The number of subsets of the set A = {a1a2, … an} which contain even number of elements is


Correct option is

For each of the first (n – 1) elements a1a2, … an – 1 we have two choices: either  lies in the subset or ai doesn’t lie in the subset. For the last element we have just one choice. If even number of elements have already been taken, we do not include an in the subset, otherwise (when odd number of elements have been added), we include it in the subset. 

Thus, the number of subsets of  which contain even number of elements is equal to .



An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 without replacement. The number of ways I which this can be done is  


The number of rational numbers lying in the interval (2008, 2009) all whose digits after the decimal point are non-zero and are in deceasing order is


The number of positive integral solutions of the equation  is


The exponent of 7 in 100C50 is


In the certain test there are n questions. In this test 2k students gave wrong answers to at least (n – k) questions, where k = 0, 1, 2, …, n. If the total number of wrong answer is 4095, then value of n is 


If n > 1 and n divides (n – 1)! + 1, then 


In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit so that two sisters are not sitting together is


The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is


The number of ways in which we can post 5 letters in 10 letter boxes is