GATE CSE 2014 SET-3

Question 1
Consider the following statements:
P: Good mobile phones are not cheap
Q: Cheap mobile phones are not good

L: P implies Q
M: Q implies P
N: P is equivalent to Q
Which one of the following about L, M, and N is CORRECT?
A
Only L is TRUE.
B
Only M is TRUE.
C
Only N is TRUE.
D
L, M and N are TRUE.
Discrete Mathematics   Propositional Logic
Question 2
Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?
A
For any subsets A and B of x, |f(A\cupB)|=|f(A)|+|f(B)|
B
For any subsets A and B of x, f(A\capB) =f(A)\capf(B)
C
For any subsets A and B of x, |f(A\capB)| = min{|f (A)| ,|f(B)|}
D
For any subsets S and T of Y, f^{-1}(S\cap T)=f^{-1}(S)\cap f^{-1}(T)
Discrete Mathematics   Set Theory
Question 3
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L\neqG and that the size of L is at least 4. The size of L is _______.
A
4
B
5
C
6
D
7
Discrete Mathematics   Group Theory
Question 4
Which one of the following statements is TRUE about every n x n matrix with only real eigenvalues?
A
If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.
B
If the trace of the matrix is positive, all its eigenvalues are positive.
C
If the determinant of the matrix is positive, all its eigenvalues are positive.
D
If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
Engineering Mathematics   Linear Algebra
Question 5
If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1\capV2 is _______.
A
1
B
2
C
3
D
4
Engineering Mathematics   Linear Algebra
Question 6
If \int_{0}^{2\pi}|x sinx| dx=k \pi, then the value of k is equal to _______.
A
2
B
4
C
6
D
8
Engineering Mathematics   Calculus
Question 7
Consider the following minterm expression for F.
F(P,Q,R,S) = \Sigma 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
A
Q\bar{S}+\bar{Q}S
B
\bar{Q}\bar{S}+QS
C
\bar{Q}\bar{R}\bar{S}+\bar{Q}R\bar{S}+Q\bar{R}S+QRS
D
\bar{P}\bar{Q}\bar{S}+\bar{P}QS+PQS+P\bar{Q}\bar{S}
Digital Logic   Boolean Algebra
Question 8
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. 
 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?
A
Full adder
B
Priority encoder
C
Multiplexor
D
Flip-flop
Digital Logic   Combinational Circuit
Question 9
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?
A
P1
B
P2
C
P3
D
P4
Computer Organization   Pipeline Processor
Question 10
Let A be a square matrix size n x n. Consider the following pseudocode. What is the expected output? 
 C = 100;
for i = 1 to n do
   for j = 1 to n do
   {
      Temp = A[ i ] [ j ] + C ;
      A [ i ] [ j ] = A [ j ] [ i ] ;
      A [ j ] [ i ] = Temp ? C ;
   }
for i = 1 to n do
    for j = 1 to n do
         output (A[ i ] [ j ]);
A
The matrix A itself
B
Transpose of the matrix A
C
Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of A
D
None of these
Engineering Mathematics   Linear Algebra
There are 10 questions to complete.

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