For any real number r, let A_r = {e^{\i\\pi\rn} : n is a natural number}be a set of complex numbers. Then -

Correct Answer is : A1,A0.3 are finite sets and A1π is an infinite sets

A_1, A _{1/\pi}, A_0.3 are all infinite sets

A_1 is a finite set and A_{ 1/\pi}, A_0.3 are infinite sets

A_1, A _{1/\pi}, A_0.3 are all finite sets

A_1, A_0.3 are finite sets and A _{1/\pi} is an infinite sets

KVPY SX SB Exam 2016 Question Paper

Question : 3 of 120

Marks: +1, -0

For any real number r, let

A_r

= {

e^{\i\π\rn}

: n is a natural number}be a set of complex numbers. Then -

Solution:

e^{\i\π\rn}

is always a finite set when r is a rational & is infinite when r

= 1/π

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