1
GATE CSE 2012
+1
-0.3
Consider the function $$f\left( x \right) = \sin \left( x \right)$$ in the interval $$x \in \left[ {\pi /4,\,\,7\pi /4} \right].$$ The number and location(s) of the local minima of this function are
A
One, at $$\pi /2$$
B
One, at $$3\pi /2$$
C
Two, at $$\pi /2$$ and $$3\pi /2$$
D
Two, at $$\pi /4$$ and $$3\pi /2$$
2
GATE CSE 2012
+2
-0.6
Which of the following graphs is isomorphic to
A
B
C
D
3
GATE CSE 2012
+2
-0.6
Let $$G$$ be a complete undirected graph on $$6$$ vertices. If vertices of $$G$$ $$\,\,\,\,$$ are labeled, then the number of distinct cycles of length $$4$$ in $$G$$ is equal to
A
$$15$$
B
$$30$$
C
$$90$$
D
$$360$$
4
GATE CSE 2012
+1
-0.3
Let $$A$$ be the $$2 \times 2$$ matrix with elements $${a_{11}} = {a_{12}} = {a_{21}} = + 1$$ and $${a_{22}} = - 1$$. Then the eigen values of the matrix $${A^{19}}$$ are
A
$$1024$$ and $$-1024$$
B
$$1024\sqrt 2 \,i$$ and $$- 1024\sqrt 2$$
C
$$4\sqrt 2$$ and $$-4\sqrt 2$$
D
$$512\sqrt 2$$ and $$-512\sqrt 2$$
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