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Recent questions tagged engineeringmathematics
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GATE2020CE11
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ ... The above equation is a second order linear equation a second degree linear equation a second order nonlinear equation a second degree nonlinear equation
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gate2020ce1
partialdifferentialequation
engineeringmathematics
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2
GATE2020CE12
The value of $\lim_{x\to\infty}\frac{x^25x+4}{4x^2+2x}$ is $0 \\$ $\large\frac{1}{4} \\$ $\large\frac{1}{2} \\$ $\:1$
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gate2020ce1
engineeringmathematics
limit
calculus
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3
GATE2020CE13
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
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gate2020ce1
engineeringmathematics
linearalgebra
linearinterpolation
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4
GATE2020CE14
The area of an ellipse represented by an equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\large\frac{\pi ab}{4}$ $\large\frac{\pi ab}{2}$ $\pi ab$ $\large\frac{4\pi ab}{3}$
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gate2020ce1
engineeringmathematics
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5
GATE2020CE118
The probability that a $50$ year flood may $\textbf{NOT}$ occur at all during $25$ years life of a project (round off to two decimal places), is _______.
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gate2020ce1
probabilityandstatistics
engineeringmathematics
probability
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6
GATE2020CE126
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
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gate2020ce1
ordinarydifferentialequation
engineeringmathematics
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7
GATE2020CE127
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finitedivideddifference scheme (with step length $=h$ ...
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Feb 28
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gate2020ce1
calculus
functions
engineeringmathematics
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8
GATE2020CE139
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral $\int_C [(y+z)dx+(x+z)dy+(x+y)dz] $ is ______
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gate2020ce1
calculus
engineeringmathematics
integrals
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9
GATE2020CE140
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&3 \\ 4&4&6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.
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gate2020ce1
matrixalgebra
linearalgebra
engineeringmathematics
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10
GATE2020 CE21
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
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Feb 13
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gate2020ce2
engineeringmathematics
differentialequations
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11
GATE2020 CE23
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NONzero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
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Feb 13
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gate2020ce2
calculus
engineeringmathematics
integrals
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12
GATE2020 CE24
The following partial differential equation is defined for $u:u (x,y)$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$ The set of auxiliary ... the equation uniquely, is three initial conditions three boundary conditions two initial conditions and one boundary condition one initial condition and two boundary conditions
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Feb 13
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gate2020ce2
partialdifferentialequation
engineeringmathematics
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13
GATE2020 CE218
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
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Feb 13
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gate2020ce2
numericalanswers
probabilityandstatistics
engineeringmathematics
probability
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14
GATE2020 CE224
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vertical coordinate $y,\: U_\infty$ is the free stream velocity and $\delta$ is the boundary layer ... $\ s^{1}$, round off to two decimal places) at $y = 0$, is ________.
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Feb 13
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gate2020ce2
numericalanswers
calculus
engineeringmathematics
gradient
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15
GATE2020 CE226
An ordinary differential equation is given below $6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}y=0$ The general solution of the above equation (with constants $C_1$ and $C_2$), is $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{x}{2}$ $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1xe^\frac{x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1e^\frac{x}{3} + C_2xe^\frac{x}{2}$
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Feb 13
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gate2020ce2
ordinarydifferentialequation
engineeringmathematics
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0
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16
GATE2020 CE227
A $4 \times 4$ matrix $[P]$ is given below $[P] = \begin{bmatrix}0 &1 &3 &0 \\2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$ The eigen values of $[P]$ are $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
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gate2020ce2
matrixalgebra
linearalgebra
engineeringmathematics
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17
GATE2020 CE239
The Fourier series to represent $x x^2$ for $\pi\leq x\leq \pi$ is given by $ xx^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.
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Feb 13
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gate2020ce2
numericalanswers
partialdifferentialequation
engineeringmathematics
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0
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18
GATE2020 CE240
The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The absolute error in the computed volume ( in $cm^3$ ,round off to three decimal places), is ________
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Feb 13
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gate2020ce2
numericalanswers
engineeringmathematics
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0
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19
GATE2017 CE21
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
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Aug 7, 2019
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gate2017ce2
engineeringmathematics
equations
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0
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20
GATE2017 CE22
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
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Aug 7, 2019
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gate2017ce2
engineeringmathematics
partialdifferentialequation
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0
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21
GATE2017 CE219
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
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Aug 7, 2019
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Calculus
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gatecse
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gate2017ce2
vectorcalculus
divergence
numericalanswers
calculus
engineeringmathematics
0
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0
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22
GATE2017 CE220
A twofaced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be ________
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gatecse
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gate2017ce2
numericalanswers
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23
GATE2017 CE226
The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$axis. The coordinates of the tangent point would be $(1,0)$ $(0, 1)$ $(1,1)$ $(\sqrt{2}, (\sqrt{2})$
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gate2017ce2
engineeringmathematics
tangentpoint
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24
GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \dfrac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
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Aug 7, 2019
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Calculus
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gatecse
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gate2017ce2
definite
integral
calculus
engineeringmathematics
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answers
25
GATE2017 CE228
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
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Aug 7, 2019
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Linear Algebra
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gatecse
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gate2017ce2
matrix
linearalgebra
engineeringmathematics
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26
GATE2017 CE229
Consider the following secondorder differential equation: $y’’ – 4y’+3y =2t 3t^2$. The particular solution of the differential solution equation is $ – 2 2tt^2$ $ – 2tt^2$ $2t3t^2$ $ – 2 2t3 t^2$
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Aug 7, 2019
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Partial Differential Equation (PDE):
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gatecse
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gate2017ce2
differentialequation
particularsolution
engineeringmathematics
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1
answer
27
GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=1$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ ... $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})= \infty$
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Feb 14, 2019
in
Calculus
by
Arjun
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2.8k
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gate2019ce1
calculus
limit
engineeringmathematics
+1
vote
0
answers
28
GATE2019 CE1: 2
Consider a twodimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace's equation of continuity is expressed as $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
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Feb 14, 2019
in
Partial Differential Equation (PDE):
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Arjun
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gate2019ce1
laplaceequation
continuity
partialdifferentialequation
engineeringmathematics
+1
vote
0
answers
29
GATE2019 CE1: 3
A simple massspring oscillatory system consists of a mass $m$, suspended from a spring of stiffness $k$. Considering $z$ as the displacement of the system at any time $t$, the equation of motion for the free vibration of the system is $m \ddot{z} + kz = 0$. The natural frequency of the system is $\dfrac{k}{m} \\$ $\sqrt{ \dfrac{k}{m}} \\$ $\dfrac{m}{k}\\$ $\sqrt{ \dfrac{m}{k}}$
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Feb 14, 2019
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by
Arjun
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gate2019ce1
engineeringmathematics
+1
vote
0
answers
30
GATE2019 CE1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}' (x) + \dfrac{h^2}{2!}{f}''(x) + \dfrac{h^3}{3!}{f}'''(x)+\dots \infty \\$ $f(x)h{f}' (x) + \dfrac{h^2}{2!}{f}''(x)  \dfrac{h^3}{3!}{f}'''(x)+ \dots \infty \\$ ... $f(x)h{f}' (x) + \dfrac{h^2}{2}{f}''(x)  \dfrac{h^3}{3}{f}'''(x)+ \dots \infty $
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Feb 14, 2019
in
Calculus
by
Arjun
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2.8k
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gate2019ce1
taylorseries
calculus
engineeringmathematics
0
votes
0
answers
31
GATE2019 CE1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flood event (in years, round off to $1$ decimal place is ________
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Feb 14, 2019
in
Probability and Statistics
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gate2019ce1
probability
numericalanswers
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
32
GATE2019 CE1: 26
Which one of the following is NOT a correct statement? The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$ The function $\sqrt[x]{x}, \: (x>0)$, has the global minima at $x=e$ The function $x^3$ has neither global minima nor global maxima The function $\mid x \mid$ has the global minima at $x=0$
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Feb 14, 2019
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Calculus
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gate2019ce1
maximaminima
calculus
engineeringmathematics
0
votes
0
answers
33
GATE2019 CE1: 27
A onedimensional domain is discretized into $N$ subdomains of width $\Delta x$ with node numbers $i=0,1,2,3, \dots , N$. If the time scale is discretized in steps of $\Delta t$, the forwardtime and centeredspace finite difference approximation at i th node and n th time step, for the ...
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Feb 14, 2019
in
Others
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Arjun
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2.8k
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gate2019ce1
probabilityandstatistics
engineeringmathematics
discreterandomvariables
0
votes
0
answers
34
GATE2019 CE1: 30
Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial x}$? $\dfrac{x \: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi 1} \\$ ... $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi 1}$
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Arjun
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2.8k
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gate2019ce1
calculus
engineeringmathematics
functions
0
votes
0
answers
35
GATE2019 CE1: 44
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off to $1$ decimal place), is _________
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Feb 14, 2019
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Ordinary Differential Equation (ODE)
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gate2019ce1
differentialequation
numericalanswers
engineeringmathematics
0
votes
0
answers
36
GATE2019 CE2: 1
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & 2 & 6 \end{bmatrix}^T$ is $\sqrt{12}$ $\sqrt{24}$ $\sqrt{48}$ $\sqrt{56}$
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Feb 12, 2019
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Arjun
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gate2019ce2
matrixalgebra
linearalgebra
engineeringmathematics
0
votes
0
answers
37
GATE2019 CE2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2a^2} \\$ $\dfrac{s}{s^2+a^2}$
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Feb 12, 2019
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Arjun
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gate2019ce2
ordinarydifferentialequation
engineeringmathematics
laplacetransform
0
votes
0
answers
38
GATE2019 CE2: 3
The following inequality is true for all $x$ close to $0$. $2\dfrac{x^2}{3} < \dfrac{x \sin x}{1 \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
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Feb 12, 2019
in
Calculus
by
Arjun
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2.8k
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gate2019ce2
limit
calculus
engineeringmathematics
0
votes
0
answers
39
GATE2019 CE2: 4
What is curl of the vector field $2x^2y \textbf{i} + 5z^2 \textbf{j} – 4yz \textbf{k}$? $6z \textbf{i} + 4x \textbf{j} – 2x^2 \textbf{k}$ $6z \textbf{i}  8xy \textbf{j} + 2x^2 y\textbf{k}$ $ 14 z \textbf{i} + 6y \textbf{j} + 2x^2 \textbf{k}$ $14z \textbf{i} – 2x^2 \textbf{k}$
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Feb 12, 2019
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Arjun
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2.8k
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gate2019ce2
curl
vectoridentities
calculus
engineeringmathematics
0
votes
0
answers
40
GATE2019 CE2: 18
The value of the function $f(x)$ is given at $n$ distinct values of $x$ and its value is to be interpolated at the point $x^*$, using all the $n$ points. The estimate is obtained first by the Lagrange polynomial, denoted by $I_L$, and then by the ... than $I_N$ $I_L$ and $I_N$ are always equal $I_L$ is always less than $I_N$ Not definite relation exists between $I_L$ and $I_N$
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Feb 12, 2019
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Others
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Arjun
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2.8k
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gate2019ce2
numericalmethods
engineeringmathematics
newton'spolynomial
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