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Option 4 : 55

Ajay ranked sixteenth from the top and twenty-ninth from the bottom among those who passed an examination. 

Total number of boys who passed the examination = 16 + 29 - 1

= 45 - 1

= 44

Six boys did not participate in the competition and five failed in it.

Therefore, total number of boys in the class = 44 + 6 + 5

= 55

Hence, '55' is the correct answer.

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