If A= [ cc & - & ] and A+A^ =I, then find the value of

If $A=\left|\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right|$ then show that $|3 A |=27| A |$

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Find $\frac{\text{dy}}{\text{dx}}$ when x and y are connected by the relation:
$\tan^{-1}(\text{x}^2+\text{y}^2)=\text{a}$

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Find the vector equation of a plane passing throught a point with position $2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and perpendicular to the vector $4\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}$

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For the principal values, evaluate the following:
$\sin^{-1}\Big(-\frac{\sqrt3}{2}\Big)+\text{cosec}^{-1}\Big(-\frac{2}{\sqrt3}\Big)$

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Represent the following families of curves by forming the corresponding differential equation:
$\text{x}^2-\text{y}^2=\text{a}^2$

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Define an associative binary operation on a set.

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Find $\frac{\text{dy}}{\text{dx}},$ when
$\text{x}=\text{a}(1-\cos\theta)\text{ and y}=\text{a}(\theta+\sin\theta)\text{ at }\theta=\frac{\pi}{1}$

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Find $\frac{{dy}}{{dx}},$ if $y = {\tan ^{ - 1}}\left( {\frac{{3x - {x^3}}}{{1 - 3{x^2}}}} \right), - \frac{1}{{\sqrt 3 }} < x < \frac{1}{{\sqrt 3 }}$

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Evaluate $\begin{vmatrix}\cos\alpha\cos\beta&\cos\alpha\sin\beta&-\sin\alpha\\-\sin\beta&\cos\beta&0\\\sin\alpha\cos\beta&\sin\alpha\sin\beta&\cos\alpha\end{vmatrix}.$

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Evaluate the following integrals:
$\int\limits^3_0\frac{1}{\text{x}^2+9}\text{ dx}$

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[ Question Bank ] — Maths STD 12 Science — Question

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