BSc Mathematics SEM I 2016 17 2016-17 ATKT MATHS II Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 , Q.2 and Q. 3 atte and any three subgy mpt any one s (each 4 marks ion (each 8 marks) from part
2. Q4 attempt arks) from part (b) Pt any three.(each 5 mark 2810m + 457) mon devisor of 2210,357 and express of
   • b) Are m,n unique? Justify ( Attempt any three. [each 4]
3. Q1 State Fir inci st principle of finite inducti by we IN. Pp inite induction that 8" — 3” is
4. Q2 Prove that
5. Q4 | Define greatest common devisor of non zero integer a & band that the positive gcd of any two integers (whenever exists) is unique
6. Q2 (a) Attempt any one. [each 8]
7. Q1 Invertible function, Bijective function and prove tbat Bis
8. Q2 ! Define’ i) Equivalence relation R empty set X
   • ii) partition of non empty set and prove that if P is partition of non empty set X then P induces Check is binary on given set
9. Q2 ; Determine Whether each relation A to B. If it is function give its Let IR — {3} > — {0} be defined by f(x) = = then prove f is bijective and Find formula for
10. Q4 Determine whether following relation R on set A is equivalence or not ak is even abEZ=A any one. [each 8] a 1), | State and prove Remainder theorem for polynomial 'f (x) compute the remainder when f(x) is divided by g(x). 4
11. Q2 . State and prove Factor theorem for f(x) F[x] Use it to determine Whether or not g(x) is factor of f(x) Attenipt any three. [each 4]
12. Q1 : Prove that a non constart polynomial f(x) can be expressed as product of linear and quadradic polynomial q 2) . Express 5i in polar form and also find magnitude and amplitude quotient and remainder when f (x) is divided by Prove that is irrational any three. [each 5] rove that two integers a and b are congruent modulo a positive integer iff b leave same remainder whe; divided by n
13. Q3 IfRisan Equivalence relation on a non set X then'prove that any two equivalence classes of X are either identical or disjoint
14. Q4 Show that f:A > B,g : B > C arc function then for any nonempty subset
15. Q5 State and prove Rational Root
16. Q6 De Moivre’s theorem to prove that

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