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The probabilities that a student passes in Mathematics, Physics, and Chemistry are $m, p,$ and $c$ respectively. Of these subjects, the student has $75$% chance of passing in at least one, a $50$% chance of passing in at least two and a $40$% chance of passing in exactly two. Following relations are drawn in $m, p, c$:

(I) $p + m + c = 27/20$

(II) $p + m + c = 13/20$

(III) $(p) \times (m) \times (c) = 1/10$

- Only relation $I$ is true.
- Only relation $II$ is true.
- Relations $II$ and $III$ are true.
- Relations $I$ and $III$ are true.

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