Mrs. Rajni deposited $Rs. 10,000$ in a bank that pays $4 \%$ interest compounded continuously. The amount she gets after $10$ years is approximately $Rs.$ . . . . . . . (Given $e^{(0.4)} = 1.49182$)

If the angle between the curves $y = a^x$ and $y = b^x$ is $\alpha$,find the modulus of $\tan \alpha$.

If $f(x) = \log_{x^2}(\log_{e} x)$,then $f^{\prime}(x)$ at $x = e$ is

If $y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$,then $\frac{d y}{d x}$ at $x=\frac{\pi}{3}$ is

$\frac{d}{dx} \left( \log \sqrt{\frac{1+\sin x}{1-\sin x}} \right) = $

If $y = f \left( \frac{3 + 2x}{3 - 2x} \right)$, where $f(x) = \tan(\log x)$ and $\frac{dy}{dx} = \left( \frac{A}{B + Cx^2} \right) \cdot \sec^2 \left( \log \left( \frac{3 + 2x}{3 - 2x} \right) \right)$, then the respective values of $A, B$ and $C$ are ......