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Most answered questions in Engineering Mathematics
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GATE2020-ME-2: 4
The solution of $\dfrac{d^2y}{dt^2}-y=1,$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is $\dfrac{1}{s(s+1)(s-1)} \\$ $\dfrac{1}{s(s+1)} \\$ $\dfrac{1}{s(s-1)} \\$ $\dfrac{1}{s-1} \\$
The solution of $$\dfrac{d^2y}{dt^2}-y=1,$$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is$\dfrac{1}...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Differential Equations
gateme-2020-set2
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE2020-ME-2: 19
Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. The number of elements in $\textbf{E}$ is _________
Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. T...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Linear Algebra
gateme-2020-set2
numerical-answers
linear-algebra
eigen-values
+
–
0
answers
0
votes
GATE2020-ME-2: 26
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is $3\hat{i} – 3 \hat{j} - \hat{k} \\$ $- \dfrac{7}{3} \\$ $\dfrac{7}{3} \\ $ $7$
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is$3\hat{i} – 3 \hat{j} - \hat{k} \\$$-...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Calculus
gateme-2020-set2
calculus
vector-identities
directional-derivatives
+
–
0
answers
0
votes
GATE2020-ME-2: 27
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be $(3xy^2-y^3) +$ constant $(3x^2y^2-y^3) +$ constant $(x^3-3x^2 y) +$ constant $(3x^2y-y^3) +$ constant
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be$(3...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Calculus
gateme-2020-set2
calculus
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE2020-ME-2: 35
For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________ (round off to one decimal place).
For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end poin...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Numerical Methods
gateme-2020-set2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
+
–
0
answers
0
votes
#MADE EASY MOCK TEST GATE2021
The area common to both circles r=a$\sqrt{2}$ and r=2a cos$\theta$.
The area common to both circles r=a$\sqrt{2}$ and r=2a cos$\theta$.
Gokulan K
160
points
Gokulan K
asked
Sep 3, 2020
Calculus
#made-easy
mock-gate
2021
+
–
0
answers
0
votes
GATE MOCK TEST(MADE EASY)
The area enclosed between the circles r=2a cos$\theta$ and r=a$\sqrt{2}$.
The area enclosed between the circles r=2a cos$\theta$ and r=a$\sqrt{2}$.
Gokulan K
160
points
Gokulan K
asked
Sep 3, 2020
Calculus
#gate-mock-test
+
–
0
answers
0
votes
#GATE QUESTION BANK
The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.
The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.
Gokulan K
160
points
Gokulan K
asked
Jul 15, 2020
Numerical Methods
#gate-question-bank
+
–
0
answers
0
votes
GATE2020-ME-1: 1
Multiplication of real valued square matrices of same dimension is associative commutative always positive definite not always possible to compute
Multiplication of real valued square matrices of same dimension isassociativecommutativealways positive definitenot always possible to compute
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Linear Algebra
gateme-2020-set1
linear-algebra
matrices
+
–
0
answers
0
votes
GATE2020-ME-1: 2
The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is $\text{c} \\$ $\text{c + 1} \\$ $\dfrac{c}{c+1} \\$ $\dfrac{c+1}{c}$
The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is$\text{c} \\$$\text{c + 1} \\$$...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Calculus
gateme-2020-set1
calculus
limits
+
–
0
answers
0
votes
GATE2020-ME-1: 3
The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is $f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t \right ) \\$ $f\left ( t \right )=\dfrac{1}{\omega}\cos\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega}\sin\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega^{2}}\left ( 1-\sin\:\omega t \right )$
The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is$f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t ...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Differential Equations
gateme-2020-set1
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE2020-ME-1: 4
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane? $f\left ( z \right )=z^{2}$ $f\left ( z \right )=e^{z}$ $f\left ( z \right )=\sin z$ $f\left ( z \right )=\log z$
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane?$f\left ( z \right )=z^{2}$$f\left ( z \right ...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Calculus
gateme-2020-set1
calculus
complex-variables
+
–
0
answers
0
votes
GATE2020-ME-1: 19
For three vectors $\overrightarrow{A}=2\widehat{j}-3\widehat{k},\:\overrightarrow{B}=-2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}-\widehat{j},\:\text{where}\:\widehat{i},\:\widehat{j}\:\text{and}\:\widehat{k}$ are ... system, the value of $\left ( \overrightarrow{A}.\left ( \overrightarrow{B}\times \overrightarrow{C} \right )+6 \right )$ is __________.
