1
GATE CSE 2011
+2
-0.6
Given $$i = \sqrt { - 1} ,$$ what will be the evaluation of the definite integral $$\int\limits_0^{\pi /2} {{{\cos x +i \sin x} \over {\cos x - i\,\sin x}}dx?}$$
A
$$0$$
B
$$2$$
C
$$-1$$
D
$$i$$
2
GATE CSE 2011
+1
-0.3
$$K4$$ and $$Q3$$ are graphs with the following structures.

Which one of the following statements is TRUE in relation to these graphs?

A
$$K4$$ is planar while $$Q3$$ is not
B
Both $$K4$$ and $$Q3$$ are planar
C
$$Q3$$ is planar while $$K3$$ is not
D
Neither $$K4$$ nor $$Q3$$ is planar
3
GATE CSE 2011
+2
-0.6
Four matrices $${M_1},\,\,\,{M_2},\,\,\,{M_3}$$ and $${M_4}$$ of dimensions $$p\,\,x\,\,q,\,\,\,\,\,q\,\,x\,\,e,\,\,\,\,\,r\,\,x\,\,s$$ and $$\,\,\,\,s\,\,x\,\,t$$ respectively can be multiplied in sevaral ways with different number of total scalar multiplications. For example when multiplied as $$\left( {\left( {{M_1}\,\,X\,\,{M_2}} \right)\,\,X\,\,\left( {{M_3}\,\,X\,\,{M_4}} \right)} \right)$$, the total number of scalar multiplications is $$\,\,\,\,$$$$pqr + rst + prt$$. When multiplied as $$\left( {\left( {\left( {{M_1}\,\,X\,\,{M_2}} \right)\,\,X\,\,{M_3}} \right)X\,\,{M_4}} \right)$$, the total number of scalar multiplications is $$pqr + prs + pst$$. If $$p = 10,\,\,q = 100,\,\,r = 20,\,\,s = 5,\,\,$$ and $$t = 80$$, then the minimum number of scalar multiplications needed is
A
$$248000$$
B
$$44000$$
C
$$19000$$
D
$$25000$$
4
GATE CSE 2011
+2
-0.6
Consider the matrix as given below. $$\left[ {\matrix{ 1 & 2 & 3 \cr 0 & 4 & 7 \cr 0 & 0 & 3 \cr } } \right]$$\$

Which of the following options provides the Correct values of the Eigen values of the matrix?

A
$$1, 4, 3$$
B
$$3, 7, 3$$
C
$$7, 3, 2$$
D
$$1, 2, 3$$
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