If the roots of the quadratic equation x² + 2x + k = 0 are real, then

If n = 100!, then what is the value of the following?

$\rm \dfrac{1}{log_2n}+\dfrac{1}{log_3n}+\dfrac{1}{log_4n}+{.....}+\dfrac{1}{log_{100}n}$

If Z = 1 + i, where i = √-1, then what is the modulus of $\rm z+\frac{2}{z}?$

If A and B are two matrices such that AB is of order n × n, then which one of the following is correct?