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

Solve the following equation `cos(tan^-1x) = sin(cot^-1  3/4)`

Show that `sin^-1  5/13 + cos^-1  3/5 = tan^-1  63/16`

Prove that `tan^-1  1/4 + tan^-1  2/9 = sin^-1  1/sqrt(5)`

All trigonometric functions have inverse over their respective domains.

If f(x) = `{{:("a"x + 1,  "if"  x ≥ 1),(x + 2,  "if"  x < 1):}` is continuous, then a should be equal to ______.

Find all points of discontinuity of the function f(t) = `1/("t"^2 + "t" - 2)`, where t = `1/(x - 1)`

Find the area of the curve y = sin x between 0 and π.

Find the area of the region bounded by the curve ay² = x³, the y-axis and the lines y = a and y = 2a.

Find the area of the region bounded by the parabola y² = 2x and the straight line x – y = 4.

Find the area of the region bounded by the parabolas y² = 6x and x² = 6y.

Find the area of the region above the x-axis, included between the parabola y² = ax and the circle x² + y² = 2ax.

The area enclosed by the circle x² + y² = 2 is equal to ______.

The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to ______.

The area of the region bounded by the curve y = x² and the line y = 16 ______.

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

The area of the region bounded by the curve y = x² + x, x-axis and the line x = 2 and x = 5 is equal to ______.

Find the area of the region bounded by the curves y² = 9x, y = 3x

Find the area of the region bounded by the parabola y² = 2px, x² = 2py

Find the area of the region bounded by the curve y = x³ and y = x + 6 and x = 0

Find the area of the region bounded by the curve y² = 4x, x² = 4y.