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JEE Advance2018

Paper-1

Multiple correct answers - Select all that apply

Question

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be two non-constant differentiable functions. If $\mathrm{f}^{\prime}(\mathrm{x})=\left(\mathrm{e}^{(\mathrm{f}(\mathrm{x})-\mathrm{g}(\mathrm{x}))}\right) \mathrm{g}^{\prime}(\mathrm{x})$ for all $\mathrm{x} \in \mathrm{R}$, and $f(1)=g(2)=1$, then which of the following statement(s) is (are) TRUE ?

Select ALL correct options:

A

(A) $\mathrm{f}(2)<1-\log _{\mathrm{c}} 2$

B

$f(2)>1-\log _c 2$

C

$g(1)>1-\log _c 2$

D

$g(1)<1-\log _c 2$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution

Question Tags

JEE Advance

Mathematics

Easy

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