HSC Science कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`

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