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

Using integration, find the area of the region {(x, y) : x² + y² ≤ 1 ≤ x + y}.

Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]

Find the area of the region. 

{(x,y) : 0 ≤ y ≤ x² , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .

Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.

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

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.

Which of the following is a homogeneous differential equation?