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Question

Assertion :2π<sinxx<1 for 0|x|π/2 Reason: f(x)=sinxx,0<xπ/2 is decreasing.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
consider, f(x)=sinxx where 0|x|π/2
f(x)=xcosxsinxx2
let u(x)=xcosxsinx
u(x)=xsinx<0 for x(0,π/2)
Therefore, u(x) is a decreasing function
Since, x0 and u(x) is a decreasing function
Therefore, u(x)<u(0)=0
thus f(x)<0
hence, f(x) is a decreasing function.
and since, 0|x|π/2
Therefore, f(π2)<f(x)<f(0)
2π<sinxx<1

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