List of top Mathematics Questions on Applications of Derivatives asked in BITSAT

Find the equation of the tangent to the curve \(y = x^2\) at the point (1,1).
A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is (5)/(4) times as thick as the plate forming the cylindrical sides, find the ratio of the radius to the height of the cylinder using minimum material for the same capacity.
Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]. I. f(x) is increasing in [-1,1] II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?
At an extreme point of a function f(x), the tangent to the curve is
The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x-4sin²x/4)+(a-1)x+sin x does not possess critical points is
A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is \(\frac{5}{4}\) times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is