The Value Of Parameter a so That Line (3 – a) x + ay + (a2n – 1) = 0 Is Normal To The Curve xy = 1, May Lie In The Interval

The third derivative of a function f’’(x) vanishes for all x. If f (0) = 1, f’ (1) = 2 and f’’ = –1, then f (x) is equal to 

The chord joining the points where x = p and x = q on the curve y = ax² + bx + c is parallel to the tangent at the point on the curve whose abscissa is 

If the tangent at (1, 1) on y² = x (2 – x)² meets the curve again at P, then P is

The distance between the origin and the normal to the curve

y = e^2x + x² at x = 0 is

If the line ax + by + c = 0 is a normal to the curve xy = 1 then

The point of intersection of the tangents drawn to the curve x²y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by

The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x² – x | is

The tangent to the graph of the function y = f (x) at the point with abscissax = 1 form an angle of π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle of π/4. The value of 

The equations of the tangents to the curve y = x⁴ from the point (2, 0) not on the curve, are given by

A cylindrical gas container is closed at the top and open at the bottom; if the iron plate forming the cylindrical sides. The ratio of the height to diameter of the diameter of the cylindrical using minimum material for the same capacity is