The equation of the plane through $$(-1,1,2)$$ whose normal makes equal acute angles with co-ordinate axes is

If $$\mathrm{T}_{\mathrm{n}}$$ denotes the number of triangles which can be formed using the vertices of regular polygon of $$\mathrm{n}$$ sides and $$T_{n+1}-T_n=21$$, then $$\mathrm{n}=$$

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks is

If $$\tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, 0 \leq \alpha \leq \frac{\pi}{2}$$, then the value of $$\cos 2 \theta$$ is