Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

For the differential equation find a particular solution satisfying the given condition:

`2xy + y^2 - 2x^2  dy/dx = 0; y = 2`   when x  = 1

A homogeneous differential equation of the from `dx/dy = h (x/y)` can be solved by making the substitution.

Which of the following is a homogeneous differential equation?

Prove that x² – y² = c (x² + y²)² is the general solution of differential equation  (x³ – 3x y²) dx = (y³ – 3x²y) dy, where c is a parameter.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is `4/27 pih^3` tan²α.

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of ______.

Find the integrals of the function:

sin² (2x + 5)

Find the integrals of the function:

sin 3x cos 4x

Find the integrals of the function:

cos 2x cos 4x cos 6x

Find the integrals of the function:

sin³ (2x + 1)

Find the integrals of the function:

sin³ x cos³ x

Find the integrals of the function:

sin x sin 2x sin 3x

Find the integrals of the function:

sin 4x sin 8x

Find the integrals of the function:

`(1-cosx)/(1 +  cos x)`

Find the integrals of the function:

`cos x/(1 + cos x)`

Find the integrals of the function:

sin⁴ x

Find the integrals of the function:

cos⁴ 2x

Find the integrals of the function:

`(sin^2 x)/(1 + cos x)`

Find the integrals of the function:

`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`

Find the integrals of the function:

`(cos x -  sinx)/(1+sin 2x)`