In a test $a_{i}$ students gave wrong answers to atleast i questions, where i $=$ 1, 2, 3, 4, ... k. No one gave wrong answer to greater than k questions. Then the total number of given wrong answers is

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

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

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

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Solution

The correct option is B $a_{1} + a_{2} + a_{3} + . . . . . . + a_{k}$
Number students who gave wrong answer to 1 question = $a_{1}$
Number students who gave wrong answer to 2 questions = $a_{2}$
Number students who gave wrong answer to 3 questions = $a_{3}$
:
:
Number students who gave wrong answer to n questions = $a_{n}$
Hence
Total number of wrong answers $= S u m$
$= a_{1} + a_{2} + a_{3} + . . a_{n}$ .

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