GATE-CS-2017 (Set 2)

Question 51

P and Q are considering to apply for job. The probability that p applies for job is 1/4. The probability that P applies for job given that Q applies for the job 1/2 and The probability that Q applies for job given that P applies for the job 1/3.The probability that P does not apply for job given that Q does not apply for the job .

• 4/5
• 5/6
• 7/8
• 11/12

Question 52

If the ordinary generating function of a sequence is: then a₃-a₀ is equal to:

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Question 53

Consider the following program

#include<stdio.h>
#include<string.h>

int main()
{
    char * c = "GATECSIT2017";
    char *p = c;
    printf("%d", (int)strlen(c+2[p]-6[p]-1));
    return 0;
}

The Output of the following program is____

Note: This question appeared as Numerical Answer Type.

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Question 54

Consider a machine with byte addressable memory of 2³² bytes divided into blocks of size 32 bytes. Assume a direct mapped cache having 512 cache lines is used with this machine. The size of tag field in bits is _____

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Question 55

Consider a binary code that consists only four valid codewords as given below.
00000, 01011, 10101, 11110
Let minimum Hamming distance of code be p and maximum number of erroneous bits that can be corrected by the code be q. The value of p and q are:

• p = 3 and q = 1
• p = 3 and q = 2
• p = 4 and q = 1
• p = 4 and q = 2

Question 56

• θ(log log n)
• θ(log n)
• θ(sqrt(n))
• θ(n)

Question 57

The next state table of a 2 bit saturating up-counter is given below.

[caption width="800"] [/caption]

The counter is built as synchronous sequential circuit using T flip-flops. The value for T

₁

and T

₀

are

• T

  ₁

  = Q

  ₀

  Q

  ₁

  T

  ₀

  = Q\'

  ₀

  Q\'

  ₁

• T

  ₁

  = Q\'

  ₁

  Q

  ₀

  T

  ₀

  = Q\'

  ₁

  + Q\'

  ₀

• T

  ₁

  = Q

  ₁

  + Q

  ₀

  T

  ₀

  = Q\'

  ₁

  + Q\'

  ₀

• T

  ₁

  = Q\'

  ₁

  Q

  ₀

  T

  ₀

  = Q

  ₁

  + Q

  ₀

Question 58

A message is made up entirely of characters from the set X = {P,Q,R,S,T} . The table of probabilities of each character is shown below : A message of 100 characters over X is encoded using Huffman coding. Then the excepted length of the encoded message in bits is _____

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• 226
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Question 59

• Nβ(1-β)
• Nβ
• N((1-β))
• Not expressible in terms of N and β

Question 60

In a B+ tree, if the search-key value is 8 bytes long, the block size is 512 bytes and the block pointer is 2 bytes, then the maximum order of the B+ tree is ____.

Note: This question appeared as Numerical Answer Type.

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