Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$$, ($$\alpha $$ $$ \in $$ R)
such that $${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$$ then a value of $$\alpha $$ is

The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is :

The sum of the series

2.²⁰C₀ + 5.²⁰C₁ + 8.²⁰C₂ + 11.²⁰C₃ + ... +62.²⁰C₂₀ is equal to :

Let A and B be two non-null events such that A $$ \subset $$ B . Then, which of the following statements is always correct?