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Question

The period of sinπ[x]12+cosπ[x]4+tanπ[x]3 where [x] represents the greatest integer less than or equal to x is

A
12
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B
4
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C
3
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D
24
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Solution

The correct option is D 24
Since the period of sin(x) is 2π, the period of sin(π[x]12), where [x] is a greatest integer function, is 2ππ12=24.
period of tanx is π and period of cosx is 2π
Similarly, the periods of cos(π[x]4) and tan(π[x]3) are 8 and 3 respectively.
Hence the period of the function sin(π[x]12)+cos(π[x]4)+tan(π[x]3) is the LCM of the periods of the three functions added.
Hence the period of the given function is LCM (24,8,3)=24.

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