For three vectors $\overrightarrow{A}=2\widehat{j}-3\widehat{k},\:\overrightarrow{B}=-2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}-\widehat{j},...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Engineering Mathematics
gateme-2020-set1
numerical-answers
engineering-mathematics
+
–
0
answers
0
votes
GATE2020-ME-1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields$0.914$$1.2...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Numerical Methods
gateme-2020-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
answers
0
votes
GATE2020-ME-1: 27
A vector field is defined as ... shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is $0$ $2\pi$ $4\pi$ $8\pi$
A vector field is defined as $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2}...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Calculus
gateme-2020-set1
calculus
vector-identities
+
–
0
answers
0
votes
GATE2020-ME-1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Engineering Mathematics
gateme-2020-set1
numerical-answers
engineering-mathematics
differential-equation
random-variables
+
–
0
answers
0
votes
GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as$$f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$$where $\psi...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Calculus
gateme-2020-set1
numerical-answers
calculus
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE2019 ME-2: 2
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is $\sqrt{2}$ $2$ $2 \sqrt{2}$ $4 \sqrt{2}$
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is$\sqrt{2}$$2$$2 \sqrt{2}$$4...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
directional-derivatives
+
–
0
answers
0
votes
GATE2019 ME-2: 18
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by $\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \\$ $\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} \\$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \\$ $\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \\$$\begin{bmatrix} -1 &...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Linear Algebra
gateme-2019-set2
linear-algebra
matrix-algebra
+
–
0
answers
0
votes
GATE2019 ME-2: 26
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $- \dfrac{\pi}{2} \\$ $\dfrac{\pi}{3} \\$ $\dfrac{\pi}{2} \\$ $\pi$
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemi...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
vector-identities
+
–
0
answers
0
votes
GATE2019 ME-2: 27
A diffferential equation is given as $x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$ The solution of the differential equation in terms of arbitrary constants $C_1$ and $C_2$ is $y=C_1x^2 +C_2 x+2 \\$ $y=\dfrac{C_1}{x^2} +C_2x+2 \\$ $y=C_1x^2+C_2x+4 \\$ $y=\dfrac{C_1}{x^2}+C_2x+4$
A diffferential equation is given as $$x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$$ The solution of the differential equation in terms of arbitrary constants $C_1$...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Engineering Mathematics
gateme-2019-set2
engineering-mathematics
differential-equation
+
–
0
answers
0
votes
GATE2019 ME-2: 28
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f'(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{Exact value - Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ ... $> 0.1 \% \text{ and } <1 \%$ $> 1 \% \text{ and } <5 \%$ $>5 \%$
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f’(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
derivatives
+
–
0
answers
0
votes
GATE2019 ME-2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at le...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Probability and Statistics
gateme-2019-set2
numerical-answers
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE2019 ME-1: 2
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis is $\dfrac{\pi}{4} \\$ $\dfrac{\pi}{2} \\$ ${\pi} \\$ $2 \pi$
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis ...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set1
calculus
area-under-curve
+
–
0
answers
0
votes
GATE2019 ME-1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Numerical Methods
gateme-2019-set1
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
answers
0
votes
GATE2019 ME-1: 26
The set of equations $\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$ has infinite solutions, if $a=$ $-3$ $3$ $4$ $-4$
The set of equations $$\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$$has infinite solutions, if $a=$$-3$$3$$4$$-4$
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Linear Algebra
gateme-2019-set1
linear-algebra
system-of-equations
+
–
0
answers
0
votes
GATE2019 ME-1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy-2x^2+2y^2+ \text{constant}$ $4y^2-4xy + \text{constant}$ $2x^2-2y^2+ xy + \text{constant}$ $-4xy+2y^2-2x^2+ \text{constant}$
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is$4...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Differential Equations
gateme-2019-set1
