Arts (English Medium) इयत्ता १२ - CBSE Important Questions

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

Find the coordinates of a point of the parabola y = x² + 7x + 2 which is closest to the straight line y = 3x − 3.

Using integration, find the area of the region bounded by the line x – y + 2 = 0, the curve x = \[\sqrt{y}\] and y-axis.

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)`.

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.