In a test there were n questions. In the test 2n−i students gave wrong answers to i questions where i=1,2,3...,n. If the total number of wrong answers given is 2047 then n is
12
11
10
none of these
A
12
B
11
C
10
D
none of these
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Solution
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Total number of wrong answers =2n−1+2n−2+...+22+2+1 =2n−1+2n−2+...+24+23+22+2+1 ⇒2n−1=2043 [Using formula for sum of G.P] ⇒2n=2048 ⇒2n=211 ⇒n=11 Hence, option 'B' is correct.
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