BSc Mathematics SEM I 2015 16 2015-16 ATKT MATHS I Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q3 For attempt any three 5 marks)
2. Q1 Attempt Any Ono : (Bach 8 marks) nL and prove that fm,
3. Q2 Find greatest common divisor of n 0 and tt in form of + 760m,
   • B) Attempt Any Three : (Each 4 marks)
4. Q1 Explain Pascal's Triangle. Use it to find (a
5. Q2 Prove that the number of primes are
6. Q3 Define least common multiple and greatest common divisor of non zoro a and Prove that ged (a, b) Lem [ab] = ab State first principle of finite induction and prove that 8" 3" is divisible by 5 Vn e N
7. Q2 A) Attempt Any One: (Each 8 marks)
8. Q1 Define invertible function, bejective function, Prove that composition of injective function is injective
9. Q2 Define:
   • i) Equivalence relation R on nonempty set A
   • ii) Partition of A. Prove that every partition of a nonempty set A induces equivalence Attempt Any Three : (Each 4 marks)
10. Q1 Check whether * is binary on given set
    • i) ii) {a, b} on IR,
11. Q2 be defined by f(x) = 7. Check whether f is bijective or not. Hence find inverse if exist
12. Q3 Determine whether following relation R on set A is equivalence a not A = list of relations among people Ris defined y) R is brother
13. Q4 Determine whether each relation from A to B is function, If it is function give its range
    • Q.P. Code - SCIM020316X
14. Q3 <A) Attempt Any One: (Each 8 marks) mial and Computer
15. Q1 State and Prove Remainder Theorem for ya remainder when is divided by not g(x) is factor of
16. Q2 State and Prove factor theorem. Use it to deter mine W
    • B) Attempt Any Three: (Each 4 marks)
17. Q1 Prove polynomial of degree has at most roots
18. Q2 Express +i in polar form, also find magnitude & amphi
19. Q3 Find quotient and remainder when f(x) is divided by g(x) roduct of lin ‘
20. Q4 Prove that a non constant polynomial F(x) can be expressed 45 P Attempt Any Three: (Each 5 marks) a State and prove Euclid's Lemma 8 marks
21. Q2 Verify Wilson Theorem for P =
22. Q3 Prove (modn) for a, n iff a,b leave same remainder when divided by
23. Q4 If Ris an equivalence relation on nonempty set X. Then Prove equivalence classes of X are either identical or disjoint
24. Q5 Use Demoivre's Theorem to prove that
25. Q6 State and prove Rational Root Theorem

Read from the scan above, so a character or two may differ. The scan is the original.