For any three positive real numbers a, b and c,

9(25$${a^2}$$ + b²) + 25(c² - 3$$a$$c) = 15b(3$$a$$ + c).
Then

If   A > 0, B > 0   and    A + B = $${\pi \over 6}$$,

then the minimum value of tanA + tanB is :

Let a₁, a₂, a₃, . . . . . . . , a_n, . . . . . be in A.P.

If a₃ + a₇ + a₁₁ + a₁₅ = 72,

then the sum of its first 17 terms is equal to :

Let z = 1 + ai be a complex number, a > 0, such that z³ is a real number.

Then the sum 1 + z + z² + . . . . .+ z¹¹ is equal to :