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Question

The number of solutions of the equation [sin1x]=[x] is (where [*] denotes the greatest integer function)

A
0
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B
1
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C
2
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D
infinitely many
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Solution

The correct option is D infinitely many

[sin1x]=0, x[0, sin 1]

[sin1x]=1, x[sin 1, π/2 ]

[sin1x]=1, x[sin 1, 0 ]

[sin1x]=2, x[π/2,sin 1 ]

[x]=0, x[0, 1 ]

For x[0, sin 1] , both LHS & RHS are zero

infinite solution


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