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Most viewed questions in Engineering Mathematics
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GATE2017 ME-1: 2
The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is $0$ $3$ $1$ $-1$
The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is$0$$3$$1$$-1$
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Calculus
gateme-2017-set1
calculus
limits
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 26
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an eigenvector of a $2\times2$ matrix $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an ei...
gatecse
1.6k
points
gatecse
asked
Feb 22, 2021
Linear Algebra
gateme-2021-set1
linear-algebra
eigen-values
eigen-vectors
+
–
0
answers
0
votes
GATE2018-2-26
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $\oint_C \frac{1}{5z-4} dz=A \pi i$, the value of $A$ is $2/5$ $1/2$ $2$ $4/5$
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $$\oint_C \frac{1}{5z-4} dz=A \pi i$$, the value of $A$ i...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 44
Consider a velocity field $\overrightarrow{V}=k(y\hat{i}+x\hat{k})$ , where $K$ is a constant. The vorticity, $Ω_Z$ , is $-K$ $K$ $-K/2$ $K/2$
Consider a velocity field $\overrightarrow{V}=k(y\hat{i}+x\hat{k})$ , where $K$ is a constant. The vorticity, $Ω_Z$ , is$-K$$K$$-K/2$$K/2$
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set4
calculus
vector-identities
velocity
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 29
Consider an ordinary differential equation $\dfrac{dx}{dt}=4t+4$. If $x = x_0$ at $t = 0$, the increment in $x$ calculated using Runge-Kutta fourth order multi-step method with a step size of $\Delta t = 0.2$ is $0.22$ $0.44$ $0.66$ $0.88$
Consider an ordinary differential equation $\dfrac{dx}{dt}=4t+4$. If $x = x_0$ at $t = 0$, the increment in $x$ calculated using Runge-Kutta fourth order multi-step metho...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Numerical Methods
gateme-2014-set4
numerical-methods
+
–
0
answers
0
votes
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
GATE2016-3-4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Probability and Statistics
gateme-2016-set3
numerical-answers
probability-and-statistics
probability
normal-distribution
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 4
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is $\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \end{bmatrix}\begin{Bmatrix} x\\y \end{Bmatrix} \\$ ...
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is$\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \e...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set1
linear-algebra
matrices
matrix-algebra
+
–
0
answers
0
votes
GATE2016-1-29
Gauss-Seidel method is used to solve the following equations (as per the given order): $x_1+2x_2+3x_3=5$ $2x_1+3x_2+x_3=1$ $3x_1+2x_2+x_3=3$ Assuming initial guess as $x_1=x_2=x_3=0$ , the value of $x_3$ after the first iteration is __________
Gauss-Seidel method is used to solve the following equations (as per the given order):$x_1+2x_2+3x_3=5$$2x_1+3x_2+x_3=1$$3x_1+2x_2+x_3=3$Assuming initial guess as $x_1=x_...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Numerical Methods
gateme-2016-set1
numerical-answers
numerical-methods
gauss-seidel-method
+
–
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
GATE2018-1-27
The value of the integral over the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\overrightarrow{n}$ is the normal to the surface $S$, is $V$ $2V$ $3V$ $4V$
The value of the integralover the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\over...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set1
calculus
surface-integral
vector-identities
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 18
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is Normal Poisson Erlang Beta
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval isNormalPoissonErlangB...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Probability and Statistics
gateme-2014-set1
probability-and-statistics
probability
poisson-distribution
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 2
$ \displaystyle{}\lim_{x\rightarrow 0} \left( \dfrac{e^{2x}-1}{\sin(4x)} \right )$ is equal to $0$ $0.5$ $1$ $2$
$ \displaystyle{}\lim_{x\rightarrow 0} \left( \dfrac{e^{2x}-1}{\sin(4x)} \right )$ is equal to$0$$0.5$$1$$2$
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set2
calculus
limits
+
–
0
answers
0
votes
GATE2020-ME-2: 27
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be $(3xy^2-y^3) +$ constant $(3x^2y^2-y^3) +$ constant $(x^3-3x^2 y) +$ constant $(3x^2y-y^3) +$ constant
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be$(3...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Calculus
gateme-2020-set2
calculus
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 3 | Question: 39
Consider an objective function $Z(x_1,x_2)=3x_1+9x_2$ and the constraints $x_1+x_2 \leq 8$ $x_1+2x_2 \leq 4$ $x_1 \geq 0$ , $x_2 \geq 0$ The maximum value of the objective function is _______
Consider an objective function $Z(x_1,x_2)=3x_1+9x_2$ and the constraints$x_1+x_2 \leq 8$$x_1+2x_2 \leq 4$$x_1 \geq 0$ , $x_2 \geq 0$The maximum value of the objective...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Numerical Methods
