If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω²)¹⁰⁰ + (1 - ω + ω²)¹⁰⁰ equal to?  

Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct? 

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 p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to?