## Question

### Solution

Correct option is

2n – 1  As r < sn – r > n – s. But the only two different factorials which are equal are 0! and 1!. Thus n – r = 1 and n – s = 0 ⇒ r = n – 1 and s = n. #### SIMILAR QUESTIONS

Q1

Let n = 2009. The least positive integer k for which for some positive integer r is

Q2 , then value of is

Q3 is maximum where m is

Q4

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

Q5

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

Q6

The number of positive integral solutions of the equation is

Q7

The exponent of 7 in 100C50 is

Q8

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

Q9

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

Q10

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