A person starts writing numbers from 1 to `n` in a row such that `i^(t h)` number is written `i^2` times then find `500^(t h)` digit from the starting.

n=12times2^(t/3) The number of mice in a certain colony is shown by the formula above, such that n is the number of mice and t is the time, in months, since the start of the colony. IF 2 years have passed since the start of the colony, how many mice does the colony contain now?

Nita starts with the number 27 and keeps subtracting 6 from it. Find the number she will arrive at if she carries out the subtraction 6 times.

A partical in SHM ha a period of 4s .It takes time t_(1) to start from mean position and reach half the amplitude. In another case it taken a time t_(2) to start from extreme position and reach half the amplitude. Find the ratio t_(1)//t_(2)

The number of times the digit 0 is used in writing the numbers from 1 to 1000 is equal to

Find the number of natural numbers which are less than 2xx10^8 and which can be written by means of the digit 1 and 2.

The number of times the digit 3 will be written when listing the integers from 1 to 1000, is

There are 2401 students in a school. P.T. teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columns. Find the number of rows.

How many five dilgit telephone numbers can be constructed using the digits 0 to 9. i. If each number starts with 59, for example 59612 etc. and no digit appears ore than once? ii. If each number starts with 67 and no digit apears more than once?

Find the number of times the digit 8 will be written when listing the integers from 1 to 10,000 .

Find the r^(t h) term from the end in the expansion of (x+a)^n .