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Q.

Which of the following functions have finite number of points of discontinuity in R([.] represents the greatest integer function)

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a

|x|x

b

x[x]

c

tanx

d

sin[πx]

answer is C.

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Detailed Solution

f(x)tanx is discontinuous

 when x=(2n+1)π/2,nZ

f(x)=x[x] is discontinuous when x=k,kZ

f(x)=sin[nπx] is discontinouswhen nπx=k,kZ

Thus,all the above function have infinite number of points of discontinuity.

But f(x)=|x|x is discontinuous where x=0 only.

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