Let A and B be two independent events such that
P(A) = $${1 \over 3}$$ and P(B) = $${1 \over 6}$$.
Then, which of the following is TRUE?

The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x² = 4y, internally in the ratio 1 : 2, is :

For which of the following ordered pairs ($$\mu $$, $$\delta $$), the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = $$\mu $$
4x + 4y + 4z = $$\delta $$
is inconsistent ?

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by p and then reduced by q, where p $$ \ne $$ 0 and q $$ \ne $$ 0. If the new mean and new s.d. become half of their original values, then q is equal to