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Question

Number of solution(s) of the equation sinx=[x] [where [.] denotes greatest integer function] is

A
1
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B
2
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C
0
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D
Infinite
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Solution

The correct option is C 2
We know that L. H. S lies between 1 and 1 and R. H. S is always an integer.
So the only possible solutions could be 1, 0 or 1
We see that for, x=0 and x=π2,
sin0=0 and sinπ2=1 and sin(π2)=1
Also,
[0]=0 and [π2]=1 and [π2]=2
Furthermore, for any other value of x that sinx takes integral values, we find that 1>[x]>1
Thus 0 and π2 satisfy the equation sinx=[x]
Hence, option 'B' is correct.

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