For positive non-zero real variables $p$ and $q$, if

$\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3$,

then, the value of $\frac{p^4 + q^4}{p^2 q^2}$ is

A series of natural numbers $$F_1,F_2,F_3,F_4,F_5,F_6,F_7,\,.....$$ obeys $$F_{n+1}=F_n+F_{n-1}$$ for all integers $$n\ge2$$.

If $$F_6=37$$, and $$F_7=60$$, then what is $$F_1$$ ?

A function y(x) is defined in the interval [0, 1] on the x-axis as

$$y(x) = \left\{ \matrix{ 2\,if\,0 \le x < {1 \over 3} \hfill \cr 3\,if\,{1 \over 3} \le x < {3 \over 4} \hfill \cr 1\,if\,{3 \over 4} \le x < 1 \hfill \cr} \right.$$

Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

Let r be a root of the equation x² + 2x + 6 = 0. Then the value of the expression (r + 2) (r + 3) (r + 4) (r + 5) is