# UGC NET CS 2017 Jan – II

• Last Updated : 18 Oct, 2019

 Question 1
Consider a sequence F00 defined as : F00(0) = 1, F00(1) = 1 F00(n) = 10 ∗ F00(n – 1) + 100 F00(n – 2) for n ≥ 2 Then what shall be the set of values of the sequence F00 ? (1, 110, 1200) (1, 110, 600, 1200) (1, 2, 55, 110, 600, 1200) (1, 55, 110, 600, 1200)

Question 1-Explanation:
``` F00(0) = 1, F00(1) = 1
F00(n) = 10 ∗ F00(n – 1) + 100
F00(2) = 10 * F00(1) + 100
= 10 * 1 + 100
= 10 + 100
= 110
Similarly:
F00(3) = 10 * F00(2) + 100
= 10 * 110 + 100
= 1100 + 100
= 1200
The sequence will be (1, 110, 1200).```
So, (A) will be the answer.
 Question 2
Match the following :  (1) (2) (3) (4)

Question 2-Explanation:
1. Absurd means Clearly impossible being contrary to some evident truth.
2. Ambiguous Capable of more than one interpretation or meaning.
3. An assertion that is accepted and used without a proof.
4. Conjecture An opinion preferably based on some experience or wisdom
So, option (A) is correct.
 Question 3
The functions mapping R into R are defined as : f(x) = x3 – 4x, g(x) = 1/(x2 + 1) and h(x) = x4. Then find the value of the following composite functions : hog(x) and hogof(x) (x2 + 1)4 and [(x3 – 4x)2 + 1]4 (x2 + 1)4 and [(x3 – 4x)2 + 1]-4 (x2 + 1)-4 and [(x3 – 4x)2 + 1]4 (x2 + 1)-4 and [(x3 – 4x)2 + 1]-4

Question 3-Explanation:
``` f(x) = x3 – 4x, g(x) = 1/(x2 + 1) and h(x) = x4
hog(x) = [g(x)]4
=  [1/(x2 + 1)]4
=  [(x2 + 1)-1]4
=  [(x2 + 1)]-4
Similarly:
hogof(x) = [gof(x)]4
= [(f(x)2 + 1)]-4
=  [((x3 – 4x)2 + 1)]-4
```
So, option (D) is correct.
 Question 4

How many multiples of 6 are there between the following pairs of numbers ? 0 and 100 and –6 and 34 16 and 6 17 and 6 17 and 7 16 and 7

Question 4-Explanation:

Between 0 and 100 multiple of 6 are: 0,6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96 ie. 17 multiple. Between -6 and 34 multiple of 6 are: -6, 0, 6, 12, 18, 24, 30. ie. 7 multiple.

So,option (C) is correct.

 Question 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 ? deg(v) ≥n/2 for each vertex v. |E(G)| ≥1/2(n – 1) (n – 2) + 2 deg (v) + deg(w) ≥ n whenever v and w are not connected by an edge All of the above

 Question 6
In propositional logic if (P → Q) ∧ (R → S) and (P ∨ R) are two premises such that (P → Q) ∧ (R → S) P ∨ R Y Y is the premise : P ∨ R P ∨ S Q ∨ R Q ∨ S

 Question 7
ECL is the fastest of all logic families. High speed in ECL is possible because transistors are used in difference amplifier configuration, in which they are never driven into ____. Race condition Saturation Delay High impedance

 Question 8
Convert the octal number 0.4051 into its equivalent decimal number. 0.51001 0.2096 0.52 0.4192

Question 8-Explanation:
Convert 0.4051 into decimal in traditional way:
```i.e.  4 * 8-1 + 0 * 8-2 + 5 * 8-3 + 1 * 8-4
= 0.5100098```
So, option (A) is correct.
 Question 9
The hexadecimal equivalent of the octal number 2357 is : 2EE 2FF 4EF 4FE

Question 9-Explanation:
First we will convert 2357 into binary: 010 011 101 111 now we will group this binary number into group of 4 → 0100 1110 1111 now place the hexadecimal equivalent ie 1111 - F, 1110 - E, 0100 - 4. Hexadecimal no is 4EF. So, option (E) is correct.
 Question 10
Which of the following cannot be passed to a function in C++ ? Constant Structure Array Header file

Question 10-Explanation:
Header file can not be passed to a function in C++. While array, constant and structure can be passed into a function. So, option (D) is correct.
There are 49 questions to complete.