HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

What is the length of the arc intercepted by a central angle of measure 41° in a circle of radius 10 ft?

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii

The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds

An airplane propeller rotates 1000 times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in 1 second

A train is moving on a circular track of 1500 m radius at the rate of 66 km/hr. What angle will it turn in 20 seconds?

A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie (a sector of the circle with thickness) of radius 16 cm and thickness 4 mm. Find the angle of the sector.

Choose the correct alternative:
A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

Find the derivatives of the following functions using first principle.

f(x) = 6

Find the derivatives of the following functions using first principle.

f(x) = – 4x + 7

Find the derivatives of the following functions using first principle.

f(x) = – x² + 2

Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = |x - 1|`

Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

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

Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = {{:(x",", x ≤ 1),(x^2",", x > 1):}`

Determine whether the following function is differentiable at the indicated values.

f(x) = x |x| at x = 0

Determine whether the following function is differentiable at the indicated values.

f(x) = |x² – 1| at x = 1

Determine whether the following function is differentiable at the indicated values.

f(x) = |x| + |x – 1| at x = 0, 1

Determine whether the following function is differentiable at the indicated values.

f(x) = sin |x| at x = 0

Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(-x + 2, x ≤ 2),(2x - 4, x > 2):}` , x = 2

Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(3x",", x < 0),(-4x",", x ≥ 0):}` , x = 0

The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.