Aman, Bhanu, and Chetna joined a business, investing Rs. 1200, Rs. 1600, and Rs. 'r', respectively. After 6 months, Aman, Bhanu, and Chetna increased their investments by Rs. 'r', Rs. 'r', and Rs. 800, respectively. At the end of 15 months, Aman's share of the total profit of Rs. 5200 is Rs. 1800. Determine the value of 'r'.

If a = 2 + √3, then the value of`(a^(6) + a^(4) + a^(2) + 1)/(a^(3))` is

If (x + y) = 35, then find the value of (x - 10)⁶ + (y - 25)⁶.

If a – b – c = 0, then the value of (a² + b² + c²)/(b + ac) is:

Rs. 25200 is invested in 3 parts in such a way that Simple Interest on 1^st Part at 4% per annum for 3 years, Simple Interest on 2^nd

The area of △ ABC is 44 cm² . If D is the midpoint of BC and E is the midpoint of AB, then the area of △ BDE is 

If  a²+2 = 2a

then find a⁴ - a³ + 2a² -2a+ 9 = ?

If 4x + 1/3x = 12 then find the value of 9x² +1/16x².

If (x² + y²) = 9 and (xy)² = 3, then find the value of (x⁴ + y⁴).