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

For a > 0, let the curves C₁ : y² = ax and C₂ : x² = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C₁ and C₂, and the area of
$$\Delta $$OQR = $${1 \over 2}$$, then 'a' satisfies the equation :