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Most viewed questions in Engineering Mathematics
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votes
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41
GATE2012-32
What is the rank of the following matrix? $\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$ $0$ $1$ $2$ $3$
What is the rank of the following matrix?$$\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$$$0$$1$$2$$3$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
42
GATE BT 2021 | Question: 41
If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________
If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatebt-2021
numerical-answers
calculus
geometry
triangles
area
+
–
0
votes
0
answers
43
GATE2015-33
Consider the following infinite series: $1+ r+r^2 +r^3+ \dots \dots \infty$ If $r = 0.3$, then the sum of this infinite series is ____________
Consider the following infinite series:$$1+ r+r^2 +r^3+ \dots \dots \infty$$ If $r = 0.3$, then the sum of this infinite series is ____________
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
numerical-answers
calculus
sequences-and-series
infinite-series
+
–
0
votes
0
answers
44
GATE2015-34
$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$ The system of linear equations in two variables shown above will have infinite solutions, if and only if, $b$ is equal to _________
$$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$$ The system of linear equations in two variables shown above will have infinite solutions, if and onl...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2015
numerical-answers
linear-algebra
system-of-equations
+
–
0
votes
0
answers
45
GATE2013-38
Evaluate $\underset{x\rightarrow\infty }{\lim}x\tan\frac{1}{x}$ $\infty$ $1$ $0$ $-1$
Evaluate $\underset{x\rightarrow\infty }{\lim}x\tan\frac{1}{x}$$\infty$$1$$0$$-1$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013
calculus
limits
+
–
0
votes
0
answers
46
GATE2020: 50
A function $f$ is given as : $f(X)=4X-X^{2}$ The function $f$ is maximized when $X$ is equal to _________________.
A function $f$ is given as :$$f(X)=4X-X^{2}$$The function $f$ is maximized when $X$ is equal to _________________.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Calculus
gate2020
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
47
GATE2014-3
The solution for the following set of equations is, $5x+4y+102=13$ $x+3y+z=7$ $4x2y+z=0$ $x=2,y=1,z=1$ $x=1,y=2,z=0$ $x=1,y=0,z=2$ $x=0,y=1,z=2$
The solution for the following set of equations is,$$5x+4y+102=13$$$$x+3y+z=7$$$$4x2y+z=0$$$x=2,y=1,z=1$$x=1,y=2,z=0$$x=1,y=0,z=2$$x=0,y=1,z=2$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014
linear-algebra
system-of-equations
+
–
0
votes
0
answers
48
GATE2018-41
Calculate the following integral (up to two decimal places) $\displaystyle \int_0^1 (x + 3)(x + 1)dx = \text{ ___________}$
Calculate the following integral (up to two decimal places)$$\displaystyle \int_0^1 (x + 3)(x + 1)dx = \text{ ___________}$$
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018
numerical-answers
calculus
definite-integrals
+
–
0
votes
0
answers
49
GATE BT 2021 | Question: 5
The Cartesian coordinates $(x,y)$ of a point $A$ with polar coordinates $\left ( 4, \pi/4 \right)$ is $ \left( \sqrt{3}, 2 \sqrt{2} \right ) \\$ $ \left( 2, 2 \sqrt{3} \right ) \\$ $ \left( 2\sqrt{2}, \sqrt{3} \right ) \\$ $ \left( 2 \sqrt{2}, 2 \sqrt{2} \right )$
The Cartesian coordinates $(x,y)$ of a point $A$ with polar coordinates $\left ( 4, \pi/4 \right)$ is$ \left( \sqrt{3}, 2 \sqrt{2} \right ) \\$$ \left( 2, 2 \sqrt{3} \rig...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatebt-2021
calculus
cartesian-coordinates
+
–
0
votes
0
answers
50
GATE2017-47
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2017
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
51
GATE2013-41
The solution to $\frac {dy}{dx}+y \cot x=\csc x$ is $y=(c+x)\cot x$ $y=(c+x)\csc x$ $y=(c+x)\csc x\cot x$ $y=(c+x)\frac{\csc x}{\cot x}$
The solution to $\frac {dy}{dx}+y \cot x=\csc x$ is$y=(c+x)\cot x$$y=(c+x)\csc x$$y=(c+x)\csc x\cot x$$y=(c+x)\frac{\csc x}{\cot x}$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2013
differential-equations
+
–
0
votes
0
answers
52
GATE2014-4
The limit of the function $e^{-2t}\sin (t)$ as t $\rightarrow\infty$ so, is
The limit of the function $e^{-2t}\sin (t)$ as t $\rightarrow\infty$ so, is
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
limits
numerical-answers
+
–
0
votes
0
answers
53
GATE2013-40
The solution of the following set of equations is $x+2y+3z=20$ $7x+3y+z=13$ $x+6y+2z=0$ $x=-2, y=2, z=8$ $x=2, y=-3, z=8$ $x=2, y=3, z=-8$ $x=8, y=2, z=-3$
The solution of the following set of equations is$$x+2y+3z=20$$$$7x+3y+z=13$$$$x+6y+2z=0$$$x=-2, y=2, z=8$$x=2, y=-3, z=8$$x=2, y=3, z=-8$$x=8, y=2, z=-3$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013
linear-algebra
matrices
system-of-equations
+
–
0
votes
0
answers
54
GATE2013-20
One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is $2$ $4$ $6$ $8$
One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is$2$$4$$6$$8$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
55
GATE BT 2021 | Question: 49
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatebt-2021
numerical-answers
calculus
definite-integrals
+
–
0
votes
0
answers
56
GATE2017-16
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2017
differential-equations
numerical-answers
+
–
0
votes
0
answers
57
GATE2014-28
Which of the following statements is true for the series given below? $S_n=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\dots+\frac{1}{\sqrt{n}} $ $S_n$ converges to $\log(\sqrt{n})$ $S_n$ converges to $\sqrt{n}$ $S_n$ converges to $\exp(\sqrt{n})$ $S_n$ diverges
Which of the following statements is true for the series given below?$$S_n=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\dots+\frac{1}{\sqrt{n}} $$$S_n$ con...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
converges
+
–
0
votes
0
answers
58
GATE2014-29
The graph of the function $F(x) =\frac{x}{k_1x^2+k_2x+1}$ for $0<x<\infty$ is
The graph of the function $F(x) =\frac{x}{k_1x^2+k_2x+1}$ for $0<x<\infty$ is
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
functions
curves
+
–
0
votes
0
answers
59
GATE2013-18
If $u=\log (e^x+e^y),$ then $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=$ $e^x+e^y$ $e^x-e^y$ $\frac{1}{e^x+e^y}$ $1$
If $u=\log (e^x+e^y),$ then $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=$$e^x+e^y$$e^x-e^y$$\frac{1}{e^x+e^y}$$1$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013
calculus
partial-derivatives
+
–
0
votes
0
answers
60
GATE2019: 50
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ ...
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Numerical Methods
gate2019
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
61
GATE2014-27
If $y =x^x$, then $\frac{dy}{dx}$ is $x^x(x-1)$ $x^{x-1}$ $x^x(1 + \log x)$ $e^x(1 + \log x)$
If $y =x^x$, then $\frac{dy}{dx}$ is$x^x(x-1)$$x^{x-1}$$x^x(1 + \log x)$$e^x(1 + \log x)$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
derivatives
+
–
0
votes
0
answers
62
GATE2017-28
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
numerical-answers
calculus
vector-calculus
vector-identities
+
–
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