If x : y : z = 6 : 7 : 11, and (2x + 3z) = 180, then find the value of y.

The sum of two numbers is 45 and their difference is 9. What is the larger number?

If x + y + z = 20, x² + Y² + z² = 160 and x z = y², then find the value of x z?

If  (a³+1)/(a+1) = (a³-1)/(a-1) and a ≠ 1, -1. Find the value of  'a'

If (10 a³ + 4b³): (11a³ — 15b³) = 7:5, then (3a + 5b): (9a - 2b) = ?

If cos(A - B) = √3/2 and cot(A + B) = 1/√3, where A - B and A + B are acute angles, then (2A - 3B) is equal to:

[a/(2a²  + 5a + 2)] = 1/6 , then find the value of (a+1)/a ?

If √e + (1/√e) = 10, then find the value of e + (1/e).

If x – 1/x = 9, then x³ – 1/x³ is: