Question 1 |

The security system at an IT office is composed of 10 computers of which exactly four are
working. To check whether the system is functional, the officials inspect four of the
computers picked at random (without replacement). The system is deemed functional if at
least three of the four computers inspected are working. Let the probability that the system is deemed functional be denoted by p. Then 100p= _____________.

9.2 | |

11.9 | |

15.6 | |

19.2 |

Question 1 Explanation:

Question 2 |

Each of the nine words in the sentence "The quick brown fox jumps over the lazy og" is
written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is
_____________. (The answer should be rounded to one decimal place)

2.5 | |

2.9 | |

3.8 | |

4.6 |

Question 2 Explanation:

Question 3 |

The maximum number of edges in a bipartite graph on 12 vertices is _____.

24 | |

36 | |

48 | |

60 |

Question 3 Explanation:

Question 4 |

If the matrix A is such that

\begin{bmatrix} 2\\ -4\\ 7 \end{bmatrix}\begin{bmatrix} 1 &9 &5 \end{bmatrix}

Then the determinant of A is equal to ________.

\begin{bmatrix} 2\\ -4\\ 7 \end{bmatrix}\begin{bmatrix} 1 &9 &5 \end{bmatrix}

Then the determinant of A is equal to ________.

0 | |

1 | |

2 | |

3 |

Question 4 Explanation:

Question 5 |

A non-zero polynomial f(x) of degree 3 has roots at x = 1,x = 2 and x = 3. Which one of the following must be TRUE?

f(0)f(4) \lt 0 | |

f(0)f(4) \gt 0 | |

f(0)+f(4) \gt 0 | |

f(0)+f(4) \lt 0 |

Question 5 Explanation:

Question 6 |

The dual of a Boolean function F(x_{1},x_{2},...,x_{n}, +, \cdot , ' ) , written as F^{D}, is the same expression as that of F with + and \cdot swapped. F is said to be self-dual if F=F^{D}. The number of self-dual functions with n Boolean variables is

2^{n} | |

2^{n-1} | |

2^{2^{n}} | |

2^{2^{n-1}} |

Question 6 Explanation:

Question 7 |

Let k = 2^{n} . A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2^{n} bit decoder. This circuit is equivalent to a

k-bit binary up counter | |

k-bit binary down counter. | |

k-bit ring counter. | |

k-bit Johnson counter |

Question 7 Explanation:

Question 8 |

Consider the equation (123)_{5}=(x8)_{y} with x and y as unknown. The number of possible
solutions is _____ .

2 | |

3 | |

4 | |

5 |

Question 8 Explanation:

Question 9 |

A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block
size of 8 words. The word length is 32 bits. The size of the physical address space is 4 GB.
The number of bits for the TAG field is _____

18 | |

19 | |

20 | |

21 |

Question 9 Explanation:

Question 10 |

Consider the function func shown below:

```
int func(int num) {
int count = 0;
while (num) {
count++;
num\gt \gt= 1;
}
return (count);
}
```

The value returned by func(435)is __________.8 | |

9 | |

10 | |

11 |

Question 10 Explanation:

There are 10 questions to complete.