## 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

2 | |

3 | |

5 | |

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.

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

all of even degree | |

all of odd degree | |

of any degree | |

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.

→ 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 unique least upper bound | |

a unique greatest lower bound | |

both (A) and (B) | |

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

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

n(n – 1) | |

n(n–1)/2 | |

n ^{2} | |

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

4 | |

5 | |

6 | |

7 |

Question 6 |

The decimal number equivalent of (4057.06)

_{8}is2095.75 | |

2095.075 | |

2095.937 | |

2095.0937 |

Question 6 Explanation:

Question 7 |

is equivalent to

Question 7 Explanation:

Question 8 |

An astable multivibrator has

one stable state | |

two stable states | |

no stable states | |

none of these |

Question 8 Explanation:

Question 9 |

12-bit 2’s complement of –73.75 is

01001001.1100 | |

11001001.1100 | |

10110110.0100 | |

10110110.1100 |

Question 9 Explanation:

Question 10 |

Encoding of data bits 0011 into 7-bit even Parity Hamming Code is

0011110 | |

0101110 | |

0010110 | |

0011100 |

Question 10 Explanation:

(m) Data = 0011

No. of parity bits needed is decided using

2

p=3

Bit pattern:

P

P

P

So encoded data = 0011110

No. of parity bits needed is decided using

2

^{p}≥ m+p+1p=3

Bit pattern:

P

_{1}(check even parity at 1, 3, 5, 7 bit) = 0P

_{2}(check even parity at 2, 3, 6, 7 bit) = 1P

_{4}(check even parity at 4, 5, 6, 7 bit) = 1So 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”;

int z = 7.0;

double void = 0.000;

short array [2] = {0, 1, 2};

char c = “\n”;

None | |

One is correct | |

Two are correct | |

All four are correct |

Question 11 Explanation:

int z = 7.0; →

double void = 0.000; →

It always return null value.

short array [2] = {0, 1, 2}; →

char c = “\n”; →

**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

5.75 | |

2.95 | |

1.4875 | |

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.

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.