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A firecracker is thrown with velocity of 30 ms1 in a direction which makes an angle of 75 degree with the vertical axis. At some point on its trajectory, the firecracker splits into two identical pieces in such a way that one piece fall 27 m far from the shooting point. Assuming that all trajectories are contained in the same plane, how far will the other
piece fall from the shooting point ? (Take g = 10 ms2 and neglect air resistance)
option
(A) 63 m or 144 m
(B) 72 m or 9 m
(C) 28 m or 72 m
(D) 63 m or 117 m

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KVPY Other Question
A train leaves Pune at 7 : 30 am and reaches Mumbai at 11 : 30 am. Another train leaves Mumbai at 9 : 30 am and reaches Pune at 1 :00 pm. Assuming that the two trains travels at constant speeds, at what time do the two trains cross each other
option
(A) 10: 20 am
(B) 11 : 30 am
(C) 10 : 26 am
(D) Data not sufficient 150 g of ice is mixed with 100 g of water at temperature 80 oC. The latent heat of ice is 80 cal/g and the specific heat of water is 1 cal/gC. Assuming no heat loss to the environment, the amount of ice which does not melt is
option
(A) 100 g
(B) 0 g
(C) 150 g
(D) 50 g