Find vector equation of line passing through the point whose position vector is 3 i-4 j+k and parallel to the vector 2 i+j-3 k. Also write the equation in Cartesian form.

Find vector equation of line passing through the point whose posi…

Integrate the following functions w.r.t x:

$\frac{4 e^x-25}{2 e^x-5}$

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For two matrices A and B, $\text{A}=\begin{bmatrix}2&1&3\\4&1&0\end{bmatrix},\text{B}=\begin{bmatrix}1&-1\\0&2\\5&0\end{bmatrix}$ verify that $(AB)^T = B^TA^T$.

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Find the probability distribution of the number of doublets in 4 throws of a pair of dice.
Also, Find the mean and variance of this distribution.

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Prove that $\sin \left[\tan ^{-1}\left(\frac{1-x^2}{2 x}\right)+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right]=1$

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Evaluate the following integrals:
$\int\text{x}\frac{\tan^{-1}\text{x}^2}{1+\text{x}^4}\text{ dx}$

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If $y=f(u)$ is a differentiable function of $u$ and $u=g(x)$ is a differentlable function of $x$, then prove that $y=f g(x)$ is a differentiable function of $x$ and $\frac{d y}{d x}=\frac{d y}{d u}. \frac{d u}{d x} \quad$

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Obtain the differential equation by eliminating the arbitrary constants from the following equations:

$y=c_1 e^{2 x}+c_2 e^{5 x}$

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Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\cos{\text{x}},0\leq\text{x}\leq\pi$

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Find the vector equation of the line passing through the point A(1, 2, -1) and parallel to the line 5x - 25 = 14 - 7y = 35z.

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Evaluate the following integrals:
$\int\frac{\cos\text{x}}{1+\cos\text{x}}\text{dx}$

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Line and Plane — Maths STD 12 Science — Question

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