Binomial theorem Questions

What is the coefficient of x¹⁰ in the expansion of (1-x² )²⁰ (2-x² -1/x²)^-5

If the 4^th term in the expansion of (mx+1/x)ⁿ is 5/2 , then what is the value of mn?

In a binomial expansion of (x + y)^{2n + 1}(x – y)^{2n + 1}, the sum of middle terms is zero. What is the value of x²/y²?

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)?

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?

What is the number of rational terms in the expansion of (3^1/2 +5^1/4)¹²?

Which one of the following is the greatest coefficient in the expansion of (1+x)¹⁰⁰?

If C₀, C₁, C₂, ..., Cₙ are the coefficients in the expansion of
(1 + x)ⁿ, then what is the value of

C₁ + C₂ + C₃ + ... + Cₙ ?

What is the coefficient of the middle term in the expansion of (1 + 4x + 4x²)⁵ ?