What is the number of rational terms in the expansion of $(\sqrt{3}+5^\frac{1}{4})^{12}$

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)?