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?

$$\underbrace {{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,.......\,{\rm{ + }}\,{\rm{a}}}_{{\rm{n}}\,{\rm{times}}} = {a^2}b$$ and $$\underbrace {b\,{\rm{ + }}\,b\,{\rm{ + }}\,b\,{\rm{ + }}\,.......\,{\rm{ + }}\,b}_{m\,\,{\rm{times}}} = a{b^2}$$, where a, b, n and m are natural numbers. What is the value of $$\left( {\underbrace {b\,{\rm{ + }}\,b\,{\rm{ + }}\,b\,{\rm{ + }}\,.......\,{\rm{ + }}\,b}_{n\,\,{\rm{times}}}} \right)\left( {\underbrace {a\,{\rm{ + }}\,a\,{\rm{ + }}\,a\,{\rm{ + }}\,.......\,{\rm{ + }}\,a}_{m\,\,{\rm{times}}}} \right)$$?