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

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)

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = x²

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

g(x) = x³ − 3x

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`h(x) = sinx + cosx, 0 < x < pi/2`

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = sinx − cos x, 0 < x < 2π

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = x³ − 6x² + 9x + 15

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`g(x) = x/2 + 2/x, x > 0`