HSC Arts इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find the asymptotes of the following curves:

f(x) = `x^2/(x^2 - 1)`

Find the asymptotes of the following curves:

f(x) = `(x^2 - 6x - 1)/(x + 3)`

Find the asymptotes of the following curves:

f(x) = `(x^2 + 6x - 4)/(3x - 6)`

Find by integration, the volume of the solid generated by revolving about the x-axis, the region enclosed by y = 2x², y = 0 and x = 1

Find, by integration, the volume of the solid generated by revolving about the x axis, the region enclosed by y = e^-2x, y = 0, x = 0 and x = 1

Find, by integration, the volume of the solid generated by revolving about the y axis, the region enclosed by x² = 1 + y and y = 3

The region enclosed between the graphs of y = x and y = x² is denoted by R. Find the volume generated when R is rotated through 360° about x-axis

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`