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

Show that `2sin^-1(3/5) = tan^-1(24/7)`

Show that the function `f(x)=|x-3|,x in R` is continuous but not differentiable at x = 3.

Using integration, find the area bounded by the curve x² = 4y and the line x = 4y − 2.

Prove that the curves y² = 4x and x² = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.

Using integration, find the area of the region bounded by the lines y = 2 + x, y = 2 – x and x = 2.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

Find the values of p and q for which

f(x) = `{((1-sin^3x)/(3cos^2x),`

is continuous at x = π/2.

Sketch the region bounded by the curves `y=sqrt(5-x^2)` and y=|x-1| and find its area using integration.

Find the principal values of `sin^(-1) (-1/2)`

Find the principal value of  `cos^(-1) (sqrt3/2)`

Find the principal value of cosec⁻¹ (2)

Find the principal value of `tan^(-1) (-sqrt3)`

Find the principal value of  `cos^(-1) (-1/2)`

Find the principal value of tan⁻¹ (−1)

Find the principal value of  `sec^(-1) (2/sqrt(3))`

Find the principal value of `cot^(-1) (sqrt3)`

Find the principal value of  `cos^(-1) (-1/sqrt2)`

Find the principal value of `cosec^(-1)(-sqrt2)`

Find the value of the following:

`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`

Find the value of the following:

`cos^(-1) (1/2) + 2 sin^(-1)(1/2)`