Arts (English Medium) इयत्ता १२ - CBSE Important Questions for Mathematics

Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.

`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.

Prove that the curves y² = 4x and x² = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.

Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).

Find the area enclosed between the parabola 4y = 3x² and the straight line 3x - 2y + 12 = 0.

Find the area of the following region using integration ((x, y) : y² ≤ 2x and y ≥ x – 4).

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

Solve the differential equation `cos^2 x dy/dx` + y = tan x

Find the particular solution of the differential equation `(x - y) dy/dx = (x + 2y)` given that y = 0 when x = 1.

Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where C is parameter

Solve the differential equation `x dy/dx + y = x cos x + sin x`,  given that y = 1 when `x = pi/2`

The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.

Form the differential equation representing the family of curves `y² = m(a² - x²) by eliminating the arbitrary constants 'm' and 'a'. 

Solve the differential equation:  ` (dy)/(dx) = (x + y )/ (x - y )`

Form the differential equation representing the family of curves y = e²x (a + bx), where 'a' and 'b' are arbitrary constants.

Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.

Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.

Find the general solution of the differential equation:

`log((dy)/(dx)) = ax + by`.