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE2019 ME-1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability di...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Probability and Statistics
gateme-2019-set1
probability-and-statistics
probability
uniform-distribution
+
–
0
answers
0
votes
GATE ME 2012 | Question: 55
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... the project remain the same critical path changes but the total duration to complete the project changes to $17$ days
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.$\begi...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
+
–
0
answers
1
votes
GATE ME 2012 | Question: 54
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... critical path for the project is $a-b-e-g-h$ $a-c-g-h$ $a-d-f-h$ $a-b-c-f-h$
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.$\begi...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
+
–
0
answers
0
votes
GATE ME 2012 | Question: 47
$x+2y+z=4$ $2x+y+2z=5$ $x-y+z=1$ The system of algebraic equations given above has a unique solution of $x=1$, $y=1$ and $z=1$ only the two solutions of $(x=1, y=1, z=1)$ and $(x=2, y=1, z=0)$ infinite number of solutions no feasible solution
$x+2y+z=4$$2x+y+2z=5$$x-y+z=1$The system of algebraic equations given above hasa unique solution of $x=1$, $y=1$ and $z=1$only the two solutions of $(x=1, y=1, z=1)$ and ...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Linear Algebra
gateme-2012
linear-algebra
system-of-equations
+
–
0
answers
0
votes
GATE ME 2012 | Question: 46
Consider the differential equation $x^2 \dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the differential equation is $x^2 \\$ $\sin \left (\dfrac{\pi x}{2} \right ) \\$ $e^x \sin \left (\dfrac{\pi x}{2} \right ) \\$ $e^{-x} \sin \left (\dfrac{\pi x}{2} \right) \\$
Consider the differential equation $x^2 \dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the diffe...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Differential Equations
gateme-2012
differential-equation
boundary-value-problems
+
–
0
answers
0
votes
GATE ME 2012 | Question: 45
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is $1/20$ $1/12$ $3/10$ $1/2$
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Probability and Statistics
gateme-2012
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE ME 2012 | Question: 36
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as $\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \end{pmatrix} \\$ ... $\begin{pmatrix} \dfrac{1}{\sqrt{5}} \\ \dfrac{2}{\sqrt{5}} \end{pmatrix}$
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as$\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \en...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Linear Algebra
gateme-2012
linear-algebra
eigen-values
eigen-vectors
+
–
0
answers
0
votes
GATE ME 2012 | Question: 25
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by $\dfrac{1}{\sqrt{2}} \hat{i} +\dfrac{1}{\sqrt{2}} \hat{j} \\$ ... $\hat{k} \\$ $\dfrac{1}{\sqrt{3}} \hat{i} +\dfrac{1}{\sqrt{3}} \hat{j} +\dfrac{1}{\sqrt{3}} \hat{k}$
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by$\dfrac{1}{\s...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
vector-identities
+
–
0
answers
0
votes
GATE ME 2012 | Question: 24
At $x=0$, the function $f(x)=x^3+1$ has a maximum value a minimum value a singularity a point of inflection
At $x=0$, the function $f(x)=x^3+1$ hasa maximum valuea minimum valuea singularitya point of inflection
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
functions-of-single-variable
maxima-minima
+
–
0
answers
0
votes
GATE ME 2012 | Question: 11
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is $1/6$ $1/4$ $1/3$ $1/2$
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is$1/6$$1/4$$1/3$$1/2$
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
definite-integrals
area-under-curve
+
–
0
answers
0
votes
GATE ME 2012 | Question: 12
Consider the function $f(x) = \mid x \mid $ in the interval $-1 \leq x \leq 1$. At the point $x=0, \: f(x)$ is continuous and differentiable non-continuous and differentiable continuous and non-differentiable neither continuous nor differentiable
Consider the function $f(x) = \mid x \mid $ in the interval $-1 \leq x \leq 1$. At the point $x=0, \: f(x)$ iscontinuous and differentiablenon-continuous and differentiab...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
continuity-and-differentiability
+
–
0
answers
0
votes
GATE ME 2012 | Question: 12
$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is $1/4$ $1/2$ $1$ $2$
$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is$1/4$$1/2$$1$$2$
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
limits
+
–
0
answers
0
votes
GATE2018-2-35
The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ has no solution one solution two solutions more than two solutions
The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ hasno solutionone solutiontwo solutionsmore tha...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Numerical Methods
gateme-2018-set2
numerical-methods
linear-programming
+
–
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