Let $$\alpha $$ and $$\beta $$ be two real roots of the equation
(k + 1)tan²x - $$\sqrt 2 $$ . $$\lambda $$tanx = (1 - k), where k($$ \ne $$ - 1) and $$\lambda $$ are real numbers. if tan² ($$\alpha $$ + $$\beta $$) = 50, then a value of $$\lambda $$ is:

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :

If y = mx + 4 is a tangent to both the parabolas, y² = 4x and x² = 2by, then b is equal to :

The area of the region, enclosed by the circle x² + y² = 2 which is not common to the region bounded by the parabola y² = x and the straight line y = x, is: