List of top Mathematics Questions on Combinatorics asked in MET

If \[ t_n = \sum_{r=0}^n \frac{1}{\left({}^nC_r\right)^k} \quad \text{and} \quad S_n = \sum_{r=0}^n \frac{r}{\left({}^nC_r\right)^k}, \] where \( k \in \mathbb{Z}^+ \), then \[ \cos^{-1}\left( \frac{S_n}{n t_n} \right) \] is:

If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is

Nishi has 5 coins each of different denomination. The number of different sums of money she can form is ________.