The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, are

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 $$\mathrm{n}=$$

The teacher wants to arrange 5 students on the platform such that the boy $$B_1$$ occupies second position and the girls $$G_1$$ and $$G_2$$ are always adjacent to each other, then the number of such arrangements is

Five students are to be arranged on a platform such that the boy $$B_1$$ occupies the second position and such that the girl $$G_1$$ is always adjacent to the girl $$G_2$$. Then, the number of such possible arrangements is