Question 1 |

Consider the following expressions:

(i) false

(ii) Q

(iii) true

(iv) P\vee Q

(v) \neg Q \vee P

The number of expressions given above that are logically implied by P \wedge (P \Rightarrow Q) is ________.

(i) false

(ii) Q

(iii) true

(iv) P\vee Q

(v) \neg Q \vee P

The number of expressions given above that are logically implied by P \wedge (P \Rightarrow Q) is ________.

2 | |

3 | |

4 | |

5 |

Question 1 Explanation:

Question 2 |

Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x)+ f(-x)) is 10, then the degree of (g(x)-g(-x)) is ________.

10 | |

9 | |

11 | |

8 |

Question 2 Explanation:

Question 3 |

The minimum number of colours that is sufficient to vertex-colour any planar graph is _________.

2 | |

3 | |

4 | |

5 |

Question 3 Explanation:

Question 4 |

Consider the systems,each consisting of m linear equations in n variables.

I. If m \lt n, then all such systems have a solution

II. If m \gt n, then none of these systems has a solution

III. If m = n, then there exists a system which has a solution

Which one of the following is CORRECT?

I. If m \lt n, then all such systems have a solution

II. If m \gt n, then none of these systems has a solution

III. If m = n, then there exists a system which has a solution

Which one of the following is CORRECT?

I, II and III are true | |

Only II and III are true | |

Only III is true | |

None of them is true |

Question 4 Explanation:

Question 5 |

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.

0.25 | |

0.55 | |

0.65 | |

0.75 |

Question 5 Explanation:

Question 6 |

Suppose that the eigen values of matrix A are 1, 2, 4. The determinant of (A^{-1})^{T} is _________.

0 | |

0.125 | |

0.25 | |

0.75 |

Question 6 Explanation:

Question 7 |

Consider an eight-bit ripple-carry Combinational Circuit for computing the sum of A and B, where A and B are integers represented in 2's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ________.

0 | |

1 | |

-1 | |

2 |

Question 7 Explanation:

Question 8 |

Let, x_{1} \oplus x_{2} \oplus
x_{3} \oplus x_{4}=0 where x_{1}, x_{2} ,
x_{3} , x_{4} are Boolean variables, and \oplus is the XOR operator.
Which one of the following must always be TRUE?

x_{1} x_{2} x_{3} x_{4}=0 | |

x_{1} x_{3}+ x_{2}=0 | |

\bar{x}_{1}\oplus \bar{x}_{3}=\bar{x}_{2}\oplus \bar{x}_{4} | |

x_{1} +x_{2}+ x_{3}+ x_{4}=0 |

Question 8 Explanation:

Question 9 |

Let X be the number of distinct 16-bit integers in 2's complement representation. Let Y be the number of distinct 16 bit integers in sign magnitude representation. Then X-Y is ________.

0 | |

1 | |

2 | |

16 |

Question 9 Explanation:

Question 10 |

A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is _______ .

14 | |

16 | |

18 | |

20 |

Question 10 Explanation:

There are 10 questions to complete.