Two particles \( A \) and \( B \) are projected with same speed so that the ratio of their maxim...

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Two particles \( A \) and \( B \) are projected with same speed so that the ratio of their maximum heights reached is \( 3: 1 \). If the speed of \( A \) is doubled without altering other parameters, the ratio of the horizontal ranges attained by \( A \) and \( B \) is
(a) \( 1: 1 \)
(b) \( 2: 1 \)
(c) \( 4: 1 \)
(d) \( 3: 2 \)
(e) \( 4: 3 \)
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