gateme-2014-set3
numerical-answers
numerical-methods
linear-programming
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 4
A box contains $25$ parts of which $10$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is $\dfrac{7}{20} \\$ $\dfrac{42}{125} \\$ $\dfrac{25}{29} \\$ $\dfrac{5}{9}$
A box contains $25$ parts of which $10$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being g...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Probability and Statistics
gateme-2014-set2
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE2018-1-1
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is $1/72$ $1/55$ $1/36$ $1/27$
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probabil...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Probability and Statistics
gateme-2018-set1
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE ME 2013 | Question: 27
The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by $\dfrac{2}{s+1} \\$ $\dfrac{4}{s+1} \\$ $\dfrac{4}{s^2+1} \\$ $\dfrac{2}{s^4+1}$
The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform ...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Differential Equations
gateme-2013
differential-equation
laplace-transforms
+
–
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
GATE2017 ME-2: 24
The standard deviation of linear dimensions $P$ and $Q$ are $3 \mu$ m and $4 \mu$ m, respectively. When assembled, the standard deviation (in $\mu$ m) of the resulting linear dimension $(P+Q)$ is _________.
The standard deviation of linear dimensions $P$ and $Q$ are $3 \mu$ m and $4 \mu$ m, respectively. When assembled, the standard deviation (in $\mu$ m) of the resulting li...
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Probability and Statistics
gateme-2017-set2
numerical-answers
probability-and-statistics
mode-and-standard-deviation
+
–
0
answers
0
votes
GATE ME 2013 | Question: 36
A linear programming problem is shown below. $\begin{array}{ll} \text{Maximize} & 3x + 7y \\ \text{Subject to} & 3x + 7y \leq 10 \\ & 4x + 6y \leq 8 \\ & x, y \geq 0 \end{array}$ It has an unbounded objective function. exactly one optimal solution. exactly two optimal solutions. infinitely many optimal solutions.
A linear programming problem is shown below.$\begin{array}{ll} \text{Maximize} & 3x + 7y \\ \text{Subject to} & 3x + 7y \leq 10 \\ & 4x + 6y \leq 8 \\ & x, y \geq 0 \end{...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Numerical Methods
gateme-2013
numerical-methods
linear-programming
+
–
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
GATE2015-1-27
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed of $1.57$ meters per second. The time taken by the ant to reach the point $(2, 2)$ is (in seconds) ____________
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed ...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2015-set1
numerical-answers
calculus
curves
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 1
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$ subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is...
gatecse
1.6k
points
gatecse
asked
Feb 22, 2021
Differential Equations
gateme-2021-set1
differential-equations
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 3 | Question: 1
Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$, $\begin{bmatrix} y_1\\ y_2\\ y_3 \end{bmatrix}$ If $a\neq b$ then $x_1y_1+x_2y_2+x_3y_3$ equals $a$ $b$ $ab$ $0$
Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bma...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set3
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
answers
0
votes
GATE ME 2013 | Question: 45
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has ... answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesse...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Probability and Statistics
gateme-2013
probability-and-statistics
probability
conditional-probability
+
–
0
answers
0
votes
GATE ME 2013 | Question: 3
Match the CORRECT pairs: ... $P-2; Q-1; R-3$ $P-3; Q-2; R-1$ $P-1; Q-2; R-3$ $P-3; Q-1; R-2$
Match the CORRECT pairs:$\begin{array}{llll} & \text{Numerical Integration Scheme} & & \text{Order of Fitting Polynomial} \\ P. & \text{Simpson's 3/8 Rule} & 1. & \text{F...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Numerical Methods
gateme-2013
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 27
If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
numerical-answers
calculus
initial-and-boundary-value-problems
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 26
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to$0$$\frac{-\p...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
calculus
definite-integrals
area-under-curve
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 18
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is $1.83$ $1.60$ $1.51$ $1.06$
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is$1.83$$1.60$$1.51$$1.06$
go_editor
5.0k
points
go_editor
asked
Mar 1, 2021
Numerical Methods
gateme-2021-set2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
answers
0
votes
GATE2018-2-36
Given the ordinary differential equation $\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}-6y=0$ with $y(0)=0$ and $\dfrac{dy}{dx}(0)=1$, the value of $y(1)$ is __________ (correct to two decimal places).
