Discrete Mathematics Week 12 NPTEL
Discrete Mathematics Week 12 NPTEL Assignment Answers
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- Which of the following options are true?
- (Z,×) is a group
- (Z,+) is not a group
- (Q,×) is a group
- (Z,−) is not a group
- (R,+) is a group
2. Let T be a group of 100 elements, what is the largest possible subgroup of T other than T itself?
- 50
- 75
- 25
- 20
3. The generating function for odd partitions of xx is:
- 1/(1−x) × 1/(1−x2) × 1/(1−x3) ×……
- 1/x × 1/(1−x)×1(1−x3)×1(1−x5) ×……
- 1/x × 1/(1−x) × 1/(1−x2) × 1/(1−x3) ×……
- 1/(1−x) × 1/(1−x3) × 1/(1−x5) ×……
These are the Discrete Mathematics Week 12 NPTEL Assignment Answers
4. For a path graph of P7P7, in how many ways can you color this graph with 4 colors so that no two adjacent nodes have the same color?
- 8748
- 2916
- 16384
- 65536
5. What are the elements of Z7Z7, i.e., integer modulo 7?
- {1, 2, 3, 4, 5, 6, 7}
- {1, 2, 3, 4, 5, 6}
- {0, 1, 2, 3, 4, 5, 6}
- {0, 1, 2, 3, 4, 5, 6, 7}
6. Which of the following statement(s) is/are true?
I) The operations of a group and its subgroup can be different.
II) (QQ, +) is a subgroup of (RR, +)
III) A group under addition modulo nn, where nn is prime, cannot have a subgroup except for a trivial subgroup identity element alone.
- II and III
- I and II
- I and III
- I II and III
These are the Discrete Mathematics Week 12 NPTEL Assignment Answers
7. State whether true/false:
Pd(n)𝑃𝑑(𝑛) is the coefficient of xn𝑥𝑛 in the function (1+x)(1+x2)(1+x3)……..(1+xn)(1+𝑥)(1+𝑥2)(1+𝑥3)……..(1+𝑥𝑛)
- True
- False
8. Let A be a group with 70 elements. Then A can not have a subgroup of cardinality
- 5
- 10
- 20
- 35
9. (Z6,+) is a group, what is the inverse of 4 in this group?
- 1
- 2
- 3
- 4
These are the Discrete Mathematics Week 12 NPTEL Assignment Answers
10. Given a complete graph with 11 vertices, in how many ways can you color this graph such that no two adjacent vertices have the same color? You are given 26 colors.
- C(K11)=26×25×24×…×1
- C(K11)=26×25×24×…×14
- C(K11)=26×25×24×…×16
- C(K11)=26×25×24×…×15
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