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

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

xy = log y + C :  `y' = (y^2)/(1 - xy) (xy != 1)`

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y – cos y = x :  (y sin y + cos y + x) y′ = y

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

x + y = tan^–1y   :   y² y′ + y² + 1 = 0

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

`y = sqrt(a^2 - x^2 )  x in (-a,a) : x + y  dy/dx = 0(y != 0)`

The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.

The number of arbitrary constants in the particular solution of a differential equation of third order are ______.

Find the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`

Show that the general solution of the differential equation  `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.

Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`

Find a particular solution of the differential equation `dy/dx + y cot x = 4xcosec x(x != 0)`, given that y = 0 when `x = pi/2.`

Find the maximum and minimum value, if any, of the following function given by f(x) = (2x − 1)² + 3. 

Find the maximum and minimum value, if any, of the following function given by f(x) = 9x² + 12x + 2

Find the maximum and minimum value, if any, of the following function given by f(x) = −(x − 1)² + 10 

Find the maximum and minimum value, if any, of the following function given by g(x) = x³ + 1.

Find the maximum and minimum value, if any, of the function given by f(x) = |x + 2| − 1.

Find the maximum and minimum value, if any, of the following function given by g(x) = − |x + 1| + 3.

Find the maximum and minimum value, if any, of the following function given by h(x) = sin(2x) + 5.

Find the maximum and minimum value, if any, of the following function given by f(x) = |sin 4x + 3|

Find the maximum and minimum value, if any, of the following function given by h(x) = x + 1, x ∈ (−1, 1)