
+
–
0
votes
0
answers
34
GATE Electrical 2012 | Question: 41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
The state variable description of an LTI system is given by$$\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 & a_1 & 0 \\ 0 & 0 & a_2 \\ a_3 & 0 & 0 \...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Linear Algebra
gate2012-ee
linear-algebra
matrices
system-of-linear-equations
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–
0
votes
0
answers
35
GATE Electrical 2012 | Question: 37
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Probability & Statistics
gate2012-ee
probability-and-statistics
probability
+
–
0
votes
0
answers
36
GATE Electrical 2012 | Question: 2
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{- \pi/2}$ $e^{\pi/2}$ $x$ $1$
If $x=\sqrt{-1}$, then the value of $x^x$ is$e^{- \pi/2}$$e^{\pi/2}$$x$$1$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Complex Variables
gate2012-ee
complex-variables
+
–
0
votes
0
answers
37
GATE Electrical 2012 | Question: 3
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oint_c f(z) dz$ is $-2$ $-1$ $1$ $2$
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oi...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Complex Variables
gate2012-ee
complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
38
GATE Electrical 2012 | Question: 14
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is $x=t-\dfrac{1}{2} \\ $ $x=t^2-\dfrac{1}{2} \\ $ $x=\dfrac{t^2}{2} \\$ $x=\dfrac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is$x=t-\dfrac{1}{2} \\ $$x=t^2-\dfrac{1}{2} \\ $$x=\dfrac{t^2}{2} \\$$x...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Differential Equations
gate2012-ee
differential-equations
+
–
0
votes
0
answers
39
GATE Electrical 2012 | Question: 26
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is$15 \: \text...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Linear Algebra
gate2012-ee
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
40
GATE Electrical 2012 | Question: 27
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Calculus
gate2012-ee
calculus
maxima-minima
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