The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is

The larger of $${99^{50}} + {100^{50}}$$ and $${101^{50}}$$ is ..............

The sum of the coefficients of the plynomial $${\left( {1 + x - 3{x^2}} \right)^{2163}}$$ is ...............

In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave more than k wrong answers. The total number of wrong answers given is.....................................