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NDA Math Application of Derivatives

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Consider the following information for the next three (03) items that follow:
Three sides of a trapezium are each equal to 6cm. Let α∈(0,‌

π

2

) be the angle between a pair of adjacent sides.

[NDA I 2018]

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Question : 39

Total: 73

If the area of the trapezium is the maximum possible, then what is α equal to ?

π
6
π
4
π
3
2π
5

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