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FIFTH SEMESTER U.G. DEGREE EXAMINATION, NOVEMBER 2021
(CBCSS-UG)
Mathematics
MTS 5B 06—BASIC ANALYSIS
(2019 Admissions)
: Two Hours and a Half Maximum : 80 Marks
Section A

Answer at least ten questions.

Each question carries 3 marks.

All questions can be attended.
Overall Ceiling 30.

Is the union of two disjoint denumerable sets denumerable ?

If a,b< R with ab = 0, then prove that either a = 0 or b = 0.

If ae R is such that 0 0, then show that a = 0.

Find all real numbers «x satisfying the inequality ,? 5 3x44.

If 0
Ifx and yeR withx
State characterization theorem for intervals.

Test the convergence of ‏جا دی و ئوہ‎

Show that every convergent sequence is a Cauchy sequence.
Define Supremum of a set and give example of a set which has no Supremum.

What can be said about the complex number z if z =-z.

Find modulus of the complex number z = - 97.
Find real and imaginary parts of the complex 7 (2) - 2 as functions of r and 9.

State nested interval property.
Write the equation of (a) a closed disk of radius p centred atz,; (b) equation of a circle with centre
20 and radius p.

(10 x 3 = 30 marks)

Turn over

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