# 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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