The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then each of them is decreased by 25, their mean remains the same. Then $$\lambda $$ is equal to :

A box 'A' contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box 'B' contains $$4$$ white, $$2$$ red and $$3$$ black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is :

If tanA and tanB are the roots of the quadratic equation, 3x² $$-$$ 10x $$-$$ 25 = 0, then the value of 3 sin²(A + B) $$-$$ 10 sin(A + B).cos(A + B) $$-$$ 25 cos²(A + B) is :

An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt 3 $$ kmabove it, is obsered at an elevation of $${60^o}$$ from a point on the ground. If, after five seconds, its elevation from the same point, is $${30^o}$$, then the speed (in km / hr) of the aeroplane, is :