BSc Mathematics SEM II 2021 2022 2022 MATHEMATICS II Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt the following 36 marks
2. Q1 The coefficient of in the expansion of (a + b
3. Q2 In the expansion of (x; + + + of terms are
4. Q3 __non-negative soiution are there for an equation a+b+c =10, where a,b,c > 0
5. Q4 ways can the letters of the word be arranged
6. Q5 At a party there are n men and n women. How many ways are there for the dance if everyone has to change partners?
7. Q6 is:
8. Q7 Degree of recurrence relation a, = + ap.) is Which of the following is a linear non honiogenous recurrence relation?
9. Q10 Characteristic roots of recurrence relation ap - + 10 = 0 are
10. Q11 A one - to- one mapping of a set A={aj, a2,.,an} onto itself is called
11. Q12 Two cycles of a set A are said to be disjoint if there is___ common element in both cycles
    • a) b)one d) many
12. Q13 The set of all subsets of set A is ca!led the set of A
13. Q14 A set which is not countable is called set
    • a) uncountable d) proper
14. Q15 Rising factorial [ 9 =
15. Q17 of 25 minimum students are there who were born in same month
16. Q18 The total number of partitions of a set with n elements is number
17. Q2 A) Attempt the following (Solve any 01) [08
18. Q1 i) IfA and B are countable sets then prove that A x B is countable
    • ii) A and B are two non-empty finite sets with ANB =@ prove that |AUB| = |A| +
19. Q2 i) Prove that Q is countable
    • ii) In how many ways can we draw a heart or a spade from an ordinary deck of playing cards? A heart or an ace? A card numbered 2 through 10?
    • B) Attempt the following (Solve any 01) [05
20. Q1 Prove that : S(n, 2) =
21. Q2 How many minimum people are required to guarantee that (i) atleast 2 of them are born exactly at same hour, minute and second? (ii) atleast 5 of them are born exactly at same hour, minute and second?
22. Q3 A) Attempt the following (Solve any 01) [08 MARKS}
23. Q1 i) State and prove the Vandermonde’s Identity
    • ii) State the Binomial theorem. Find the coefficient of x’y in the expansion of (x +
24. Q2 i) State and prove Pascai’s Identity
    • ii) State the Multinomial number. Find the coefficient of in expression
    • B) Attempt the following (Solve any 01) [05 MARKS}
25. Q2 How many non- negative solutions are there to the equation <21?
26. Q4 A) Attempt the following (Solve any 01) [08 MARKS}
27. Q1 i) Prove that the product of two even permutation is even
    • ii) Define the terms a) cyclic Permutation b) Even and odd permutation
    • B) Attempt the following (Solve any 01) 5
28. Q1 Solve the recurrence relation 2,, = - + 2 a3=8
29. Q2 Soive the recurrence relation a, = a =4

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