Let two points be A(1, –1) and B(0, 2). If a point P(x', y') be such that the area of $$\Delta $$PAB = 5 sq. units and it lies on the line, 3x + y – 4$$\lambda $$ = 0, then a value of $$\lambda $$ is :

Let ƒ : R $$ \to $$ R be such that for all x $$ \in $$ R
(2^1+x + 2^1–x), ƒ(x) and (3^x + 3^–x) are in A.P.,
then the minimum value of ƒ(x) is

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 :