Consider a sequence of numbers $${a_1},{a_2},{a_3},....,{a_n}$$ where $${a_n} = {1 \over n} - {1 \over {n + 2}}$$, for each integer n > 0. What is the sum of the first 50 terms?

Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A $$ \times $$ B $$ \times $$ C), (B $$ \times $$ G $$ \times $$ E) and (D $$ \times $$ E $$ \times $$ F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F or G?

Which of the following function(s) is an accurate description of the graph for the range(s) indicated? $$\eqalign{ & (i)\,\,y = 2x + 4\,for\, - 3 \le x \le - 1 \cr & (ii)\,y = \,|x - 1|\,for\, - 1 \le x \le 2 \cr & (iii)\,y = \,\left| {\left| x \right| - 1} \right|\,for\, - 1 \le x \le 2 \cr & (iv)\,y = 1\,for\,2 \le x \le 3 \cr} $$

The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in Rs.) of two wires of lengths 4 m and 6m?