Given the ordinary differential equation $$\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}-6y=0$$ with $y(0)=0$ and $\dfrac{dy}{dx}(0)=1$, the value of $y(1)$ is __________ (correct to...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Differential Equations
gateme-2018-set2
numerical-answers
differential-equations
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 27
The value of the integral $\int_{0}^{2}\int_{0}^{x}e^{x+y}dydx$ is $\dfrac{1}{2}(e-1) \\$ $\dfrac{1}{2}(e^2-1)^2 \\$ $\dfrac{1}{2}(e^2-e) \\$ $\dfrac{1}{2}(e-\frac{1}{e})^2$
The value of the integral $\int_{0}^{2}\int_{0}^{x}e^{x+y}dydx$ is$\dfrac{1}{2}(e-1) \\$$\dfrac{1}{2}(e^2-1)^2 \\$$\dfrac{1}{2}(e^2-e) \\$$\dfrac{1}{2}(e-\frac{1}{e})^2$
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set4
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 5
The best approximation of the minimum value attained by $e^{-x}\sin(100x)$ for $x\geq 0$ is _______
The best approximation of the minimum value attained by $e^{-x}\sin(100x)$ for $x\geq 0$ is _______
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Numerical Methods
gateme-2014-set2
numerical-answers
numerical-methods
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 29
Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Numerical Methods
gateme-2014-set1
numerical-answers
numerical-methods
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 5
Which one of the following describes the relationship among the three vectors, $\hat{i}+\hat{j}+\hat{k}$ , $2\hat{i}+3\hat{j}+\hat{k}$ and $5\hat{i}+6\hat{j}+4\hat{k}$ ? The vectors are mutually perpendicular The vectors are linearly dependent The vectors are linearly independent The vectors are unit vectors
Which one of the following describes the relationship among the three vectors, $\hat{i}+\hat{j}+\hat{k}$ , $2\hat{i}+3\hat{j}+\hat{k}$ and $5\hat{i}+6\hat{j}+4\hat{k}$ ?T...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1calculus
vector-identities
+
–
0
answers
0
votes
GATE ME 2013 | Question: 25
Choose the CORRECT set of functions, which are linearly dependent. $\sin x , \sin^2 x$ and $\cos^2 x$ $\cos x , \sin x$ and $\tan x$ $\cos 2x, \sin^2 x$ and $\cos^2 x$ $\cos 2x , \sin x$ and $cos x$
Choose the CORRECT set of functions, which are linearly dependent.$\sin x , \sin^2 x$ and $\cos^2 x$$\cos x , \sin x$ and $\tan x$$\cos 2x, \sin^2 x$ and $\cos^2 x$$\cos ...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Calculus
gateme-2013
calculus
functions
+
–
0
answers
0
votes
GATE2020-ME-2: 26
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is $3\hat{i} – 3 \hat{j} - \hat{k} \\$ $- \dfrac{7}{3} \\$ $\dfrac{7}{3} \\ $ $7$
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is$3\hat{i} – 3 \hat{j} - \hat{k} \\$$-...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Calculus
gateme-2020-set2
calculus
vector-identities
directional-derivatives
+
–
0
answers
0
votes
GATE2016-2-28
The probability that a screw manufactured by a company is defective is $0.1$. The company sells screws in packets containing $5$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________
The probability that a screw manufactured by a company is defective is $0.1$. The company sells screws in packets containing $5$ screws and gives a guarantee of replaceme...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Probability and Statistics
gateme-2016-set2
numerical-answers
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 1
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is $\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$ $\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\$ $\begin{Bmatrix} 2\\ -1 \end{Bmatrix} \\$ $\begin{Bmatrix} 1\\ 1 \end{Bmatrix} \\$
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is$\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$$\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set2
linear-algebra
eigen-values
eigen-vectors
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 1
Given that the determinant of the matrix $\begin{bmatrix} 1 & 3 & 0\\ 2 & 6 & 4\\ -1 & 0 & 2 \end{bmatrix}$ is $-12$, the determinant of the matrix $\begin{bmatrix} 2 & 6 & 0\\ 4 & 12 & 18\\ -2 & 0 & 4 \end{bmatrix}$ is $-96$ $-24$ $24$ $96$
Given that the determinant of the matrix $\begin{bmatrix} 1 & 3 & 0\\ 2 & 6 & 4\\ -1 & 0 & 2 \end{bmatrix}$ is $-12$, the determinant of the matrix $\begin{bmatrix} 2 & 6...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set1
linear-algebra
matrices
determinant
+
–
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