Let `x = 0.123456789101112 ... 998999,` where the digits are obtained by writing the integers 1 through `999` in order. Find the `1983^(rd)` digit to the right of the decimal point.

An infinite sequence of digits is obtained by writing the natural numbers in order 123456789101112...... Define f(n)=m, if the 10^(th) digit forms part of an m digit number. eg. f(2)=2 because 100^(th) digit is 55 & it's a two digit number. The value of f(1987) is

Two-digit numbers are formed from the digits 0,1,2,3,4 where the digits are not repeated. Find the probability that the number so formed is a prime numbers.

Two-digit numbers are formed from the digits 0,1,2,3,4 where the digits are not repeated. Find the probability that the number so formed is a prime numbers.

Write the digits 0, 1, 2, 3, ..., 9 in this order and insert '+' or '-' between them to get the result 3.

There are 10 tickets numbered 0,1,2,3,.....9 . Two tickets are drawn at random. If the number obtained by writing the digits together is a perfect square then the probability that sum of digits is 9 is

Two-digit numbers are formed from the digits 0,1,2,3,4 where repetition of the digits are allowed. Find the probability of the events (i) the number is composite (ii) the number is a multiple of 7 (iii) the number is odd.

Find the equation of a st. line drawn at right angles to the st. line x/a+y/b=1 through the point, where it meets the x-axis.

The binary number 0.111111…. (where the digit 1 is recurring) is equivalent in decimal system to which one of the following?

Find the equation of a st.line drawn at right angles to the st.line (x)/(a)+(y)/(b)=1 through the point, where it meets the x-axis.