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

Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.

Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.

Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).

Find the area of the region bounded by the curve y² = x and the lines x = 1, x = 4 and the x-axis.

Find the area of the region bounded by y² = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

Find the area of the region bounded by x² = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

Find the area of the region bounded by the ellipse  `x^2/16 + y^2/9 = 1.`

Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`

Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x² + y² = 4.

Find the area of the smaller part of the circle x² + y² = a² cut off by the line  `x = a/sqrt2`

The area between x = y² and x = 4 is divided into two equal parts by the line x = a, find the value of a.

Find the area of the region bounded by the parabola y = x2 and y = |x| .

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