Where is the National Botanical Research Institute $(NBRI)$ located?

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$,then the probability of non-occurrence of at least one of the events $E$ and $F$ is

Four numbers are chosen at random from $\{1, 2, 3, \ldots, 40\}$. The probability that they are not consecutive is:

The equations of the circle which pass through the origin and make intercepts of lengths $4$ and $8$ on the $x$ and $y$-axes respectively are

If $\hat{i}+2 \hat{j}+3 \hat{k}$ and $3 \hat{i}+2 \hat{j}+\hat{k}$ are sides of a parallelogram, then a unit vector parallel to one of the diagonals of the parallelogram is