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Questions without answers in Engineering Mathematics

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gate question from engineering mathematics in ordinary differential equation
for the differential equation ,d^2y/dx^2+3dy/dx+4y=3cos2x,then value of particular integral is
for the differential equation ,d^2y/dx^2+3dy/dx+4y=3cos2x,then value of particular integral is
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GATE Civil 2021 Set 2 | Question: 1
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is $0$ $1.0$ $0.5$ $\infty$
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is$0$$1.0$$0.5$$\infty$
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GATE Civil 2021 Set 2 | Question: 2
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is $1$ $2$ $3$ $4$
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is$1$$2$$3$$4$
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GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$
If $\text{A}$ is a square matrix then orthogonality property mandates$AA^{T}=I$$AA^{T}=0$$AA^{T}=A^{-1}$$AA^{T}=A^{2}$
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GATE Civil 2021 Set 2 | Question: 18
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
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GATE Civil 2021 Set 2 | Question: 26
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of$y=x\text{ ln}(kx)$$y=k\text{ ln}(kx)$$y=x\text{ ln}(x)$$y=xk\t...
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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$$4$
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GATE Civil 2021 Set 1 | Question: 3
The shape of the cumulative distribution function of Gaussian distribution is Horizontal line Straight line at $45$ degree angle Bell-shaped $S$-shaped
The shape of the cumulative distribution function of Gaussian distribution isHorizontal lineStraight line at $45$ degree angleBell-shaped$S$-shaped
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GATE Civil 2021 Set 1 | Question: 18
Consider the limit: $\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x} - \frac{1}{x-1}\right )$ The limit (correct up to one decimal place) is _____________
Consider the limit:$$\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x} - \frac{1}{x-1}\right )$$The limit (correct up to one decimal place) is _____________
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GATE Civil 2021 Set 1 | Question: 19
The volume determined from $\int \int \int _{V}\:8\:xyz\:dV$ for $V=\left [ 2,3 \right ]\times \left [ 1,2 \right ]\times \left [ 0,1 \right ]$ will be ($\textit{in integer}$) _____________
The volume determined from $\int \int \int _{V}\:8\:xyz\:dV$ for $V=\left [ 2,3 \right ]\times \left [ 1,2 \right ]\times \left [ 0,1 \right ]$ will be ($\textit{in integ...
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GATE Civil 2021 Set 1 | Question: 27
The value of $\int_{0}^{1}\:e^{x}\:dx$ using the trapezoidal rule with four equal subintervals is $1.718$ $1.727$ $2.192$ $2.718$
The value of $\int_{0}^{1}\:e^{x}\:dx$ using the trapezoidal rule with four equal subintervals is$1.718$$1.727$$2.192$$2.718$
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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:$$\begin{array}{|cl|cI|}\hline&x & y\\ \hline & \text{$2.0$} & \text{$5.00$} \\ \hline & \text{$2...
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GATE2020-CE-1-3
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round ...
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GATE2020-CE-1-4
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is$\dfrac{\pi ab}{4} \\$$\dfrac{\pi ab}{2} \\$$\pi ab \\$$\dfrac{4\pi ab}{3}$
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GATE2020-CE-1-27
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step length $=h$ ...
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step ...
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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$$\int_C [(y+z)dx+(x...
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26
GATE2020 CE-2-1
The ordinary differential equation $\dfrac{d^2u}{dx^2}$- 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous
The ordinary differential equation $\dfrac{d^2u}{dx^2}$$- 2x^2u +\sin x = 0$ islinear and homogeneouslinear and nonhomogeneousnonlinear and homogeneousnonlinear and nonho...
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27
GATE2020 CE-2-2
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
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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30
GATE2020 CE-2-18
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
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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33
GATE2020 CE-2-27
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 $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
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,...
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38
GATE2017 CE-2-19
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
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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40
GATE2017 CE-2-26
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 $(1,0)$ $(0, 1)$ $(1,1)$ $(\sqrt{2}, (\sqrt{2})$
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$(...
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