HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Find, by integration, the volume of the container which is in the shape of a right circular conical frustum as shown in the Fig 9.46

A watermelon has an ellipsoid shape which can be obtained by revolving an ellipse with major-axis 20 cm and minor-axis 10 cm about its major-axis. Find its volume using integration

Choose the correct alternative:

The volume of solid of revolution of the region bounded by y² = x(a – x) about the x-axis is

Find the value, if it exists. If not, give the reason for non-existence

`sin^-1 (cos pi)`

Find the value, if it exists. If not, give the reason for non-existence

`tan^-1(sin(- (5pi)/2))`

Find the value, if it exists. If not, give the reason for non-existence

`sin^-1 [sin 5]`

Find the value of the expression in terms of x, with the help of a reference triangle

sin (cos^–1(1 – x))

Find the value of the expression in terms of x, with the help of a reference triangle

cos (tan^–1 (3x – 1))

Find the value of the expression in terms of x, with the help of a reference triangle

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

Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`

Find the value of `cot[sin^-1  3/5 + sin^-1  4/5]`

Find the value of  `tan(sin^-1  3/5 + cot^-1  3/2)`

Prove that `tan^-1  2/11 + tan^-1  7/24 = tan^-1  1/2`

Prove that `sin^-1  3/5 - cos^-1  12/13 = sin^-1  16/65`

Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`

If tan^–1x + tan^–1y + tan^–1z = π, show that x + y + z = xyz

Simplify: `tan^-1  x/y - tan^-1  (x - y)/(x + y)`

Solve: `sin^-1  5/x + sin^-1  12/x = pi/2`

Solve: `tan^-1x = cos^-1  (1 - "a"^2)/(1 + "a"^2) - cos^-1  (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`

Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec"  x)`