If the sum of binomial coefficients in the expansion of $(x+y){}^n$ is 256, then the greatest binomial coefficient occurs in which one of the following terms?

If $k<(\sqrt{2}+1)^3<k+2,$ where k is a natural number, the value of k?

In the expansion of (1 + x)^p (1 + x)^q, if the coefficient of x³ is 35, then what is the value of (p + q)? 

What is the remainder when 7ⁿ - 6n is divided by 36 for n = 100?