GATE-CS-2014-(Set-2)

Question 11

Each of the nine words in the sentence ”The quick brown fox jumps over the lazy dog” 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.)

• 3.8 to 3.9

Question 12

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

• 36
• 48
• 12
• 24

Question 13

If the matrix A is such that 

[caption width="800"] [/caption]

 then the determinant of A is equal to

• 0

• 1

• 2

• 3

Question 14

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) < 0
• f(0)f(4) > 0
• f(0) + f(4) < 0
• f(0) + f(4) > 0

Question 15

The dual of a Boolean function f(x1, x2, … , xn, +, ∙ , ′ ), written as F^D, is the same expression as that of F with + and . swapped. F is said to be self-dual if F = F^D. The number of self-dual functions with n Boolean variables is

• 2ⁿ
• 2^n-1
• 2²ⁿ
• 2^2n-1

Question 16

Let k = 2ⁿ. A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2ⁿ 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 17

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

• 1
• 2
• 3
• 4

Question 18

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 _____

• 5

• 15

• 20

• 25

Question 19

Consider the function func shown below:

C

int func(int num)
{
    int count = 0;
    while (num)
    {
        count++;
        num >>= 1;
    }
    return (count);
}

The value returned by func(435)is __________.

• 8
• 9
• 10
• 11

Question 20

Suppose n and p are unsigned int variables in a C program. We wish to set p to ⁿC₃. If n is large, which of the following statements is most likely to set p correctly?

• p = n * (n-1) * (n-2) / 6;
• p = n * (n-1) / 2 * (n-2) / 3;
• p = n * (n-1) / 3 * (n-2) / 2;
• p = n * (n-1) * (n-2) / 6.0;