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Definite Integration question

2020 · Shift 2 · Q25

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2020 · Shift 2 · Q25

Definite Integration question

2020 · Shift 2 · Q25

JEE AdvancedMathematicsDefinite IntegrationMultiple correct+4 / −2

Let b be a nonzero real number. Suppose f : R

\to

R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the equation

f'(x) = {{f(x)} \over {{b^2} + {x^2}}}

for all x

\in

R, then which of the following statements is/are TRUE?

A
If b > 0, then f is an increasing function
B
If b < 0, then f is a decreasing function
C
f(x) f( $-$ x) = 1 for all x $\in$ R
D
f(x) $-$ f( $-$ x) = 0 for all x $\in$ R

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