If [sinx]+[x/(2pi)]+[(2x)/(5pi)]=(9x)/(1...

If `[sinx]+[x/(2pi)]+[(2x)/(5pi)]=(9x)/(10pi)`, where `[*]` denotes the greatest integer function, the number of solutions in the interval (30,40) is ………… .

A

0

B

1

C

2

D

infinite

Text Solution

Verified by Experts

The correct Answer is:

B

The given equation is valid, if
`(9x)/(10pi)` is an integer
`implies x=10pi, 20pi,30pi`,….
`implies x=10pi " " [:' 30 lt x lt 40]`
Hence, the given equation has only one solution.

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