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Recent questions in Engineering Mathematics
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1
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 $0$ $1.0$ $0.5$ $\infty$
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Calculus
Mar 1, 2021
by
go_editor
5.3k
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gatecivil-2021-set2
calculus
limits
0
votes
0
answers
2
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 $1$ $2$ $3$ $4$
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asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
3
GATE Civil 2021 Set 2 | Question: 3
The unit normal vector to the surface $X^{2} + Y^{2} + Z^{2} – 48 = 0$ at the point $(4, 4, 4)$ is $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ $\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}}$ $\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}}$
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asked
in
Calculus
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
calculus
vector-calculus
vector-identities
unit-normal-vector
0
votes
0
answers
4
GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$
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asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
linear-algebra
matrices
matrix-algebra
0
votes
0
answers
5
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 ______________
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asked
in
Calculus
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
numerical-answers
calculus
definite-integral
0
votes
0
answers
6
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 $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$
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asked
in
Ordinary Differential Equation (ODE)
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
ordinary-differential-equation
0
votes
0
answers
7
GATE Civil 2021 Set 2 | Question: 27
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are $1.55$ and $\begin{Bmatrix} 2.00\\ 0.45 \end{Bmatrix}$ $2.00$ ... and $\begin{Bmatrix} -2.55\\ -0.45 \end{Bmatrix}$ $1.55$ and $\begin{Bmatrix} 2.00\\ -0.45 \end{Bmatrix}$
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asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
8
GATE Civil 2021 Set 2 | Question: 36
A function is defined in Cartesian coordinate system as $f(x,y)=xe^{y}$. The value of the directional derivative of the function ($\textit{in integer}$) at the point $(2,0)$ along the direction of the straight line segment from point $(2, 0)$ to point $\left ( \dfrac{1}{2} ,2\right )$ is _________
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in
Calculus
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
numerical-answers
calculus
directional-derivatives
0
votes
0
answers
9
GATE Civil 2021 Set 2 | Question: 46
Numerically integrate, $f(x)=10x-20x^2$ from lower limit $a=0$ to upper limit $b=0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in $\text{units}, \textit{round off to two decimal places}$) obtained is ________________
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asked
in
Numerical Methods
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
10
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 $1$ $2$ $3$ $4$
Arjun
asked
in
Linear Algebra
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
linear-algebra
matrices
rank-of-matrix
0
votes
0
answers
11
GATE Civil 2021 Set 1 | Question: 2
If $P=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^{T}\:P^{T}$ is $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ $\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}$ $\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$ $\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$
Arjun
asked
in
Linear Algebra
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
linear-algebra
matrices
matrix-algebra
0
votes
0
answers
12
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
Arjun
asked
in
Probability and Statistics
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
probability-and-statistics
statistics
gaussian-distributions
0
votes
0
answers
13
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 _____________
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asked
in
Calculus
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
numerical-answers
calculus
limits
0
votes
0
answers
14
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 ($\textit{in integer}$) _____________
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
numerical-answers
calculus
tripple-integrals
volume
0
votes
0
answers
15
GATE Civil 2021 Set 1 | Question: 26
The solution of the second-order differential equation $\dfrac{d^{2}y}{dx^{2}}+2\dfrac{dy}{dx}+y=0$ with boundary conditions $y\left ( 0 \right )=1$ and $y\left ( 1 \right )=3$ is $e^{-x}+\left ( 3e-1 \right )xe^{-x}$ ... $e^{-x}-\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$
Arjun
asked
in
Ordinary Differential Equation (ODE)
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
ordinary-differential-equation
second-order-differential-equation
0
votes
0
answers
16
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 $1.718$ $1.727$ $2.192$ $2.718$
Arjun
asked
in
Numerical Methods
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
17
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 __________________
Arjun
asked
in
Numerical Methods
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
numerical-answers
numerical-methods
simpsons-rule
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
18
GATE2020-CE-1-1
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 non-linear equation a second degree non-linear equation
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asked
in
Partial Differential Equation (PDE)
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
partial-differential-equation
0
votes
1
answer
19
GATE2020-CE-1-2
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
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asked
in
Calculus
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
calculus
limits
0
votes
0
answers
20
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 $35$ $48$ $69$ $84$
go_editor
asked
in
Numerical Methods
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
numerical-methods
linear-interpolation
0
votes
0
answers
21
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 $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
calculus
curves
area-under-curve
0
votes
0
answers
22
GATE2020-CE-1-18
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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asked
in
Probability and Statistics
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
probability-and-statistics
probability
numerical-answers
0
votes
0
answers
23
GATE2020-CE-1-26
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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asked
in
Ordinary Differential Equation (ODE)
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
ordinary-differential-equation
0
votes
0
answers
24
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 $=h$ ...
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asked
in
Calculus
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
calculus
derivatives
continuous-function
0
votes
0
answers
25
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 ______
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asked
in
Calculus
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
calculus
line-integral
0
votes
0
answers
26
GATE2020-CE-1-40
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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asked
in
Linear Algebra
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
linear-algebra
matrices
system-of-equations
numerical-answers
0
votes
0
answers
27
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
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asked
in
Ordinary Differential Equation (ODE)
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
ordinary-differential-equation
0
votes
0
answers
28
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
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asked
in
Calculus
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
calculus
limits
0
votes
0
answers
29
GATE2020 CE-2-3
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 ... NON-zero 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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asked
in
Numerical Methods
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
30
GATE2020 CE-2-4
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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asked
in
Partial Differential Equation (PDE)
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
partial-differential-equation
0
votes
0
answers
31
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 _______.
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asked
in
Probability and Statistics
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
32
GATE2020 CE-2-24
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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asked
in
Calculus
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-answers
calculus
gradient
0
votes
0
answers
33
GATE2020 CE-2-26
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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in
Ordinary Differential Equation (ODE)
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
ordinary-differential-equation
0
votes
0
answers
34
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 $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
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in
Linear Algebra
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
linear-algebra
matrices
eigen-values
0
votes
0
answers
35
GATE2020 CE-2-39
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by $ x-x^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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in
Partial Differential Equation (PDE)
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-answers
partial-differential-equation
fourier-series
0
votes
0
answers
36
GATE2020 CE-2-40
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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in
Numerical Methods
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-answers
numerical-methods
0
votes
0
answers
37
GATE2017 CE-2-1
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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Linear Algebra
Aug 7, 2019
by
gatecse
4.0k
points
gate2017-ce-2
linear-algebra
system-of-equations
0
votes
0
answers
38
GATE2017 CE-2-2
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 $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
gatecse
asked
in
Calculus
Aug 7, 2019
by
gatecse
4.0k
points
gate2017-ce-2
calculus
partial-derivatives
0
votes
0
answers
39
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 ________
gatecse
asked
in
Calculus
Aug 7, 2019
by
gatecse
4.0k
points
gate2017-ce-2
calculus
vector-calculus
divergence
numerical-answers
0
votes
0
answers
40
GATE2017 CE-2-20
A two-faced 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 ________
gatecse
asked
in
Probability and Statistics
Aug 7, 2019
by
gatecse
4.0k
points
gate2017-ce-2
numerical-answers
probability-and-statistics
probability
conditional-probability
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