Let be a binary operation on set Q of rational numbers defined as a = ab 5 . Write the identity for .

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

The maximum value of $\triangle=\begin{vmatrix}1&1&1\\1&1+\sin\theta&1\\1+\cos\theta&1&1\end{vmatrix}$ is $(\theta$ is real$):$

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The value of $\int_0^{\pi /4} {\frac{{1 + \tan x}}{{1 - \tan x}}\,dx} $ is

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A particle moves so that $S = 6 + 48t - {t^3}$. The direction of motion reverses after moving a distance of

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Let $\vec{a}$ and $\overrightarrow{ b }$ be two non-zero vectors perpendicular to each other and $|\overrightarrow{ a }|=|\overrightarrow{ b }| .$ If $|\overrightarrow{ a } \times \overrightarrow{ b }|=|\overrightarrow{ a }|,$ then the angle between the vectors $(\vec{a}+\vec{b}+(\vec{a} \times \vec{b}))$ and $\vec{a}$ is equal to

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Choose the correct answer from the given four option.
Integrating factor of $\frac{\text{xd}\text{y}}{\text{d}\text{x}}-\text{y}=\text{x}^4-3\text{x}$ is:

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Find all the points of discontinuity of the function $f$ defined by

$f(x) = \left\{ {\begin{array}{*{20}{c}}
{x + 2,}&{if\,\,x\,\, < \,\,1}\\
{0,}&{if\,\,\,x = 1}\\
{x - 2,}&{if\,\,x\,\, > \,\,1}
\end{array}} \right.$

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$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{ dx}$ is equal to:

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Which of these is equal to $\int 2^{(x+3)} d x$, where $C$ is the constant of integration?

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$\int {\frac{{x\,\,dx}}{{{x^2} + 4x + 5}} = } $

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Let $f:\left[ {4,\infty } \right) \to \left[ {1,\infty } \right)$ be a function defined by $f\left( x \right) = {5^{x\left( {x - 4} \right)}}$ then $f^{-1}(x)$ is

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