Discrete Mathematics Week 12 NPTEL

Discrete Mathematics Week 12 NPTEL Assignment Answers

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1. 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) ×……

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These are the Discrete Mathematics Week 12 NPTEL Assignment Answers

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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

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These are the Discrete Mathematics Week 12 NPTEL Assignment Answers

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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

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These are the Discrete Mathematics Week 12 NPTEL Assignment Answers

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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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