Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Find the area bounded by the curve x² = 4y and the line x = 4y – 2

Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is ______.

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is ______.

Find the area under the given curve and given line:

y = x², x = 1, x = 2 and x-axis

Find the area under the given curve and given line:

y = x⁴, x = 1, x = 5 and x-axis

Find the area between the curves y = x and y = x²

Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`

Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12

Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`

Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b =   1`

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).

Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}

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.

The volume of a sphere is increasing at the rate of 8 cm³/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm