First slide

Introduction to ITF

Question

$If \sum_{i = 1}^{2 n} \cos^{- 1} x_{i} = 0, then \sum_{i = 1}^{2 n} x_{i} is$

Moderate

A

n
B

2n
C

$\frac{n (n + 1)}{2}$
D

none of these

Solution

$Since, 0 \leq \cos^{- 1} x_{i} \leq π, ∴ \cos^{- 1} x_{i} = 0 for all i ∴ x_{i} = 1 {for all}_{i} ∴ \sum_{i = 1}^{2 n} x_{i} = 2 n$

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