Question

The number of natural numbers which are smaller than 2 × 108 and which can be written by means of the digits and 2 is ………..

Solution

Correct option is

766

The required number are 1, 2, 11, 12, 21, 22, …, 122222222. 

Let us calculate how many numbers are these.

There are 2 one digit such numbers. There are 22 two digit such numbers. And so on. 

There are 28 eight digit such numbers. All the nine digit numbers beginning with 1 and written by means of 1 and 2 are smaller than 2.108. Thus, there are 28 such nine digit numbers. 

Hence, the required number of numbers is  

       

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SIMILAR QUESTIONS

Q1

Let S = {1, 2, 3, ... n}. if X denote the set of all subsets of S containing exactly two elements, then the value of   

Q2

Let a be a factor of 120, then the number of integral solution of x1x2x3 = a is 

Q3

There are 15 points in a plane of which exactly 8 are collinear. Find the number of straight lines obtained by joining there points.   

Q4

If n is the number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any quation find n/40.

Q5

Find the number of rectangles that you can find on a chessboard.

Q6

Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9, no digit being repeated.

Q7

Ten persons, amongst whom are A, B and C, are to speak at a function. If n is the number of ways in which it can be done if A wants to speak before B, and B wants to speak before C find n/800.

Q8

Find the largest  such that 

      

Q9

Find the largest integer n for which 35! Is divisible by 3n.

Q10

Find the exponent of 2 in 50!?