If $$ {3\sqrt{{1-a}\over{a}}}+9={19-3\sqrt{{a}\over{1-a}}}$$, then what is the value of a?

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 $$ [{ {y\over {y-z}}}] +[{ {x\over {x-z}}}]$$.

Who is the Grand Old Man of India?

Who was the Governor General during the independence of India?