GATE-CS-2014-(Set-3)

Question 11

Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?

• A

• B

• C

• D

Question 12

Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L != G and that the size of L is at least 4. The size of L is __________.

• 3
• 5
• 7
• 9

Question 13

Which one of the following statements is TRUE about every 

• If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
  

• 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 trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.
  

Question 14

If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1 ∩ V2 is ______.

• 1
• 2
• 3
• 4

Question 15

If [Tex]\\int_{0}^{2\\Pi} |x sinx|dx = k \\Pi,[/Tex] then the value of k is equal to __________.

• 2
• 3
• 4
• 5

Question 16

Consider the following minterm expression for F : F(P,Q,R,S) = ∑ (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 :

• QS\' + Q\'S
• Q\'S\' + QS
• Q\'R\'S\' + Q\'RS\' + QR\'S + QRS
• P\'Q\'S\' + P\'QS + PQS + PQ\'S\'

Question 17

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.

C

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
• Multiplexer
• Flip-flop

Question 18

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
• P2
• P3
• P4

Question 19

Consider the following rooted tree with the vertex P labeled as root The order in which the nodes are visited during in-order traversal is

• SQPTRWUV
• SQPTURWV
• SQPTWUVR
• SQPTRUWV

Question 20

Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _________.

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