Let $$\overline{\mathrm{A}}$$ be a vector parallel to line of intersection of planes $$P_1$$ and $$P_2$$ through origin. $$P_1$$ is parallel to the vectors $$2 \hat{j}+3 \hat{k}$$ and $$4 \hat{j}-3 \hat{k}$$ and $$P_2$$ is parallel to $$\hat{j}-\hat{k}$$ and $$3 \hat{i}+3 \hat{j}$$, then the angle between $$\bar{A}$$ and $$2 \hat{i}+\hat{j}-2 \hat{k}$$ is

$$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$

If the variance of the numbers $$-1,0,1, \mathrm{k}$$ is 5, where $$\mathrm{k} > 0$$, then $$\mathrm{k}$$ is equal to

The differential equation $$\cos (x+y) \mathrm{d} y=\mathrm{d} x$$ has the general solution given by