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81
GATE2017 CE-1: 3
Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to $e^{e^{-x}}$ $e^{-e^{-x}}$ $e^{-e^{x}}$ $e^{-x}$
Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to$e^{e^{-x}}$$...
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83
GATE2014-2-2
The determinant of matrix $\begin{bmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 0 \\ 2 & 3 & 0 & 1 \\ 3 & 0 & 1 & 2 \end{bmatrix}$ is ________
The determinant of matrix $\begin{bmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 0 \\ 2 & 3 & 0 & 1 \\ 3 & 0 & 1 & 2 \end{bmatrix}$ is ________
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84
GATE Civil 2012 | Question: 1
The estimate of $\int_{0.5}^{1.5} \dfrac{dx}{x}$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by $0.235$ $0.068$ $0.024$ $0.012$
The estimate of $$\int_{0.5}^{1.5} \dfrac{dx}{x}$$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by$0.235$$0.068$$0.024$$0....
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85
GATE2014-1-4
The sum of Eigen values of the matrix, $[M]$ is where $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$ $915$ $1355$ $1640$ $2180$
The sum of Eigen values of the matrix, $[M]$ iswhere $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$$915$$1355$$1640$$2180$
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86
GATE2018 CE-2: 28
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$ $1$ $2$ $3$ $4$
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$$1$$2$$3$$4$
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87
GATE Civil 2021 Set 1 | Question: 36
The value of abscissa $(x)$ and ordinate $(y)$ ... $1/3^\text{rd}$ rule, the area under the curve $\textit{(round off to two decimal places)}$ is __________________
The value of abscissa $(x)$ and ordinate $(y)$ of a curve are as follows:$$\begin{array}{|cl|cI|}\hline&x & y\\ \hline & \text{$2.0$} & \text{$5.00$} \\ \hline & \text{$2...
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88
GATE2017 CE-1: 21
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________
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89
GATE Civil 2013 | Question: 3
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in each of two successive years is $0.04$ $0.2$ $0.02$ $0.0004$
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in eac...
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92
GATE2018 CE-2: 27
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is $\dfrac{1}{s+a} \\$ $\dfrac{1}{s-a} \\$ $\dfrac{1}{a-s} \\$ $\infty$
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is$\dfrac{1}{s+a} \\$$\dfrac{1}{s-a} \\...
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93
GATE2016-2-29
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
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94
GATE2020-CE-1-39
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 ______
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$$\int_C [(y+z)dx+(x...
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96
GATE2018 CE-1: 26
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is $\pi^2/8$ $\pi^2/4$ $\pi^2/2$ $\pi^2$
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is$\pi^2/8$$\pi^2/4$$\pi^2/2$$\pi^2$
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97
GATE Civil 2021 Set 1 | Question: 1
The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3\\ 3 & 4 & 2 & 5\\ 5 & 6 & 2 & 7\\ 7 & 8 & 2 & 9 \end{bmatrix}$ is $1$ $2$ $3$ $4$
The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3\\ 3 & 4 & 2 & 5\\ 5 & 6 & 2 & 7\\ 7 & 8 & 2 & 9 \end{bmatrix}$ is$1$$2$$3$$4$
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100
GATE2015-1-30
The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.
The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.
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102
GATE2015-2-5
Let $A=[a_{ij}], \: 1 \leq i, j \leq n$ with $n \geq 3$ and $a_{ij}=i \cdot j$. The rank of $A$ is: $0$ $1$ $n-1$ $n$
Let $A=[a_{ij}], \: 1 \leq i, j \leq n$ with $n \geq 3$ and $a_{ij}=i \cdot j$. The rank of $A$ is:$0$$1$$n-1$$n$
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103
GATE2017 CE-2-27
Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is$\dfrac{\pi ^3}{24} \\$$\dfr...
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106
GATE2020 CE-2-1
The ordinary differential equation $\dfrac{d^2u}{dx^2}$- 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous
The ordinary differential equation $\dfrac{d^2u}{dx^2}$$- 2x^2u +\sin x = 0$ islinear and homogeneouslinear and nonhomogeneousnonlinear and homogeneousnonlinear and nonho...
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108
GATE Civil 2021 Set 2 | Question: 18
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
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110
GATE2017 CE-1: 2
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are $2$ and $2$ $1$ and $2$ $2$ and $1$ $1$ and $1$
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are$2$ and $2$$1$ and $2$$2$ and $1$$1$ and $1$
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111
GATE2015-2-3
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is: $1$ $-1$ $i$ $-i$
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is:$1$$-1$$i$$-i$
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112
GATE2015-2-27
Consider the following second order linear differential equation $\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$ The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: y=21$. The value of $y$ at $x=1$ is _________.
Consider the following second order linear differential equation$$\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$$The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: ...
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113
GATE2016-2-30
The quadratic approximation of $f(x)=x^3 – 3x^2 -5$ at the point $x=0$ is $3x^2 -6x-5$ $-3x^2-5$ $-3x^2+6x-5$ $3x^2-5$
The quadratic approximation of $f(x)=x^3 – 3x^2 -5$ at the point $x=0$ is$3x^2 -6x-5$$-3x^2-5$$-3x^2+6x-5$$3x^2-5$
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118
GATE Civil 2013 | Question: 2
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ columns, and matrix R has $4$ rows and $1$ column. __________
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ column...
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