If $$\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}$$ has $$\alpha$$ and $$\beta$$ as its roots, then the value of $$\tan \alpha+\tan \beta$$ is

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is

Given $$0 \leq x \leq \frac{1}{2}$$, then the value of $$\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)-\sin ^{-1} x\right)$$ is

A vector parallel to the line of intersection of the planes $$\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1$$ and $$\bar{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2$$ is