The equations of tangents to the ellipse , which are inclined at 60° to x-axis, are

The area of the triangle formed by the lines joining the vertex of the parabola to the ends of its latus rectum is

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola

Area bounded by curve ‐axis between and is

For such questions, we should know different formulas of integrals.

If , then is equal to

The integral is equal to

The solution for of the equation is

If the differential equation representing the family of all circles touching ‐axis at the origin is equals

Which one of the following is a differential equation of the family of curves

A function has a second‐order derivatives 1) If its graph passes through the point and at that point the tangent to the grraph , then the function is

For such questions, the important part is integration. We should know the methods to integrate the derivate. We should know the properties of a tangent.

The differential equation ( is any constant) represents

For such questions, we know different methods to solve differential equations. We should also know the formulas of different shapes.

An integrating factor of the differential equation is

The solution of the differential equation is

For such questions, we should know different methods to solve differential equation.

The solution of is

is a solution of the differential equation —.

For such questions, we should know different method to solve differential equation.

The degree of the differential equation is

For such questions, we should know the definition of power.