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In a certain test there are n questions.In this test 2^n-k students gave wrong answers to at least k questions, where k= 1,2,3,4......n . If total wrong questions are 2047 then n is equal to=?... please also wrtie a little discription..

In a certain test there are n questions.In this test 2^n-k students gave wrong answers to at least k questions, where k= 1,2,3,4......n . If total wrong questions are 2047 then n is equal to=?... please also wrtie a little discription..

Grade:11

1 Answers

Amit Jain
askIITians Faculty 32 Points
7 years ago

Note that 2^0 = 1 + 2^1 = 3 = 2^2 - 1 

In general the sum of powers of 2 equal one less than 2 to the next power. Since 2048 is 2^11, 2047 is the sum of powers of 2 up to 2^10. (We start at 0, because n-i = 0 when i goes to n). So n= 10.

 


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