1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left( {r,s} \right)} \right) \in R$$ if and only if $$p - s = q - r.$$ Which one of the following is true about $$R$$?
A
Both reflexive and symmetric
B
Reflexive but not symmetric
C
Not reflexive but symmetric
D
Neither reflexive nor symmetric
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
In the given matrix $$\left[ {\matrix{ 1 & { - 1} & 2 \cr 0 & 1 & 0 \cr 1 & 2 & 1 \cr } } \right],$$ one of the eigenvalues is $$1.$$ The eigen vectors corresponding to the eigen value $$1$$ are
A
$$\left\{ {\alpha \left( {4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
B
$$\left\{ {\alpha \left( { - 4,2,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
C
$$\left\{ {\alpha \left( {\sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
D
$$\left\{ {\alpha \left( { - \sqrt 2 ,0,1} \right)\left| {\alpha \ne 0,\alpha \in \left. R \right\}} \right.} \right.$$
3
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
A function $$f(x)$$ is linear and has a value of $$29$$ at $$x=-2$$ and $$39$$ at $$x=3.$$ Find its value at $$x=5.$$
A
$$59$$
B
$$45$$
C
$$43$$
D
$$35$$
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If for non-zero $$x,$$ $$af\left( x \right) + bf\left( {{1 \over x}} \right) = {1 \over x} - 25$$
where $$a \ne b$$ then $$\int\limits_1^2 {f\left( x \right)dx} \,$$ is
A
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {\ln \,2 - 25} \right) + {{47b} \over 2}} \right]$$
B
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {2\ln \,2 - 25} \right) - {{47b} \over 2}} \right]$$
C
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {2\ln \,2 - 25} \right) + {{47b} \over 2}} \right]$$
D
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {\ln \,2 - 25} \right) - {{47b} \over 2}} \right]$$
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