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Question

f(x)=cos[2π]x+cos[2π]x, where [x] stands for the greatest integer function, then

A
f(π/2)=1
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B
f(π)=+1
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C
f(π)=0
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D
f(π/4)=1
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Solution

The correct options are
A f(π/2)=1
C f(π)=0
{x} gives greatest integer less than or equal to x As 2π6.28,[2π]=6 And 2π6.28[6,28]=7
f(x)=cos6x+cos7x {cos(θ)=cosθ}
f(π/2)=cos6π2+cos7π2=1+0=1
f(π)=cos6π+cos7π=11=0
f(π)=cos(6π)+cos(7π)=11=0
f(π/4)=cos6π4+cos7π4=0+12
(A),(C)

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