Simplify the following expression.

$${\left({375+125} \right)^2-\left({125-375} \right)^2}\over 375×375-125×125$$

If a ≠ b, then which of the following statement is true ?

Directions: In each of these questions, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly.

(i) 6x² – 11x + 4 = 0
 (ii) 3y² – 5y + 2 = 0

Given that x³ + y³ = 72 and xy = 6 with x > y. Then the value of (x – y) is

P = 12xy – 10y² – 18x²,

Q = 14x² + 12y² + 9xy, and

R = 5y² – x² + xy

then (P + Q) – R =

If (m + 1) = √n + 3, the value of   $${1\over 2}\left({m^3-6m^2+12m-8\over \sqrt { n}}-n \right)  \ $$ is

If   $$x+{1\over x}=2 $$ then the value of    $$x^{12}-{1\over x^{12}} $$ is

Directions: In each of these questions, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly.

(i) 2x³ = $$ \sqrt {256}$$
 (ii) 2y² – 9y + 10 = 0