1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following graphs is NOT planar? GATE CSE 2005 Discrete Mathematics - Graph Theory Question 32 English
A
G1
B
G2
C
G3
D
G4
2
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-0.3
Let $$G$$ be the simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of $$G$$ is 8. Then, the size of the maximum independent set of $$G$$ is:
A
12
B
8
C
Less than 8
D
More than 12
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
What are the eigen values of the following $$2x2$$ matrix? $$$\left[ {\matrix{ 2 & { - 1} \cr { - 4} & 5 \cr } } \right]$$$
A
$$-1$$ and $$1$$
B
$$1$$ and $$6$$
C
$$2$$ and $$5$$
D
$$4$$ and $$-1$$
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the set $$H$$ of all $$3$$ $$X$$ $$3$$ matrices of the type $$$\left[ {\matrix{ a & f & e \cr 0 & b & d \cr 0 & 0 & c \cr } } \right]$$$

Where $$a, b, c, d, e$$ and $$f$$ are real numbers and $$abc$$ $$ \ne \,\,0$$. Under the matrix multiplication operation, the set $$H$$ is:

A
$$a$$ group
B
$$a$$ monoid but not $$a$$ group
C
$$a$$ semigroup but not $$a$$ monoid
D
neither $$a$$ group nor $$a$$ semigroup