UGC NET CS 2017 Jan – II

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 ?

• A. (1, 110, 1200)
• B. (1, 110, 600, 1200)
• C. (1, 2, 55, 110, 600, 1200)
• D. (1, 55, 110, 600, 1200)

Answer: (A)

 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 :

• A. (1)
• B. (2)
• C. (3)
• D. (4)

Answer: (A)

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)

• A. (x² + 1)⁴ and [(x³ – 4x)² + 1]⁴
• B. (x² + 1)⁴ and [(x³ – 4x)² + 1]^-4
• C. (x² + 1)^-4 and [(x³ – 4x)² + 1]⁴
• D. (x² + 1)^-4 and [(x³ – 4x)² + 1]^-4

Answer: (D)

 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

• A. 16 and 6
• B. 17 and 6
• C. 17 and 7
• D. 16 and 7

Answer: (C)

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 ?

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

Answer: (D)

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 :

• A. P ∨ R
• B. P ∨ S
• C. Q ∨ R
• D. Q ∨ S

Answer: (D)

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 ____.

• A. Race condition
• B. Saturation
• C. Delay
• D. High impedance

Answer: (B)

Question 8

Convert the octal number 0.4051 into its equivalent decimal number.

• A. 0.5100098
• B. 0.2096
• C. 0.52
• D. 0.4192

Answer: (A)

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 :

• A. 2EE
• B. 2FF
• C. 4EF
• D. 4FE

Answer: (C)

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++ ?

• A. Constant
• B. Structure
• C. Array
• D. Header file

Answer: (D)

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.