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
c1,...,cn be scalars, not all zero, such that
where ai
are column vectors in Rn.
Consider the
set of linear equations
Ax=b
where A=[a1,...,an]
and
The set of
equations has
(A) a unique
solution at x=Jn where Jn 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, log2n,
100/n
The CORRECT
arrangement of the above functions in increasing order of asymptotic complexity
is:
(A) log2n,
100/n, 10, √n, n
(B) 100/n,
10, log2n, √n, n
(C) 10, 100/n,
√n, log2n, n
(D) 100/n,
log2n, 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 2i
(B) 2-f
to (2i – 2-f)
(C) 0 to 2i
(D) 0 to (2i
– 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)ncbm1cbm2
... ,cbmn | n, m1, m2, ..., mn ≥ 1)
(C) ((ab)n
(cbm)n | m, n ≥ 1 }
(D) {(ab)n(cbn)m
| m, n ≥ 1 }
Answer: B
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