Most viewed questions in Engineering Mathematics

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Consider an unfair coin. The probability of getting heads is $0.6$. If you toss this coin twice, what is the probability that the fast or the second toss is heads?$0.56$$...
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A disease is inherited by a child with a probability of $1/4$. In a family with two children, the probability that exactly one sibling is affected by this disease is$1/4$...
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The value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________
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$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = ...
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The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.
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The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$
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The Laplace transform of $f(t) = 2t + 6$ is$\frac{1}{s}+\frac{2}{s^2}$$\frac{3}{s}-\frac{6}{s^2}$$\frac{6}{s}+\frac{2}{s^2}$$-\frac{6}{s}+\frac{2}{s^2}$
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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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The value of the integral $\displaystyle \int_0^{0.9} \dfrac{dx}{(1-x)(2-x)}$ is ____________
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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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17
The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
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18
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
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The variable $z$ has a standard normal distribution. If $P(0 \leq z \leq 1)= 0.34$ then $P(z^2 1)$ is equal to (up to two decimal places) ____________
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22
The solution to the following set of equations is$$2x+3y=4$$$$4x+6y=0$$$x=0,y=0$$x=2, y=0$$4x=-6y$No solution
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23
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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25
The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.
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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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28
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}$$e^x$
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29
The Laplace transform $F(s)$ of the function $f(t) = \cos (at)$, where $a$ is constant, _________$\dfrac{s^2}{s^2+a^2} \\$$\dfrac{a}{s^2+a^2} \\$$\dfrac{s}{s^2+a^2} \\$$\...
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30
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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31
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
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32
If $1+r + r^2+ r^3 +\dots \infty = 1.5$, then, $1 + 2r + 3r^2 + 4r^3 + \dots \infty = $ (up to two dcimal places) ________
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33
If $P=\begin{bmatrix}1&1\\2&2\end{bmatrix}, Q=\begin{bmatrix}2&1\\2&2\end{bmatrix}$ and $R=\begin{bmatrix}3&0\\1&3\end{bmatrix}$, which one of the following statements is...
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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$$-2$ and $-3$
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37
What is the rank of the following matrix?$$\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$$$0$$1$$2$$3$
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Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
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39
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 ____________