Question

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 

Solution

Correct option is

12

The number of students answering at least r questions incorrectly is 2n – r

∴the number of students answering exactly r(1 ≤ r ≤ n – 1) questions incorrectly is .  

Also, the number of students answering all questions wrongly is 2o = 1.  

Thus, the total number of wrong answer is  

   

                                                           

                           

SIMILAR QUESTIONS

Q1

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

  

for some positive integer r is  

Q2

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

Q3

, then value of is

Q4

 is maximum where m is   

 

Q5

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  

Q6

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

Q7

The number of positive integral solutions of the equation  is

Q8

The exponent of 7 in 100C50 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