1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If the following system has non - trivial solution $$$px+qy+rz=0$$$ $$$qx+ry+pz=0$$$ $$$rx+py+qz=0$$$

Then which one of the following Options is TRUE?

A
$$p-q+r=0$$ or $$p=q=-r$$
B
$$p+q-r=0$$ or $$p=-q=r$$
C
$$p+q+r=0$$ or $$p=q=r$$
D
$$p-q+r=0$$ or $$p=-q=-r$$
2
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
$$35$$
3
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
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {\ln \,2 - 25} \right) - {{47b} \over 2}} \right]$$
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
The value of $$\mathop {\lim }\limits_{x \to \alpha } {\left( {1 + {x^2}} \right)^{{e^{ - x}}}}\,\,$$ is
A
$$0$$
B
$${{1 \over 2}}$$
C
$$1$$
D
$$\infty $$
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