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JEE Main 2000 Mathematics question on Application of Derivatives

For all x∈(0,1)x \in (0, 1)
  1. A.
    ex<1+xe^x < 1 + x
  2. B.
    log⁡e(1+x)<x\log_e(1 + x) < x
  3. C.
    sin⁡x>x\sin x > x
  4. D.
    log⁡ex>x\log_e x > x
Show answer

Correct option: C

[2000]

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