DECEMBER 2010 PAPER SOLVED QUESTIONS 1 - 10

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
Ans:- B. There are 3 integers between 1 and 250 that are divisible by 2,5 and 7. They are 70,140 and 210.

2. An undirected graph possess 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
Ans:- A. According to Euler's theorem 1, if a graph is undirected then it has an eulerian circuit if and only if it is connected and each vertex has an even degree.
***It would be useful to know about the Hamiltonian circuit as well.

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.

Ans:- C.

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
Ans:- D. The formula for counting the minimum number of edges in a connected graph is (n-1).

5. Would be done later.....

6. The decimal number equivalent of (4057.06)₈ is :
A) 2095.75   (B)2095.075
C) 2095.937   (D)2095.09375
Ans:- D.

7. Would be done later...

8. An astable multivibrator has
A)one stable state   (B)two stable states
C)no stable states   (D)none of these

Ans:- C. An astable multivibrator has two states but neither of them are stable.

9.12-bit 2's complement of -73.75 is
A) 01001001.1100   (B)11001001.1100
C) 10110110.0100   (D)10110110.1100
Ans:- B

10. Encoding of data bits 0011 into 7-bit even parity Hamming code is
A)0011110   (B)0101110
C)0010110   (D)0011100
Ans:- A.
The explanation is quite lengthy. If you google the question, you would get a link to the book "Fundamentals of digital circuit" by A.Anand Kumar. The explanation is great there.

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
Ans:-The second declaration is for sure wrong because we cannot have a keyword as a variable name. The last declaration is also wrong because we cannot assign anything within double quotes to a character variable. So we are left with only the first and the array declaration.I think those two would still not give errors in c. So 'C' could be the answer for this question.

To be continued later...