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?

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?

For non-negative integers, a, b, c, what would be the value of a + b + c if $$$\log \,a\, + \,\log \,b\, + \,\log \,c\, = \,0?$$$

A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?