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

Using integration, find the area of the region bounded by y = mx (m > 0), x = 1, x = 2 and the X-axis.

Make a rough sketch of the region {(x, y) : 0 ≤ y ≤ x² + 1, 0 ≤ y ≤ x + 1, 0 ≤ x ≤ 2} and find the area of the region, using the method of integration.

Find the particular solution of the differential equation  `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

Show that the differential equation 2y^x/y dx + (y − 2x e^x/y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

Solve the differential equation :

`y+x dy/dx=x−y dy/dx`

Find the differential equation representing the curve y = cx + c².

Write the integrating factor of the following differential equation:

(1+y²) dx−(tan⁻¹ y−x) dy=0

Find the the differential equation for all the straight lines, which are at a unit distance from the origin.

Show that the differential  equation `2xydy/dx=x^2+3y^2`  is homogeneous and solve it.

Find the particular solution of differential equation:

`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`

Find the differential equation of the family of lines passing through the origin.

Find the integrating factor for the following differential equation:`x logx dy/dx+y=2log x`

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

Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.

Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.

Find the particular solution of the differential equation x (1 + y²) dx – y (1 + x²) dy = 0, given that y = 1 when x = 0.

For the differential equation, find the general solution:

sec² x tan y dx + sec² y tan x dy = 0

Which of the following is a homogeneous differential equation?