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




There are 5 questions to complete.

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