is A Polynomial Of Degree

Sum of the last 30 coefficients in the expansion of (1 + x)⁵⁹ when expanded in ascending powers of x is

 then k is equal to:

 is maximum when m is

If ω ≠ 1 is a cube root of unity and (ω + x)n = 1 + 12ω + 69ω +…. Then values of n and x are respectively.

If ω ≠ 1, is nth root of unity, and  then value of x is

The remainder when  (24 times 5) is divided by 24 is

 divided by 7 is

If in the expansion of (a – 2b)ⁿ. the sum of 4^th and 5^th term is 0, then value of  is

The coefficient of t⁵⁰ in (1 + t²)²⁵ (1 + t²⁵) (1 + t⁴⁰) (1 + t⁴⁵) (1 + t⁴⁷)……(1) is

 is a polynomial of degree