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.