###### Advertisements

###### Advertisements

Solve the following question and mark the best possible option.

Using the digits 1,2 find the number of natural numbers, which are smaller than 2 × 10^{8}.

#### Options

512

255

256

766

###### Advertisements

#### Solution

The number can contain maximum of 9 digits and for every place, there are 2 choices either 1 or 2.

If no. is 1-digited = 2 nos. are possible

If no. is 2-digited = 2^{2} nos. are possible

If no. is 3-digited = 2^{3} nos. are possible

If no. is 4-digited = 2^{4} nos. are possible

If no. is 5-digited = 2^{5} nos. are possible

If no. is 6-digited = 2^{6} nos. are possible

If no. is 7-digited = 2^{7} nos. are possible

If no. is 8-digited = 2^{8} nos. are possible

If no. is 9-digited = first place can be filled in the way i.e. by taking 1. Reaming 8 places can be filled either by 1 or by 2 i.e. 2 choices. So, 1 x 2^{8} nos. are possible in this case.

So, required answer = (2^{1} + 2^{2} + ------ + 2^{8}) + 2^{8} = 766.

#### RELATED QUESTIONS

The 10th term of the series: 5, 8, 11, 14, ... is:

`pi pi^2 0 "sin x"/sqrt(1 + "sin 2x")`dx is equal to :

If (1 + x)^{n} = C_{0} + C_{2}x + C_{2}X^{n} then `"C"_1/"C"_0 + "2C"_2/"C"_1 + "3C"_3/"C"_2+ .......+ "nC"_"n"/"C"_"n-1"` is equal to:

If A = `(("d"_1,0,0),(0,"d"_1,0),(0,0,"d"_3))` then adj A =

Which terms of the series `1/2,-1/2,1-2`, .... is -128:

Vertical angles that are opposite to each other are also

Surds having no irrational factor are called

Which one is rational number ?

Find the factors of 1122

In a family, the father took one-fourth of the cake and he had three times more than the others had. The total number of family members is

If x =`(3/2)^2(2/3)^-4`, the value of `"x"^-2` is

If `"x"+1/"x"=3`, then `"x"^2+1/"x"^2` will be

Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2, the third number is

A man went to the Reserve Bank of India with ₹2000. He asked the cashier to give him ₹10 and ₹20 notes only in return. The man got 150 notes in all. How many notes of ₹10 did he receive?

Which one of the following is not a prime number?

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is

Three numbers which are coprimes to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is

Three numbers are in the ratio of 3:4:5 and their LCM is 2400. Then, their HCF is

In GP find 1 + `1/2`+ `1/4` + ... up to 5 terms.

Which one of the following numbers is completely divisible by 99?

If x and y are natural numbers such that x + y = 2017, then what is the value of (−1)^{x} + (−1)^{y}?

The smallest number added to 680621 to make the sum a perfect square is ______.

If N = 9^{8} + 9^{9} + 9^{10} + 9^{11}, then how many positive factors of N are there?

If the fractions `5/14, 6/11, 7/9, 8/13` and `9/10` are arranged in ascending order of their values, which one will be the fourth?

If `11 5/21` is subtracted from `15 3/14` and the difference is multiplied by 504, what will be the number?

Find the least number by which 77, 175 should be divided to make it a perfect cube number.

Five consecutive even integers are such that two times the second integer is ten more than the 5th integer. Find the sum of all five integers.

If 9 mangoes cost as much as 5 oranges, 5 oranges as much as 3 apples, 4 apples as much as 9 pineapples and if 3 pineapples cost ₹ 48, what will a mango cost?

If a + b > c + d and b + c > a + d then it is definite that

2 oranges, 3 bananas and 4 apples taken together cost ₹ 15.00. 3 oranges, 2 bananas and 1 apple cost ₹ 10.00. Then the cost of 3 oranges, 3 bananas and 3 apples cost.