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

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.

First ball is drawn. What is the probability of getting an orange ball in the next draw?