Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is

If the line $$r=(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$$ is parallel to the plane $$r \cdot(3 \hat{i}-2 \hat{\mathbf{j}}+m \hat{\mathbf{k}})=10$$, then the value of $$m$$ is

Let $$G$$ be the centroid of a $$\triangle A B C$$ and $$\mathrm{O}_{b_\theta}$$ other point in that plane, then $$\mathrm{OA}+\mathrm{OB}+\mathrm{OC}+\mathrm{CG}=$$

The points $$A(-a,-b), B(0,0), C(a, b)$$ and $$D\left(a^2, a b\right)$$ are