If x, y are two positive real number and  $$x^{1/3}=y^{1/4}$$, then which of the following relations is true?

Among three numbers, the first is twice the second and thrice the third. If the average of the three numbers is 49.5, then the difference between the first and the third number is: 

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}$$.

The average of 8 readings is 24.3, out of which the average of the first two is 18.5 and that of next three is 21.2. If the sixth reading is 3 less than seventh and 8 less than eight, what is the sixth reading? 

What annual instalment will discharge a debt of ₹ 6450 due in 4 years at 5% simple interest?

A sum of Rs. 12,000, deposited at compound interest becomes double after 5 years. How much will it be after 20 years? 

If $$\sqrt { 3}=1.732$$ then the find the value of $${9+2{ \sqrt { 3}}}\over  \sqrt { 3}$$  

The zeros of the cubic polynomial $$ {2x^{3}-x^{2}-2x+1}$$ are a, b and c respectively. Find ab + bc + ca =?