For how many integral values of k, the equation x² - 4x + k = 0, where k is an integer has real roots and both of them lie in the interval (0, 5) ? 

In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ?

Consider the following statements :

1. (25)! + 1 is divisible by 26

2. (6)! + 1 is divisible by 7

Which of the above statements is/are correct ? 

If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?