If $$ I=\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=P \cos x+Q \log \left|\frac{\sqrt{2} \cos x-1}{\sqrt{2} \cos x+1}\right| $$ (where $$c$$ is a constant of integration), then values of $$\mathrm{P}$$ and $$\mathrm{Q}$$ are respectively

The negation of the statement $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is

The probability mass function of random variable X is given by

$$P[X=r]=\left\{\begin{array}{ll} \frac{{ }^n C_r}{32}, & n, r \in \mathbb{N} \\ 0, & \text { otherwise } \end{array} \text {, then } P[X \leq 2]=\right.$$

The distance of a point $$(2,5)$$ from the line $$3 x+y+4=0$$ measured along the line $$L_1$$ and $$L_1$$ are same. If slope of line $$L_1$$ is $$\frac{3}{4}$$, then slope of the line $$\mathrm{L}_2$$ is