Question

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

  

for some positive integer r is  

Solution

Correct option is

2

We can rewrite the given expression as    

       

                                                  

     

    

∴ To convert L.H.S. to a factorial, we required, k = 2 which will convert it into (2n)!.

SIMILAR QUESTIONS

Q1

If 0 < r < s ≤ n and nPr = nPs, then value of r + s 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