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Limits Continuity and Differentiability question

2017 · Shift 1 · Q20

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2017 · Shift 1 · Q20

Limits Continuity and Differentiability question

2017 · Shift 1 · Q20

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1

Let f : R

\to

(0, 1) be a continuous function. Then, which of the following function(s) has (have) the value zero at some point in the interval (0, 1) ?

A
${e^x} - \int_0^x {f(t)\sin t\,dt}$
B
$f(x) + \int_0^{{\pi \over 2}} {f(t)\sin t\,dt}$
C
$f(x) - \int_0^{{\pi \over 2} - x} {f(t)\cos t\,dt}$
D
x9 $-$ f(x)

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