JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Analyzing +4 | -1

The largest possible value of the expression

S=\sin x_1 \cdot \cos x_2+\sin x_2 \cdot \cos x_3+\ldots . .+\sin x_{99} \cdot \cos x_{100}+\sin x_{100} \cdot \cos x_1, \text { where } x_1, x_2, x_3, \ldots ., x_{100}

are arbitrary real numbers is

View answer and explanation

Correct option: A

Option A (50) is correct because using the inequality

2ab \leq a^2 + b^2

, the expression S can be bounded by 50.

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