Applications of...

If a st. line is tangent to one point and normal to another point on the curve y = 8t³ − 1, x = 4t² + 3, then the equation of such line is :

Let f(x) = 1 + 2²x²+ 3²x⁴ + 4²x⁶ …. + n²x^2n–2= + (n+1)²x²ⁿ, then f(x) has :

Kamal has x children by hist first wife. Ritu has (x + 1) children by her first busband. They marry and have children of their own. The whole family has 24 children. Assuming the two children of the same parents do not fight, then the maximum possible number of fights that can take place is :

A given right circular cone has a volume p and the longest right circular cylinder that can be inscribed in the cone has a volume q. Then p : q is :

Let h(x) = f(x) − (f(x))² + (f(x))³ for every real number x. Then :

The function f(x) = sin⁴ x + cos⁴x increases in