## Solved Questions Paper-2 UGC-NET Computer Science December 2015

1. | How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women? | ||||||||||

A. | 75240 | ||||||||||

B. | 52492 | ||||||||||

C. | 41800 | ||||||||||

D. | 9900 | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

2. | Which of the following statement(s) is/are false? (a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree. (b) A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree. (c) A complete graph (Kn) has a Hamilton Circuit whenever n?3 (d) A cycle over six vertices (C6) is not a bipartite graph but a complete graph over 3 vertices is bipartite. Codes: | ||||||||||

A. | (a) only | ||||||||||

B. | (b) and (c) | ||||||||||

C. | (c) only | ||||||||||

D. | (d) only | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

3. | Which of the following is/are not true? (a) The set of negative integers is countable. (b) The set of integers that are multiples of 7 is countable. (c) The set of even integers is countable. (d) The set of real numbers between 0 and 1/2 is countable. | ||||||||||

A. | (a) and (c) | ||||||||||

B. | (b) and (d) | ||||||||||

C. | (b) only | ||||||||||

D. | (d) only | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

4. | Consider the graph given below: Check graph from question paper The two distinct sets of vertices, which make the graph bipartite are: | ||||||||||

A. | (v1, v4, v6); (v2, v3, v5, v7, v8) | ||||||||||

B. | (v1, v7, v8); (v2, v3, v5, v6) | ||||||||||

C. | (v1, v4, v6, v7); (v2, v3, v5, v8) | ||||||||||

D. | (v1, v4, v6, v7, v8); (v2, v3, v5) | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

5. | A tree with n vertices is called graceful, if its vertices can be labelled with integers 1,2,...,n such that the absolute value of the difference of the labels of adjacent vertices are all different. which of the following trees are graceful ? (a) (b) (c) | ||||||||||

A. | (a) and (b) | ||||||||||

B. | (b) and (c) | ||||||||||

C. | (a) and (c) | ||||||||||

D. | (a),(b) and (c) | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

6. | Which of the following arguments are not valid ? (a) "if gora gets the job and works hard, then he will be promoted. if gora gets promotion, then he will be happy. he will not be happy, therefore, either he will not get the job or he will not work hard" (b)"Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty." (c) if n is a real number such that n>1, then n ^{2} > 1. suppose that n^{2} > 1, then n>1 | ||||||||||

A. | (a) and (c) | ||||||||||

B. | (b) and (c) | ||||||||||

C. | (a), (b) and (c) | ||||||||||

D. | (a) and (b) | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

7. | Let P(m,n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions. (a) ?m ?n P(m,n) (b) ?n P(1,n) (c) ?m ?n P(m,n) | ||||||||||

A. | (a)-True; (b)-True; (c)-False | ||||||||||

B. | (a)-True; (b)-False; (c)-False | ||||||||||

C. | (a)-False; (b)-False; (c)-False | ||||||||||

D. | (a)-True; (b)-True; (c)-True | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

8. | Match the following terms
Codes : (a) (b) (c) (d) | ||||||||||

A. | (i) (ii) (iii) (iv) | ||||||||||

B. | (ii) (iii) (i) (iv) | ||||||||||

C. | (iii) (ii) (iv) (i) | ||||||||||

D. | (iv) (iii) (ii) (i) | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

9. | Consider the compound propositions given below as: (a) p?~(p?q) (b) (p?~q)?~(p?q) (c) p?(q?r) Which of the above propositions are tautologies? | ||||||||||

A. | (a) and (c) | ||||||||||

B. | (b) and (c) | ||||||||||

C. | (a) and (b) | ||||||||||

D. | (a), (b) and (c) | ||||||||||

View/Hide Ans | |||||||||||

Explanation | |||||||||||

10. | Which of the following property/ies a Group G must hold, in order to be an Abelian group? (a) The distributive property (b) The commutative property (c) The symmetric property Codes: | ||||||||||

A. | (a) and (b) | ||||||||||

B. | (b) and (c) | ||||||||||

C. | (a) only | ||||||||||

D. | (b) only | ||||||||||

View/Hide Ans | |||||||||||

Explanation |

Author Does Not claim of any answer these answers are as per expert opinion