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Old Exam Papers June 2012 (Set 2)

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A<br />

MT-04<br />

B.A./B.Sc. (Part II) EXAMINATION, <strong>June</strong>,<br />

<strong>2012</strong><br />

MATHEMATICS<br />

Paper-MT-04<br />

(Real Analysis and Metric Space)<br />

Time allowed : Three hours<br />

Maximum marks : 67<br />

Attempt any five questions. All<br />

questions carry equal marks.<br />

fdUgha ik¡p iz'uksa ds mÙkj nhft;sA lHkh iz'uksa<br />

ds vad leku gSaA<br />

1. (a) Prove that between any two different real numbers,<br />

there lie an infinite number of rational numbers.<br />

fl) dhft;s fd fdUgha nks fHkUu okLrfod la[;kvksa ds<br />

e/; vuUr ifjes; la[;k,¡ fo|eku gksrh gSaA<br />

(b) Prove that every infinite bounded set has a limit point<br />

i.e. at least one limit point.<br />

PTO

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