1
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
$$A$$ graph $$G$$ $$=$$ $$(V, E)$$ satisfies $$\left| E \right| \le \,3\left| V \right| - 6.$$ The min-degree of $$G$$ is defined as $$\mathop {\min }\limits_{v \in V} \left\{ {{{\mathop{\rm d}\nolimits} ^ \circ }egree\left( v \right)} \right\}$$. Therefore, min-degree of $$G$$ cannot be
A
$$3$$
B
$$4$$
C
$$5$$
D
$$6$$
2
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
How many perfect matchings are there in a complete graph of 6 vertices?
A
$$15$$
B
$$24$$
C
$$30$$
D
$$60$$
3
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix containing coefficients has a non-trival solution when $$A$$ is.
A
non-singular
B
singular
C
symmetric
D
Hermitian
4
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$
A
$$0$$
B
$$\infty $$
C
$$1$$
D
$$-1$$
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