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FIFTH SEMESTER U.G. DEGREE EXAMINATION, NOVEMBER 1
(CBCSS—UG)
Mathematics
MTS 5B 05—THEORY OF EQUATIONS AND ABSTRACT ALGEBRA
(2019 Admissions)
Time : 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.

1. Show that 5 _ 3४4 + x? — 2x —8 is divisible by x —3.
2. Factorize into linear factors the polynomial 2८4 - 1.

3. Write a cubic equation with roots1, 1+i, 1-7.
4. State Identity theorem.

5. How many real roots has the equation x* _ 40: + ® = 0.
6. Make addition and multiplication tables for Zy.

7. Check whether the relation on R defined by a ~b if a—beQ is an equivalence relation.

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8. Consider the permutations o= and t= . Compute o t andto.
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9. Let G bea group and a,beG. Show that (ab) " = ९101.

10. Write a subgroup of (Z, +).

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