1.
The statement (¬p) ⇒ (¬q) is
logically equivalent to which of the statements below?

I. p⇒q

II. q⇒p

III. (¬q) ∨ p

IV. (¬p) ∨ q

(A) I only

(B) I and IV
only

(C) II only

(D) II and
III only

Answer: D

2. Consider
the first-order logic sentence F: ∀x(∃yR(x,y)). Assuming non-empty logical domains,
which of the sentences below are implied by F?

I. ∃y(∃xR(x,y))

II. ∃y(∀xR(x,y))

III. ∀y(∃xR(x,y))

IV. ¬∃x(∀y¬R(x,y))

(A) IV only

(B) I and IV
only

(C) II only

(D) II and
III only

Answer: B

3. Let
c

_{1},...,c_{n}be scalars, not all zero, such that
where a

_{i}are column vectors in R^{n}.
Consider the
set of linear equations

Ax=b

where A=[a

_{1},...,a_{n}] and
The set of
equations has

(A) a unique
solution at x=J

_{n}where J_{n}denotes a n-dimensional vector of all 1
(B) no
solution

(C)
infinitely many solutions

(D) finitely
many solutions

Answer: C

4. Consider
tile following functions from positive integers to real numbers:

10, √n, n, log

_{2}n, 100/n
The CORRECT
arrangement of the above functions in increasing order of asymptotic complexity
is:

(A) log

_{2}n, 100/n, 10, √n, n
(B) 100/n,
10, log

_{2}n, √n, n
(C) 10, 100/n,
√n, log

_{2}n, n
(D) 100/n,
log

_{2}n, 10, √n, n,
Answer: B

5. Consider
the following table:

Match the
algorithms to the design paradigms they are based on.

(A)
(P)↔(ii), (Q)↔(iii), (R)↔(i)

(B)
(P)↔(iii), (Q)↔(i), (R)↔(ii)

(C)
(P)↔(ii), (Q)↔(i), (R)↔(iii)

(D) (P)↔(i),
(Q)↔(ii), (R)↔(iii)

Answer: C

6. Let
T be a binary search tree with 15 nodes. The minimum and maximum possible
heights of T are:

*Note: The height of a tree with a single node is 0.*

(A) 4 and 15
respectively

(B) 3 and 14
respectively

(C) 4 and 14
respectively

(D) 3 and 15
respectively

Answer: B

7. The
n-bit fixed-point representation of an unsigned real number X uses f bits for
the fraction part. Let i = n-f. The range of decimal values for X in this
representation is

(A) 2

^{-f}to 2^{i}
(B) 2

^{-f}to (2^{i}– 2^{-f})
(C) 0 to 2

^{i}
(D) 0 to (2

^{i}– 2^{-f})
Answer: D

8. Consider
the C code fragment given below.

typedef
struct node {

int
data;

node*
next;

} node;

void
join(node* m, node* n){

node*
p = n;

while(p
->next != NULL) {

p
= p->next;

}

p->next
= m;

}

Assuming
that m and n point to valid NULL-terminated linked lists, invocation of

*join*will
(A) append
list m to the end of list n for all inputs.

(B) either
cause a null pointer dereference or append list m to the end of list n.

(C) cause a
null pointer dereference for all inputs.

(D) append
list n to the end of list m for all inputs.

Answer: B

9. When
two 8-bit numbers A7...A0 and B7...B0 in 2’s complement representation (with A0
and B0 as the least significant bits) are added using a

**ripple-carry adder,**the sum bits obtained are S7...S0 and the carry bits are C7...C0. An overflow is said to have occurred if
Answer: C

10. Consider
the following context-free grammar over the alphabet ∑ = (a, b, c) with S as
the start symbol:

S→abScT |
abcT

T→bT | b

Which one of
the following represents the language generated by the above grammar?

(A) {(ab)

^{n}(cb)^{n}| n≥1)
(B) {(ab)

^{n}cb^{m1}cb^{m2}... ,cb^{mn}| n, m_{1}, m_{2}, ..., mn ≥ 1)
(C) ((ab)

^{n}(cb^{m})^{n}| m, n ≥ 1 }
(D) {(ab)

^{n}(cb^{n})^{m}| m, n ≥ 1 }
Answer: B

## 0 Comments