If the difference between the roots of the equation Ax²+BX+C = 0 is 4, then which of the following is TRUE?

If one root of the equation Ax²+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 x² - 2x + 4 - 0, then what is the equation whose roots are α³/β² and β³/α²?

A trader had 2000 kgs of rice. He sold a part of it at 10 % profit and the rest at 16 % profit so that he made a total profit of 14.2%. How much rice (in kg) did he sell at 10 % profit? 

If average of two x and $$1\over x$$ (where x ≠ 0) is A, what will be the average of x³ and $$1\over {x^3}$$?

A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is: 

The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator 7 + C ( C > - 7 ) is a constant, then the minimum value of the fraction is :

The principal which gives ₹ 1 interest per day at a rate of 5 % simple interest per annum is