The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n - 1) divisions of main scale. The least count of the vernier callipers is?

A vernier works on the principle that

n V = (n - 1) S

n is the number of divisions on the main scale

S is the length of the smallest main scale division

V is the length of a division on the vernier scale

We can rewrite our above equation as

Least count = S - V = S / n

For a simple caliper the main scale would be graduated in mm

There would be 10 vernier divisions for each 9 main scale divisions

The least count would be 0.1 mm

because growing process had stoped after 4-5 year

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .