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Permutation

In a certain ...

Question

In a certain test $a_{i}$ students gave wrong answers to at least i questions where i = 1, 2, 3, ....k. No student gave more than k wrong answers. The total number of wrong answers given is

A

a_{1} + 2 a_{2} + 3 a_{3} + . . . . . . k a_{k}

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B

a_{1} + a_{2} + a_{3} + . . . . . . a_{k}

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C

Z e r o

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D

N o n e o f t h e s e

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Solution

The correct option is B $a_{1} + a_{2} + a_{3} + . . . . . . a_{k}$
Total number of wrong answers
$= 1 (a_{1} - a_{2}) + 2 (a_{2} - a_{3}) + . . . . . + (k - 1) (a_{k - 1} - a_{k}) + k a_{k} = a_{1} + a_{2} + . . . . . . + a_{k} .$

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