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Previous Year Paper

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CAT-2003-Previous Years Paper

Question
40 out of 50
 

A square tin sheet of side 12 inches is converted into a box with open top in the following steps. The sheet is placed horizontally. Then, equal-sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?



A 3
B 4

C 1
D 2

Ans. D

Volume = l × b × h

V = (12−2x) (12−2x) × x

V = (12−2x) (12−2x) 4x

Where V = 4V

Now sum = 12 – 2x + 12 – 2x + 4x = 24 (constant)

As sum is constant for the maximum product 12 – 2x = 12 – 2x = 4x

Therefore, x = 2.

CAT-2003-Previous Years Paper Flashcard List

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