If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then

$A$ ball is dropped from a height of $5 \ m$. The time after which the ball stops rebounding,if the coefficient of restitution between the ball and the ground is $e = 1/2$,is ................. $s$.

The number of nuclei of a radioactive substance at time $t = 0$ is $1000$,and at time $t = 2 \ s$,it is $900$. Then,the number of nuclei at time $t = 4 \ s$ will be:

What is obtained by the reaction of $HCOOH$ with concentrated $H_2SO_4$?

The rate constant,$k$,of a zero order reaction $2 NH_3(g) \xrightarrow[1130 \ K]{Pt} N_2(g) + 3 H_2(g)$ is $y \times 10^{-4} \ mol \ L^{-1} \ s^{-1}$. The rate of formation of hydrogen (in $mol \ L^{-1} \ s^{-1}$) is

If $0 < p < q$,then $\lim _{n \rightarrow \infty}\left(q^n+p^n\right)^{1 / n}$ is equal to :