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) ×……

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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Discrete Mathematics Week 12 NPTEL Assignment Answers