31.
Let A be n x n real valued square symmetric
matrix of rank 2 with

Consider the
following statements.

(I) One
eigen value must be in [-5, 5]

(II) The
eigen value with the largest magnitude must be strictly greater than 5

Which of the
above statements about eigen values of A is/are necessarily CORRECT?

(A) Both (I)
and (II)

(B) (I) only

(C) (II)
only

(D) Neither
(I) nor (II)

Answer: B

32. A
computer network uses polynomials over GF(2) for error checking with 8 bits as
information bits and uses x

^{3}+x+1 as the generator polynomial to generate the check bits. In this network, the message 01011011 is transmitted as
(A)
01011011010

(B) 01011011011

(C)
01011011101

(D) 01011011100

Answer: C

33. Consider
a combination of T and D flip-flops connected as shown below. Tile output of the
D flip-flop is connected to the input of the T flip-flop and the output of the
T flip-flop is connected to the input of the D flip-flop.

Initially,
both Q

_{0}and Q_{1}are set to 1 (before the 1^{st}clock cycle). The outputs
(A) Q

_{1}Q_{0}after the 3^{rd}cycle are 11 and after the 4^{th}cycle are 00 respectively
(B) Q

_{1}Q_{0}after the 3^{rd}cycle are 11 and after the 4^{th}cycle are 01 respectively
(C) Q

_{1}Q_{0}after the 3^{rd}cycle are 00 and after the 4^{th}cycle are 11 respectively
(D) Q

_{1}Q_{0}after the 3^{rd}cycle are 01 and after the 4^{th}cycle are 01 respectively
Answer: B

34. If
G is a grammar with productions

S→SaS | aSb
| bSa | SS | Îµ

where S is
the start variable, then which one of the following strings is not generated by
G?

(A) abab

(B) aaab

(C) abbaa

(D) babba

Answer: D

35. Consider
the following two functions.

void fun1(int
n) {

if(n
== 0) return;

printf(“%d”,
n);

fun2(n-2);

printf(“%d”,
n);

}

void
fun2(int n) {

if(n
== 0) return;

printf
(“%d”, n);

fun1
(++n);

printf(“%d”,
n);

}

The output
printed when fun1 (5) is called is

(A)
53423122233445

(B) 53423120112233

(C)
53423122132435

(D)
53423120213243

Answer: A

36. Consider
the C functions

**foo**and**bar**given below:
int foo(int
val) {

int
x=0;

while(val
> 0) {

x
= x + foo(vaI--);

}

return val;

}

int bar(int val)
{

int
x =0;

while(val
> 0) {

x
= x + bar(val-1);

}

return val;

}

Invocations
of foo (3) and bar (3) will result in:

(A) Return
of 6 and 6 respectively.

(B) Infinite
loop and abnormal termination respectively.

(C) Abnormal
termination and infinite loop respectively.

(D) Both
terminating abnormally.

Answer: C

37. Consider
the context-free grammars over the alphabet {a, b, c} given below. S and T are
non-terminals.

G

_{1}:S → aSb | T, T → cT | Îµ
G

_{2}:S → bSa | T, T → cT | Îµ
The language
L(G

_{1}) ∩ L(G_{2}) is
(A) Finite.

(B) Not finite
but regular.

(C)
Context-Free but not regular.

(D)
Recursive but not context-free.

Answer: B

38. Consider
the following languages over the alphabet ∑= {a, b, c}

Let L

_{1}= {a^{n}b^{n}c^{m}| m, n ≥ 0} and L_{2}= { a^{m}b^{n}c^{n}| m, n ≥ 0}
Which of the
following are context-free languages?

I. L

_{1 }U L_{2}
II. L

_{1}∩ L_{2}
(A) I only

(B) II only

(C) I and II

(D) Neither
I nor II

Answer: A

39. Let
A and B be finite alphabets and let # be a symbol outside both A and B. Let

*f*be a total function from A* to B*. We say*f is computable*if there exists a Turing machine M which given an input x in A*, always halts with*f(x)*on its tape. Let*L*denote the language {x # f(x) | xÎµA*}._{f}
Which of the
following statements is true?

(A) f is
computable if and only if

*L*is recursive._{f}
(B) f is
computable if and only if

*L*is recursively enumerable._{f}
(C) if f is
computable then

*L*is recursive, but not conversely._{f}
(D) if f is
computable then

*L*is recursively enumerable, but not conversely._{f}
Answer: A

40. Recall
that Belady’s anomaly is that the page-fault rate may increase as the number of
allocated frames increases. Now, consider the following statements:

S1: Random
page replacement algorithm (where a page chosen at random is replaced) suffers
from Belady’s anomaly

S2: LRU page
replacement algorithm suffers from Belady’s anomaly

Which of the
following is CORRECT?

(A) S1 is
true, S2 is true

(B) S1 is
true, S2 is false

(C) S1 is
false, S2 is true

(D) S1 is
false, S2 is false

Answer: B

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