If $$ {a^4+1}={{a^2}\over{b^2}}{(4b^2-b^4-1)}$$,then what is the value of $${a^4+b^4}$$?

If $$ {x^2-12x+33=0}$$, then what is the value of $${(x-4)^2+[{1\over({x-4})^2}}]$$.

If one root of the equation $$ {Ax^2+Bx+C=0}$$ is two and a half times the others, then which of the following is True?

If α and β are the roots of equation $$ {x^2-2x+4=0}$$, then what is the equation whose roots are ${α^3}\over{β^2}$$ and $${β^3}\over{α^2}$$.

If $$ ({x+y\over z})=2$$ , then what is the value of $$ [{ {y\over {y-z}}}] +[{ {x\over {x-z}}}]$$.

The average age of a cricket team of 11 players is the same as it was 3 years back because 3 of the players whose current average age of 33 years are replaced by 3 youngsters. The average age of the new comers is: 

A can do a piece of work in 12 days. When he had worked for 3 days. B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work? 

Three pipes A , B and C takes 15, 24 and 36 minutes respectively to fill a tank. Pipe D can empty it in 1 hour. If all the four pipes are kept open then find the time taken to fill the tank.