Hema's age is 5 years more than twice Hari's age. Suresh's age is 13 years less than 10 times Hari's age. If Suresh is 3 times as old as Hema, how old is Hema?

The temperature T in a room varies as a function of the outside temperature T₀ and the number of persons in the room p, according to the relation $$T = K(\Theta p + {T_0})$$, where $$\Theta $$ and K are constants. What would be the value of $$\Theta $$ given the following data?

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

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?