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Limits Continuity and Differentiability question

2018 · Shift 1 · Q23

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2018 · Shift 1 · Q23

Limits Continuity and Differentiability question

2018 · Shift 1 · Q23

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1

Let f : R

\to

R and g : R

\to

R be two non-constant differentiable functions. If f'(x) = (e(f(x)

-

g(x))) g'(x) for all x

\in

R and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?

A
f(2) < 1 $-$ loge 2
B
f(2) > 1 $-$ loge 2
C
g(1) > 1 $-$ loge 2
D
g(1) < 1 $-$ loge 2

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