The difference between the roots of the equation $x^2 + 2x + 4 = 0$ is $\ldots$ (where $i = \sqrt{-1}$)

In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is $\ldots$

Let $f_k(x) = \dfrac{1}{k}(\cos^k x + \sin^k x)$ where $k \in N$, then $f_6(x) - f_4(x) = \ldots$

The coordinates of the orthocenter of the triangle whose sides are represented by the lines $4x - 7y + 10 = 0$, $x + y = 5$ and $7x + 4y = 15$ are $\ldots$