Question

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

Solution

Correct option is

There are exactly (n – 1) subsets of S containing to elements having 1 as least element; exactly (n – 2) subsets of S having 2 as least element and so on. Thus   

   

                       

                       

                       

                     .

SIMILAR QUESTIONS

Q1

The range of function 

Q2

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

Q3

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

Q4

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 

Q5

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

Q6

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

Q7

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    

Q8

The sum of the factors of 9! Which are odd and are of the form 3m + 2, where m is a natural number is 

Q9

Sum of all three digit numbers (no digit being zero) having the property that all digit are perfect squares, is

Q10

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