There are two value of a which makes the determinant = 1&-2&5 2&a&-1 0&4&2a equal to 86. The sum of these two values is:

There are two value of a which makes the determinant = 1&-2&5 2&a…

Distance of the point $(\alpha, \beta, \gamma)$ from y-axis is:

$\beta$
$\mid\beta\mid$
$\mid\beta+\gamma\mid$
$\sqrt{\alpha^2+\gamma^2}$

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Evaluate : $\int_0^2 e^{3-4 x} d x$

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Let $\text{U}=\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ and $\text{V}=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ then $\frac{\text{dU}}{\text{dV}}=$

$\frac{1}{2}$
$\text{x}$
$\frac{1-\text{x}^2}{\text{x}^2-4}$
$1$

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if $\text{ax}+\frac{\text{b}}{\text{x}}\geq\text{c}$ for all positive x where a, b, > 0, then.

$\text{ab} < \frac{\text{c}^{2}}{4}$
$\text{ab} > \frac{\text{c}^{2}}{4}$
$\text{ab} > \frac{\text{c}}{4}$
$\text{None of these}$

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Solve: $\int\frac{\text{x}^2+1}{\text{x}^2+1}\text{dx}=$

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The differential equation of all parabolas whose axes are parallel to y-axis is:

$\frac{\text{dy}}{\text{dx}}=-\frac{\text{c}^2}{\text{x}^2}$
$\frac{\text{d}^2\text{x}}{\text{dy}^2}=\text{c}$
$\frac{\text{d}^3\text{y}}{\text{dx}^3}+\frac{\text{d}^2\text{x}}{\text{dy}^2}=0$
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}=0$

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If A is a skew symmetric matrix, then ∣A∣ is:

11
-1
0
None

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The number of distinct real roots of $\begin{vmatrix}\text{cosec}&\sec\text{x}&\sec\text{x}\\\sec\text{x}&\text{cosec}\text{x}&\sec\text{x}\\\sec\text{x}&\sec\text{x}&\text{cosecx}\end{vmatrix}=0$ lies in the interval $-\frac{\pi}{4}\leq\text{x}\leq\frac{\pi}{4}$ is:

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If $y=\cos ^2\left(\frac{3 x}{2}\right)-\sin ^2\left(\frac{3 x}{2}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to

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$\tan^{-1}(\sqrt{3})$

$\frac{\pi}{6}$
$\frac{\pi}{3}$
$\frac{2\pi}{3}$
$\frac{5\pi}{6}$

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DETERMINANTS — MATHS STD 12 Science — Question

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