Question 1 |
Consider the following statements:
P: Good mobile phones are not cheap
Q: Cheap mobile phones are not good
L: P implies Q
M: Q implies P
N: P is equivalent to Q
Which one of the following about L, M, and N is CORRECT?
P: Good mobile phones are not cheap
Q: Cheap mobile phones are not good
L: P implies Q
M: Q implies P
N: P is equivalent to Q
Which one of the following about L, M, and N is CORRECT?
Only L is TRUE. | |
Only M is TRUE. | |
Only N is TRUE. | |
L, M and N are TRUE. |
Question 1 Explanation:
Question 2 |
Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?
For any subsets A and B of x, |f(A\cupB)|=|f(A)|+|f(B)| | |
For any subsets A and B of x, f(A\capB) =f(A)\capf(B) | |
For any subsets A and B of x, |f(A\capB)| = min{|f (A)| ,|f(B)|} | |
For any subsets S and T of Y, f^{-1}(S\cap T)=f^{-1}(S)\cap f^{-1}(T) |
Question 2 Explanation:
Question 3 |
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L\neqG and that the size of L is at least 4. The size of L is _______.
4 | |
5 | |
6 | |
7 |
Question 3 Explanation:
Question 4 |
Which one of the following statements is TRUE about every n x n matrix with only real
eigenvalues?
If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. | |
If the trace of the matrix is positive, all its eigenvalues are positive. | |
If the determinant of the matrix is positive, all its eigenvalues are positive. | |
If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive. |
Question 4 Explanation:
Question 5 |
If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1\capV2 is _______.
1 | |
2 | |
3 | |
4 |
Question 5 Explanation:
Question 6 |
If \int_{0}^{2\pi}|x sinx| dx=k \pi, then the value of k is equal to _______.
2 | |
4 | |
6 | |
8 |
Question 6 Explanation:
Question 7 |
Consider the following minterm expression for F.
F(P,Q,R,S) = \Sigma 0, 2, 5, 7, 8, 10, 13, 15
The minterms 2, 7, 8 and 13 are 'do not care terms. The minimal sum of-products form for F is
F(P,Q,R,S) = \Sigma 0, 2, 5, 7, 8, 10, 13, 15
The minterms 2, 7, 8 and 13 are 'do not care terms. The minimal sum of-products form for F is
Q\bar{S}+\bar{Q}S | |
\bar{Q}\bar{S}+QS | |
\bar{Q}\bar{R}\bar{S}+\bar{Q}R\bar{S}+Q\bar{R}S+QRS | |
\bar{P}\bar{Q}\bar{S}+\bar{P}QS+PQS+P\bar{Q}\bar{S} |
Question 7 Explanation:
Question 8 |
Consider the following combinational function block involving four Boolean variables x, y, a, b where x, a, b are inputs and y is the output.
f (x, y, a, b)
{
if (x is 1) y = a;
else y = b;
}
Which one of the following digital logic blocks is the most suitable for implementing this function?Full adder | |
Priority encoder | |
Multiplexor | |
Flip-flop |
Question 8 Explanation:
Question 9 |
Consider the following processors (ns stands for nanoseconds).
Assume that the pipeline registers have zero latency.
P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns.
P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns.
P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns.
P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns.
Which processor has the highest peak clock frequency?
P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns.
P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns.
P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns.
P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns.
Which processor has the highest peak clock frequency?
P1 | |
P2 | |
P3 | |
P4 |
Question 9 Explanation:
Question 10 |
Let A be a square matrix size n x n. Consider the following pseudocode. What is the
expected output?
C = 100;
for i = 1 to n do
for j = 1 to n do
{
Temp = A[ i ] [ j ] + C ;
A [ i ] [ j ] = A [ j ] [ i ] ;
A [ j ] [ i ] = Temp ? C ;
}
for i = 1 to n do
for j = 1 to n do
output (A[ i ] [ j ]);
The matrix A itself | |
Transpose of the matrix A | |
Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of A | |
None of these |
Question 10 Explanation:
There are 10 questions to complete.