Questions without answers in Engineering Mathematics

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$\dfrac{d}{dx} \left [ \ln (2x) \right ]$ is equal to$1/2x \\$$1/x \\$$1 /2 \\$$x$
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The value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________
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If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________
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The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.
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Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
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The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
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10
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$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...
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12
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
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14
The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.
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15
A function $f$ is given as :$$f(X)=4X-X^{2}$$The function $f$ is maximized when $X$ is equal to _________________.
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16
An infinite series $S$ is given as:$S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity)The value of $S$ is ______________________ (round off to $2$ decimal places).
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A function $f$ is as follows:$$f(x) = \begin{cases} 15 & \text{if }x<1 \\ cx& \text{if } x\geq 1 \end{cases}$$The function $f$ is a continuous function when $c$ is equal ...
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Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
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20
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The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$
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22
The Laplace transform $F(s)$ of the function $f(t) = \cos (at)$, where $a$ is constant, _________$\dfrac{s^2}{s^2+a^2} \\$$\dfrac{a}{s^2+a^2} \\$$\dfrac{s}{s^2+a^2} \\$$\...
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23
The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________
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24
$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = ...
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25
The value of determinant $A$ given below is ________.$A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
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26
The surface area (in $m^2$) of the largest sphere that can fit into a hollow cube with edges of length $1$ meter is ______Given data: $\pi=3.14$
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27
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
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28
The angle (in degrees) between the vectors $\overrightarrow{x}= \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{y} = 2 \hat{i} – \hat{j}-1.5 \hat{k}$ is _________
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31
Consider the following infinite series:$$1+ r+r^2 +r^3+ \dots \dots \infty$$ If $r = 0.3$, then the sum of this infinite series is ____________
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32
$$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$$ The system of linear equations in two variables shown above will have infinite solutions, if and onl...
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33
What are the eigenvalues of the following matrix? $$\begin{bmatrix} 1 & 1 \\ -2 & 4 \end{bmatrix}$$$2$ and $3$$-2$ and $3$$2$ and $-3$$-2$ and $-3$
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35
The limit of the function $\bigg (1 + \dfrac{x}{n} \bigg )^n$ as $n \to \infty$ is$\ln x$$\ln \dfrac{1}{x}$$e^{-x}$$e^x$
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37
The eigenvalues of A =$\begin{bmatrix} 1&-4\\2 & -3 \end{bmatrix} $are$2\underline{+}i$$-1, -2$$-1\underline{+}2i$non-existent
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39
The solution for the following set of equations is,$$5x+4y+102=13$$$$x+3y+z=7$$$$4x2y+z=0$$$x=2,y=1,z=1$$x=1,y=2,z=0$$x=1,y=0,z=2$$x=0,y=1,z=2$
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40
The limit of the function $e^{-2t}\sin (t)$ as t $\rightarrow\infty$ so, is
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