UGC NET CS 2010 Dec-Paper-2

Question 1
The number of integers between 1 and 250 that are divisible by 2, 5 and 7 is
A
2
B
3
C
5
D
8
Question 1 Explanation: 
Here, we have to find all possible integers between 250 which was divisible by 2,5 and 7.
Solving this problem by 2 methods:
1. Venn diagram
2. Mathematical substitution.
In this problem, we are using Mathematical substitution method.
Step-1: According to condition, we can perform least common multiple(LCM) of 2,5 and 7=70
Step-2: Total number of integers= ⌊250/70⌋
= 3
Note: Divisible numbers are 70,140 and 210.
Question 2
An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are
A
all of even degree
B
all of odd degree
C
of any degree
D
even in number
Question 2 Explanation: 
→ An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices all of even degree.
→ Eulerian circuit (or) Euler tour in an undirected graph is a cycle that uses each edge exactly once.
Question 3
A partially ordered set is said to be a lattice if every two elements in the set have
A
a unique least upper bound
B
a unique greatest lower bound
C
both (A) and (B)
D
none of the above
Question 3 Explanation: 
A partially ordered set is said to be a lattice if every two elements in the set have
1. Unique least upper bound
2. Unique greatest lower bound
Question 4
The minimum number of edges in a connected graph with ‘n’ vertices is equal to
A
n(n – 1)
B
n(n–1)/2
C
n2
D
n – 1
Question 4 Explanation: 

Question 5
Consider the problem of connecting 19 lamps to a single electric outlet by using extension cords each of which has four outlets. The number of extension cords required is
A
4
B
5
C
6
D
7
Question 6
The decimal number equivalent of (4057.06)8 is
A
2095.75
B
2095.075
C
2095.937
D
2095.0937
Question 6 Explanation: 

Question 7
 is equivalent to
A

B

C

D

Question 7 Explanation: 

Question 8
An astable multivibrator has
A
one stable state
B
two stable states
C
no stable states
D
none of these
Question 8 Explanation: 

Question 9
12-bit 2’s complement of –73.75 is
A
01001001.1100
B
11001001.1100
C
10110110.0100
D
10110110.1100
Question 9 Explanation: 


Question 10
Encoding of data bits 0011 into 7-bit even Parity Hamming Code is
A
0011110
B
0101110
C
0010110
D
0011100
Question 10 Explanation: 
(m) Data = 0011
No. of parity bits needed is decided using
2p≥ m+p+1
p=3
Bit pattern:

P1(check even parity at 1, 3, 5, 7 bit) = 0
P2(check even parity at 2, 3, 6, 7 bit) = 1
P4(check even parity at 4, 5, 6, 7 bit) = 1
So encoded data = 0011110
Question 11
How many of the following declarations are correct ?
int z = 7.0;
double void = 0.000;
short array [2] = {0, 1, 2};
char c = “\n”;
A
None
B
One is correct
C
Two are correct
D
All four are correct
Question 11 Explanation: 
int z = 7.0; → Incorrect. Given data type is integer but given floating point number. It is wrong declaration.
double void = 0.000; → Incorrect. void is a keyword but can’t use with variable declaration.
It always return null value.
short array [2] = {0, 1, 2}; → Correct. It is right format. We can declare static values here itself.
char c = “\n”; → Incorrect. It is character data type but given in double quotes. It should be single quote instead of double quote.
Question 12
The value of the following expression (13 / 4 * 3) % 5 + 1 is
A
5.75
B
2.95
C
1.4875
D
5
Question 12 Explanation: 
(13 / 4 * 3) % 5 + 1
Step-1: (13 / 4 * 3) % 5 + 1
Step-2: (3.25*3)%5+1
Step-3: 9.75%5+1
Step-4: 4.75+1
Step-5: 5.75
Note: ( ) having highest precedence then *,/ and % have same precedence order.
There are 12 questions to complete.

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