Question

The number of positive integers n such that 2n divides n! is

Solution

Correct option is

None of these

 

The exponent of 2 in n! is given by 

              

where [x] is denotes greatest integer  after finite number of terms. Thus we get    

              

Thus, there is no positive for which integer for which 2n divides n!

SIMILAR QUESTIONS

Q1

Four dice are rolled. The number of possible outcomes in which least one die shows 2 is

Q2

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of choosing P and Q so that P  Q = Ï• is

Q3

Let E = {1, 2, 3, 4} and F = {ab}. then the number of onto functions from E to F is

Q4

The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

Q5

The range of function 

Q6

The number of ways of arranging letters of the word RACHIT so that the vowels are in alphabetical order is

Q7

A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

Q8

The number of ways in which a mixed double game can be arranged from amongst 9 married couple if no husband and wife play in the same game is 

Q9

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

Q10

A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is