The arithmetic mean of a set of observations is $\bar{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is:

Which system of classification is used by most of the world's well-known herbaria?

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

The major product of the following reaction is

Which of the following interhalogen compounds does not exist?

$A$ particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude.