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121
GATE Civil 2012 | Question: 30
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is $y=e^{-2x}$ $y=2e^{-2x}$ $y=10.95 e^{-2x}$ $y=36.95 e^{-2x}$
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is$y=e^{-2x}$$y=2e^{-2x}$$y=10.95 e^{-2x}$$y=36.95 e^{...
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123
GATE2018 CE-2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{-1}$ $x^{-2}$
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is$x$$x^2$$x^{-1}$$x^{-2}$
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124
GATE2019 CE-2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2-a^2} \\$ $\dfrac{s}{s^2+a^2}$
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$$\dfrac{a}{s^2 + a^2} \\$$\dfrac{s}{s^2-a^2} \\$$\dfrac{s}{s^2+a^2}$
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130
GATE2016-1-28
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is $\dfrac{59}{6} \\$ $\dfrac{9}{2} \\$ $\dfrac{10}{3} \\$ $\dfrac{7}{6}$
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is$\dfrac{59}{6} \\$$\dfrac{9}{2} \\$$\dfrac{10}{3} \\$$\dfrac{7}{6}$
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133
GATE2014-2-4
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is $e^{-k_1t} \\$ $e^{-k_2t} \\$ $e^{k_1t} \\$ $e^{k_2t}$
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is$e^{-k_1t} \\$$e^{-k_2t} \\$$e^{k_1t} \\$$e^{k_2t}$
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134
GATE Civil 2013 | Question: 28
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is $0 \\$ $\dfrac{1}{15} \\$ $1 \\$ $\dfrac{8}{3}$
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is$0 \\$$\dfrac{1}{15} \\$$1 \\$$\dfrac{8}{3}$
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135
GATE Civil 2012 | Question: 3
The infinite series $1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!} + \dots $ corresponds to $\sec x$ $e^x$ $\cos x$ $1+\sin^2x$
The infinite series $1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!} + \dots $ corresponds to$\sec x$$e^x$$\cos x$$1+\sin^2x$
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136
GATE2017 CE-1: 27
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is $Q(t)=e^{-t}-1$ $Q(t)=1+ e^{-t}$ $Q(t)=1 -e^t$ $Q(t)=1- e^{-t}$
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is$Q(t)=e^{-t}-1$$Q(t)=1+ e^{-t}$$Q(t)=1 -e^t$$Q(t)=1- e^{-t}$
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137
GATE2016-1-1
Newton-Raphson method is to be used to find root of equation $3x-e^x+ \sin x=0$.If the initial trial value for the root is taken as $0.333$, the next approximation for the root would be _______ (note: answer up to three decimal)
Newton-Raphson method is to be used to find root of equation $3x-e^x+ \sin x=0$.If the initial trial value for the root is taken as $0.333$, the next approximation for th...
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138
GATE2015-2-28
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values have the same ratio of $3:1$? $-2$ $1$ $7/3$ $14/3$
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values...
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139
GATE2015-2-4
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to $e^{-2}$ $e$ $1$ $e^2$
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to$e^{-2}$$e$$1$$e^2$
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141
GATE2014-2-28
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
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144
GATE2015-2-1
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are: $f’(x_0) > 0$ and $f’’(x_0)=0$ $f’(x_0) < 0$ and $f’’(x_0)=0$ $f’(x_0) = 0$ and $f’’(x_0)<0$ $f’(x_0) = 0$ and $f’’(x_0)>0$
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are:$f’(x_0) 0$ and $f’’(x_0)=0$$f’(x_0) < 0$ and $f�...
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145
GATE2014-1-2
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _______
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _...
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146
GATE2014-2-3
$z=\dfrac{2-3i}{-5+i}$ can be expressed as $-0.5-0.5i$ $-0.5+0.5i$ $0.5-0.5i$ $0.5+0.5i$
$z=\dfrac{2-3i}{-5+i}$ can be expressed as$-0.5-0.5i$$-0.5+0.5i$$0.5-0.5i$$0.5+0.5i$
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148
GATE2015-1-1
For what value of $p$ the following set of equations will have no solution? $2x+3y=5$ $3x+py=10$
For what value of $p$ the following set of equations will have no solution?$2x+3y=5$$3x+py=10$
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149
GATE2014-2-26
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to $\log x$ $0$ $x \log x$ $\infty$
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to$\log x$$0$$x \log x$$\infty$
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150
GATE2016-1-3
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is $4$ $3$ $2$ $1$
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is$4$$3$$2$$1$
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151
GATE2014-1-1
$\underset{x \to \infty}{\lim} \bigg( \dfrac{x+\sin x}{x} \bigg)$ equals to $- \infty$ $0$ $1$ $\infty$
$\underset{x \to \infty}{\lim} \bigg( \dfrac{x+\sin x}{x} \bigg)$ equals to$- \infty$$0$$1$$\infty$
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153
GATE2016-1-27
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is $\dfrac{\pi}{2} \\$ $\pi \\$ $\dfrac{3 \pi}{2} \\$ $1$
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is$\dfrac{\pi}{2} \\$$\pi \\$$\dfrac{3 \pi}{2} \\$$1$
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