# 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 1 Explanation:
 Question 2
Let x and Y be finite sets and f:x$\rightarrow$Y be a function. Which one of the following statements is TRUE?
 A For any subsets A and B of x, |f(A$\cup$B)|=|f(A)|+|f(B)| B For any subsets A and B of x, f(A$\cap$B) =f(A)$\cap$f(B) C For any subsets A and B of x, |f(A$\cap$B)| = 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 2 Explanation:
 Question 3
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L$\neq$G 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 3 Explanation:
 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 4 Explanation:
 Question 5
If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1$\cap$V2 is _______.
 A 1 B 2 C 3 D 4
Engineering Mathematics   Linear Algebra
Question 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 8 Explanation:
 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 9 Explanation:
 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
Question 10 Explanation:
There are 10 questions to complete.