The sum of all values of x in [0, 2$$\pi$$], for which sin x + sin 2x + sin 3x + sin 4x = 0, is equal to :

If 15sin⁴$$\alpha$$ + 10cos⁴$$\alpha$$ = 6, for some $$\alpha$$$$\in$$R, then the value of

27sec⁶$$\alpha$$ + 8cosec⁶$$\alpha$$ is equal to :

The number of solutions of the equation x + 2tanx = $${\pi \over 2}$$ in the interval [0, 2$$\pi$$] is :

The number of roots of the equation, (81)^sin2x + (81)^cos2x = 30 in the interval [ 0, $$\pi$$ ] is equal to :