If A = [ * 20 c 2&5 3&7 ]and B = [ * 20 c 0&3 4&1 ],then

$f(x)\, = \left\{ {\begin{array}{*{20}{c}}{x\,\sin \,\left( {\frac{1}{x}}\right)\,\,\,\,\,\,\,for\,\, - 1 \le x \le 1\,\,and\,\,x \ne \,0}\\
{0\,\,\,\,\,\,\,\,\,\,\,\,for\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \,0}
\end{array}} \right.$

$g(x)\, = \left\{ {\begin{array}{*{20}{c}}{{x^2}\,\sin \,\left( {\frac{1}{x}} \right)\,\,\,\,\,\,\,for\,\, - 1 \le x \le 1\,\,and\,\,x \ne \,0}\\{0\,\,\,\,\,\,\,\,\,\,\,\,for\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \,0}\end{array}} \right.$ $h (x) = | x |^3$ for $- 1 \le x \le 1$ Which of these functions are differentiable at $x = 0$ ?

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The equation of tangent to the curve $y(1 + x^2) = 2 - x, w$ here it crosses $x-$axis is:

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$\int\limits^{\infty}_0\log\Big(\text{x}+\frac{1}{\text{x}}\Big)\frac{1}{1+\text{x}^2}\text{ dx}=$

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Let $f: R \rightarrow R$ be given by $\text{f(x)}=\tan\text{x}.$ Then,$f^{-1}(1)$ is:

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Let $f:\left[ { - 2,3} \right] \to \left[ {0,\infty } \right)$ be a continuous function such that $f(1-x) = f(x)$ for all $x \in \left[ { - 2,3} \right]$ . If $R_1$ is the numerical value of the area of the region bounded by $y =f (x), x = -2, x = 3$ and the axis of $x$ and ${R_2} = \int\limits_{ - 2}^3 {x\,f\left( x \right)} dx$ , then

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If $\left[\begin{array}{ccc}x+3 & z+4 & 2 y-7 \\ -6 & a-1 & 0 \\ b-3 & -21 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & 6 & 3 y-2 \\ -6 & -3 & 2 c+2 \\ 2 b+4 & -21 & 0\end{array}\right]$ then find the values of $a,\, b, \,c, \,x, \,y$ and $z$.

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The reflection of the point $(\text{a}, \beta, \gamma) $ in the $xy-$plane is: