Let × be a binary operation on set Q of rational numbers defined as a = ab 5 . Write the identity for ×. 1. 5 2. 3 3. 1 4. 6

Let × be a binary operation on set Q of rational numbers defined …

In which of the following differential equations is the degree equal to its order?

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The area bounded by the parabola y² = 4ax and x² = 4ay is:

$\frac{8\text{a}^3}{3}$
$\frac{16\text{a}^2}{3}$
$\frac{32\text{a}^2}{3}$
$\frac{64\text{a}^2}{3}$

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The differential coefficient of ${\cos ^{ - 1}}\left\{ {\sqrt {{{1 + x} \over 2}} } \right\}$ with respect to $x$ is

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If $\int\limits_{a}^{x}{ty(t)dt={{x}^{2}}+y(x)}$ then $y$ as a function of $x$ is

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$ \begin{bmatrix}1 & \text{x} & \text{x}^2 \\1 & \text{y} & \text{y}^2 \\1 & \text{z} & \text{z}^2\end{bmatrix}$

(x - y) (y + z)(z + x)
(x + y) (y - z)(z - x)
(x - y) (y - z)(z + x)
(x - y) (y - z) (z - x)

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$\left| {\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\sin }^2}\theta }&{{{\sin }^2}\theta }\\{{{\cos }^2}\theta }&{1 + {{\cos }^2}\theta }&{{{\cos }^2}\theta }\\{4\sin 4\theta }&{4\sin 4\theta }&{1 + 4\sin 4\theta }\end{array}} \right| = 0$ then $\sin \,4\theta $ equal to

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The position vector of the point (1, 2, 0) is:

i + j +k
i + 2j + k
i + 2j
2j + k

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The unit vector perpendicular to the vectors $6i + 2j + 3k$ and $3i - 6j - 2k,$ is

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The interval in which the function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{x}}, \mathrm{x}>0$, is strictly increasing is

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$\int_{\, - 1}^{\,2} {|x|\,dx} =$

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