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Question

An open box A is made from a square piece of tin by cutting equal squares S at the corners and folding up the remaining flaps. Another open box B is made similarly using one of the squares S. If U and V are the volumes of A and B respectively, then which of the following is not possible?

A
U > V
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B
V > U
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C
U = V
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D
Minimum value of U > maximum value of V
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Solution

The correct option is D Minimum value of U > maximum value of V
Let the side of tin be a
U=(a2x)2x, where x is the side of a square which have been cut.
Similarly, V=(a2y)2y, where y is the side of a square which have been cut.
Minimum value of U=0
Minimum value of V=0
U>V, or V>U or U=V
But minimum value of U=0. So, it can't be greater than maximum value of V.
Hence, minimum value of U> Maximum value of V is not possible.

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