If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

If the tangents drawn to the hyperbola 4y² = x² + 1 intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB 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 :

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 :