Which of the following statement is correct for the function g ( α ) for α ∈ R such that g…

Which of the following statement is correct for the function g(α) for αR such that gα=π6π3sinαxcosαx+sinαxdx
  1. g(α) is a strictly increasing function
  2. g(α) has an inflection point at α=-12
  3. g(α) is a strictly decreasing function
  4. g(α) is an even function

Solution

gα=π6π3sinαxsinαx+cosαxdx i

gα=π6π3cosαxsinαx+cosαxdx ii

Adding 1+2

2gα=π3-π6=π6

gα=π12

Which is constant and an even function.

Asked in: JEE Main 2021 (17 Mar Shift 1)

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