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For the function \(f(x)={e}^{\sin |x|}-|x|,x\in R\), consider the following statements: Statement I: \(f\) is differenti…

Q1

For the function \(f(x)={e}^{\sin |x|}-|x|,x\in R\), consider the following statements:

Statement I: \(f\) is differentiable for all \(x\in R\)

Statement II: \(f\) is increasing in \(\left(-\pi ,-\frac{\pi }{2}\right)\)
In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2026, 8 Apr (Shift 2)]

a

Both Statement I and Statement II are true

b

Both Statement I and Statement II are false

c

Statement I is true but Statement II is false

d

Statement I is false but Statement II is true

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