Science (English Medium) Class 12 - CBSE Important Questions for Mathematics

Using integration, find the area of the region bounded by the parabola y² = 4x and the circle 4x² + 4y² = 9.

Using the method of integration, find the area of the region bounded by the lines 3x − 2y + 1 = 0, 2x + 3y − 21 = 0 and x − 5y + 9 = 0

Using integration, find the area of the smaller region bounded by the ellipse `"x"^2/9+"y"^2/4=1`and the line `"x"/3+"y"/2=1.`

Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y² = x and the x-axis.

Using integration, find the area of the region `{(x, y): 0 ≤ y ≤ sqrt(3)x, x^2 + y^2 ≤ 4}`

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

Using integration, find the area of the region bounded by the curves x² + y² = 4, x = `sqrt(3)`y and x-axis lying in the first quadrant.

Find the area of the region enclosed by the curves y² = x, x = `1/4`, y = 0 and x = 1, using integration.

Using Integration, find the area of triangle whose vertices are (– 1, 1), (0, 5) and (3, 2).

Find the area of the smaller region bounded by the curves `x^2/25 + y^2/16` = 1 and `x/5 + y/4` = 1, using integration.

Find the area of the minor segment of the circle x² + y² = 4 cut off by the line x = 1, using integration.

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