If the plane 2x – y + 2z + 3 = 0 has the distances $${1 \over 3}$$ and $${2 \over 3}$$ units from the planes 4x – 2y + 4z + $$\lambda $$ = 0 and 2x – y + 2z + $$\mu $$ = 0, respectively, then the maximum value of $$\lambda $$ + $$\mu $$ is equal to :

Let f(x) = log_e(sin x), (0 < x < $$\pi $$) and g(x) = sin^–1 (e^–x ), (x $$ \ge $$ 0). If $$\alpha $$ is a positive real number such that a = (fog)'($$\alpha $$) and b = (fog)($$\alpha $$), then :

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : $$\sqrt 3 $$. If c = 4 cm, then the area (in sq. cm) of this triangle is :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :