$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

The scientific name of the earthworm is ....

In an atom,the order of increasing energy of electrons with quantum numbers $(i)$ $n=4, l=1$,$(ii)$ $n=4, l=0$,$(iii)$ $n=3, l=2$,and $(iv)$ $n=3, l=1$ is:

Let $\vec{p}$ and $\vec{q}$ be the position vectors of points $P$ and $Q$ with respect to the origin $O$,and $|\vec{p}| = p$,$|\vec{q}| = q$. If points $R$ and $S$ divide the line segment $PQ$ internally and externally in the ratio $2:3$ respectively,and if $\vec{OR} \perp \vec{OS}$,then:

Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R$. At time $t = 0$,the number of $P$ species is $4N_0$ and that of $Q$ is $N_0$. The half-life of $P$ is $1$ minute,while that of $Q$ is $2$ minutes. Initially,there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ are equal,the number of nuclei of $R$ present in the sample would be:

$A$ bag contains $5$ black balls,$4$ white balls,and $3$ red balls. If a ball is selected at random,the probability that it is a black or red ball is