If p, q, r are any real numbers, then

Prove that $${7^{2n}} + \left( {{2^{3n - 3}}} \right)\left( {3n - 1} \right)$$ is divisible by 25 for any natural number $$n$$.

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

The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to