Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

For the differential equation, find the general solution:

`(x + y) dy/dx = 1`

For the differential equation, find the general solution:

y dx + (x – y²) dy = 0

For the differential equation, find the general solution:

`(x + 3y^2) dy/dx = y(y > 0)`

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

`dy/dx + 2y tan x = sin x; y = 0 " when x " = pi/3`

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

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

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

`dy/dx - 3ycotx = sin 2x; y = 2`  when `x = pi/2`

Find the equation of the curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is ______.

The integrating factor of the differential equation.

`(1 - y^2) dx/dy + yx = ay(-1 < y < 1)` is ______.

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?

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)