Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variable of number of jacks obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals

The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to

Let $\mathrm{P}(2,3,6)$ be a point in space and Q be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+4 z=1$ is

Consider the following statements

p : the switch $\mathrm{S}_1$ is closed.

q : the switch $\mathrm{S}_2$ is closed.

$r$ : the switch $\mathrm{S}_3$ is closed.

Then the switching circuit represented by the statement $(p \wedge q) \vee(\sim p \wedge(\sim q \vee p \vee r))$ is