$f(x) = e^x \sin x$, then $f^{(6)}(x)$ is equal to :

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

Intercalary meristem results in

$A$ carrier signal $60 \sin(2\pi \times 10^6 t)$ is used to modulate an audio signal $15 \sin(300\pi t)$. The depth of modulation is .........$\%$.

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?

$A$ metal $M$ and its compound can give the following observable changes in a sequence of reactions: $M$ $\xrightarrow{\text{dil. } HNO_3} M(NO_3)_2$ $\xrightarrow{NaOH} \text{White ppt.}$ $\xrightarrow{\text{Excess } NaOH} \text{Colourless solution}$ $\xrightarrow{H_2S} \text{White ppt.}$. Identify the metal $M$.