HSC Science Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

What must be the radius of a circular running path, around which an athlete must run 5 times in order to describe 1 km?

In a circle of diameter 40 cm, a chord is of length 20 cm. Find the length of the minor arc of the chord

Find the degree measure of the angle subtended at the centre of circle of radius 100 cm by an arc of length 22 cm

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