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

If the sides of a cubic box are increased by 1, 2, 3 units respectively to form a cuboid, then the volume is increased by 52 cubic units. Find the volume of the cuboid

Find all the values of x such that – 10π ≤ x ≤ 10π and sin x = 0

Find all the values of x such that Find all the values of x such that −3π ≤ x ≤ 3π and sin x = −1

Find the period and amplitude of y = sin 7x

Find the period and amplitude of y = `- sin(1/3 x)`

Find the period and amplitude of y = 4 sin(– 2x)

Sketch the graph of y = `sin(1/3 x)` for 0 ≤ x ≤ 6π

Find the domain of the following

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

Find the domain of the following

`g(x) = 2sin^-1(2x - 1) - pi/4`

Choose the correct alternative:

`sin^-1(cos x) = pi/2 - x` is valid for

Choose the correct alternative:

If `cot^-1x = (2pi)/5` for some x ∈ R, the value of tan^-1 x is

Choose the correct alternative:

The domain of the function defined by f(x) = `sin^-1 sqrt(x - 1)` is

A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t² + 3t metres. Find the average velocity between t = 3 and t = 6 seconds

A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t² + 3t metres. Find the instantaneous velocities at t = 3 and t = 6 seconds

A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t² in t seconds. How long does the camera fall before it hits the ground?

A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t² in t seconds. What is the average velocity with which the camera falls during the last 2 seconds?

A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t² in t seconds. What is the instantaneous velocity of the camera when it hits the ground?

A particle moves along a line according to the law s(t) = 2t³ – 9t² + 12t – 4, where t ≥ 0. At what times the particle changes direction?

A particle moves along a line according to the law s(t) = 2t³ – 9t² + 12t – 4, where t ≥ 0. Find the total distance travelled by the particle in the first 4 seconds

A particle moves along a line according to the law s(t) = 2t³ – 9t² + 12t – 4, where t ≥ 0. Find the particle’s acceleration each time the velocity is zero