D 30569 (Pages : 3) ಸ ಭಾ ಕ್ಷ ಿುುಿು್ತ

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FIFTH SEMESTER (CBCSS-UG) DEGREE EXAMINATION
NOVEMBER 2022

Mathematics
MTS 5B 06—BASIC ANALYSIS

(2020 Admission onwards)

: Two Hours and a Half Maximum : 80 Marks

Section A

Answer any number of questions.
Each question carries 2 Marks.
Maximum 25 Marks.

Define denumerable set. Give an example.

If ae R, then prove that a-0=0.

Let a, b, c be elements of R andifa>b and b ><, then prove that a > ©.
Prove that |- al = (| for allaecR.

Describe Fibonacci sequence.
State Monotone Convergence Theorem.
Define Cauchy sequence. Give an example.

Define properly divergent sequence.
Show that R = (-<0, ©) is open.

Describe any two properties of Cantor Set.

1,1
Whether the sequence ட 2° 3, ‏.سط‎ is convergent ? Justify your answer.

Find the principal cube root at the point 2 ८४ .

Define bounded subset of the complex plane.

Turn over

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