# UGC NET CS 2016 Aug – II

 Question 1
The Boolean function [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] is equal to the Boolean function:
 A q B p ∧ r C p ∨ q D p
Propositional and First Order Logic.    UGC NET CS 2016 Aug – II
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Question 1 Explanation:
We have Boolean function: [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] = [(p ∨ ~q) ∧ (p ∨ q ) ∨ (p ∧ r)] = [p ∨ (p ∧ q) ∨ (p ∧ ~q) ∨(p ∧ r)] = p[1 ∨ q ∨ ~q ∨ r] = p So, option (D) is correct.
 Question 2
Let us assume that you construct ordered tree to represent the compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q). Then, the prefix expression and post-fix expression determined using this ordered tree are pgiven as ____ and _____ respectively.
 A ↔~∧pq∨ ~ ~ pq, pq∧~p~q~∨↔ B ↔~∧pq∨ ~ p~q, pq∧~p~q~∨↔ C ↔~∧pq∨ ~ ~ pq, pq∧~p~~q∨↔ D ↔~∧pq∨ ~ p~ q, pq∧~p~ ~q∨↔
Propositional and First Order Logic.    UGC NET CS 2016 Aug – II
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Question 2 Explanation:
We have compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q): Now we will construct ordered tree: We are asked to determine pre-order (i.e. parent-node left-node right-node), we will drive it from ordered tree i.e. ↔ ~ ∧ p q ∨ ~ p ~q And post-order(i.e. left-node right-node parent-node) from the ordered tree it is p q ∧ ~ p ~ q ~ ∨ ↔. So, option (B) is correct.
 Question 3
Let A and B be sets in a finite universal set U. Given the following: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B| Which of the following is in order of increasing size ?
 A |A – B| < |A ⊕ B| < |A| + |B| < |A ∪ B| B |A ⊕ B| < |A – B| < |A ∪ B| < |A| + |B| C |A ⊕ B| < |A| + |B| < |A – B| < |A ∪ B| D |A – B| < |A ⊕ B| < |A ∪ B| < |A| + |B|
Propositional and First Order Logic.    UGC NET CS 2016 Aug – II
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Question 3 Explanation:
We will draw venn diagram for all set: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B| So, option (D) is correct. Alternative way -
```|A – B| = |A| - |A ∩ B|
|A ⊕ B| = |A| + |B| - 2|A ∩ B|
|A ∪ B| = |A| + |B| - |A ∩ B|```
Therefore,
`|A – B| < |A ⊕ B| < |A ∪ B| < |A| + |B|`
 Question 4
What is the probability that a randomly selected bit string of length 10 is a palindrome?
 A 1/64 B 1/32 C 1/8 D 1/4
Probability    UGC NET CS 2016 Aug – II
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Question 4 Explanation:
In the given question we have a palindrome: in even length palindrome half length is fixed and rest is repeated. So, in 10 bit palindrome, we have 5 position to be filled with 2 choices each- i.e. 25 choices for first half and 25 choices for second half.
```Probability = favorable outcome / total outcome
=  25/ 210
=  1 / 25
=  1 / 32.```
So, option (B) is correct.
 Question 5
Given the following graphs: Which of the following is correct?
 A G1 contains Euler circuit and G2 does not contain Euler circuit. B G1 does not contain Euler circuit and G2 contains Euler circuit. C Both G1 and G2 do not contain Euler circuit. D Both G1 and G2 contain Euler circuit.
Graph Theory    UGC NET CS 2016 Aug – II
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Question 5 Explanation:
Euler circuit does not contain odd length cycle. Refer: Eulerian path and circuit for undirected graph None of the above graph is Eulerian. So, option (C) is correct.
 Question 6
The octal number 326.4 is equivalent to
 A (214.2)10 and (D6.8))16 B (212.5)10 and (D6.8))16 C (214.5)10 and (D6.8))16 D (214.5)10 and (D6.4))16
Digital Logic & Number representation    Number Representation    UGC NET CS 2016 Aug – II
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Question 6 Explanation:
To solve this question we will apply traditional approach: (326.4)8 = 82 * 3 + 81 * 2 + 80 * 6 . 8-1 * 4 = ( 214.5)10 is decimal representation. For hexadecimal representation group binary sequence of (214.5) = (011010110.100)2 into group of 4. i.e. 0 1101 0110. 1000 (0 can be padded after decimal) this is equivalent to- (D6.8)16. So, option (C) is correct.
 Question 7
Which of the following is the most efficient to perform arithmetic operations on the numbers?
 A Sign-magnitude B 1’s complement C 2’s complement D 9’s complement
Digital Logic & Number representation    Number Representation    UGC NET CS 2016 Aug – II
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Question 7 Explanation:
Sign's magnitude is only for sign convention (MSB is 1 then no is negative and if 0 then no is positive). Main difference is that while adding numbers using 1′ s complement, we first do binary addition, then add in an end-around carry value. But, 2′ s complement has only one value for zero, and doesn’t require carry values. 9’s complement of a decimal number is the subtraction of it’s each digits from 9. Like 1’s complement, 9’s complement is used to subtract a number using addition. 2's complement representation is unambiguous for 0 (i.e., only positive 0), but Sign-magnitude, 1’s complement and 9’s complement are ambiguous representation for 0 (i.e., both positive and negative 0). So, option (C) is correct.
 Question 8
The Karnaugh map for a Boolean function is given as The simplified Boolean equation for the above Karnaugh Map is
 A AB + CD + A`B + AD B AB + AC + AD + BCD C AB + AD + BC + ACD D AB + AC + BC + BCD
Digital Logic & Number representation    UGC NET CS 2016 Aug – II    Logic functions and Minimization
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Question 8 Explanation: By grouping we will simply get AB + AC + AD + BCD. So, option (B) is correct.
 Question 9
Which of the following logic operations is performed by the following given combinational circuit? A EXCLUSIVE-OR B EXCLUSIVE-NOR C NAND D NOR
Digital Logic & Number representation    UGC NET CS 2016 Aug – II    Combinational Circuits
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Question 9 Explanation: F is EXCLUSIVE-OR between X and Y. So, option (A) is correct.
 Question 10
Match the following: A (1) B (2) C (3) D (4)
Digital Logic & Number representation    UGC NET CS 2016 Aug – II    Combinational Circuits
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Question 10 Explanation:
Controlled Inverter is a circuit that transmits a binary word or its 1’s complement. Full adder is a circuit that can add 3 bits. Half adder is a logic circuit that adds 2 bits. Binary adder is a circuit that can add two binary numbers. So, option (D) is correct.
There are 50 questions to complete.
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