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CBSE UGC NET Computer Science Paper II January 2017 Solved Paper

1. Consider a sequence F_{00} defined as:

Then what shall be the set of values of the sequence F_{00}?

(1) (1, 110, 1200)

(2) (1, 110, 600, 1200)

(3) (1, 2, 55, 110, 600, 1200)

(4) (1, 55, 110, 600, 1200)

Answer: 1

__Explanation:__

We have given, F_{00}(0) = 1, F_{00}(1) = 1

F_{00}(2) = (10*F_{00}(1) + 100)/F_{00}(0) = 110

F_{00}(3) = (10*F_{00}(2) + 100)/F_{00}(1) = 1200

F_{00}(4) = (10*F_{00}(3) + 100)/F_{00}(2) = 110

Since the values repeats after the first three values, the set of values of F_{00} will be (1,110,1200).

2. Match the following:

**List-I List-II**

a. Absurd i. Clearly impossible being

contrary to some evident truth.

b. Ambiguous ii. Capable of more than one

interpretation or meaning.

c. Axiom iii. An assertion that is accepted

and used without a proof.

d. Conjecture iv. An opinion Preferably based

on some experience or wisdom.

**Codes:**

a b c d

(1) i ii iii iv

(2) i iii iv ii

(3) ii iii iv i

(4) ii i iii iv

Answer: 1

Absurd- à¤¬ेà¤¤ुà¤•ा

Ambiguous-à¤…à¤¨ेà¤•ाà¤¥ी

Axiom-à¤¸्à¤µà¤¯ंà¤¸िà¤¦्à¤§

Conjecture-à¤…à¤¨ुà¤®ाà¤¨ à¤¸े à¤¨िà¤°्à¤£à¤¯ à¤•à¤°à¤¨ा

3. The functions mapping R into R are defined as:

f(x) = x^{3}-4x, g(x)=1/(x^{2}+1) and h(x)=x^{4}

Then find the value of the following composite functions:

hog(x) and hogof(x)

(1) (x^{2}+1)^{4} and [(x^{3}-4x)^{2}+1]^{4}

(2) (x^{2}+1)^{4} and [(x^{3}-4x)^{2}+1]^{- 4}

(3) (x^{2}+1)^{- 4} and [(x^{3}-4x)^{2}+1]^{4}

(4) (x^{2}+1)^{‑ 4} and [(x^{3}-4x)^{2}+1]^{- 4}

Answer: 4

__Explanation:__

hog(x) = h(1/(x^{2}+1))

= [(1/(x^{2}+1))]^{4} = (x^{2}+1)^{- 4}

hogof(x) = hog(x^{3}-4x)

= hog(x^{3}-4x)

= [(x^{3}-4x)^{2}+1]^{- 4} [since hog(x) = (x^{2}+1)^{- 4}]

4. How many multiples of 6 are there between the following pairs of numbers?

0 and 100 and -6 and 34

(1) 16 and 6

(2) 17 and 6

(3) 17 and 7

(4) 16 and 7

Answer: 3

__Explanation:__

Number of multiples of 6 between 1 and 100 = 100/6 = 16

Since the range starts from zero, we need to take zero too. [zero is a multiple of every integer (except zero itself)].

So, answer = 16+1 = 17

Number of multiples of 6 between 1 and 34 = 34/6 = 5

Since the range is -6 to 34, we need to take -6 and zero.

So, answer = 5+2 = 7

5. Consider a Hamiltonian Graph G with no loops or parallel edges and with |V(G)|=n≥3. Then which of the following is true?

(1) deg(v) ≥ n/2 for each vertex v.

(2) |E(G)| ≥ 1/2(n-1)(n-2)+2

(3) deg(v)+deg(w) ≥ n whenever v and w are not connected by an edge.

(4) All of the above

Answer: 4

__Explanation:__

**Dirac's theorem: **A simple graph with n vertices (n ≥ 3) is Hamiltonian if every vertex

has degree n/2 or greater.

**Ore's theorem: **deg(v) + deg(w) ≥ n for every pair of distinct non-adjacent vertices v

and w of G (*), then G is Hamiltonian.

6. In propositional logic if (P→Q)˄(R→S) and (P˅R) are two premises such that

Y is the premise:

(1) P˅R

(2) P˅S

(3) Q˅R

(4) Q˅S

Answer: 4