1
GATE EE 1994
+1
-0.3
The number of linearly independent solutions of the system of equations
$$\left[ {\matrix{ 1 & 0 & 2 \cr 1 & { - 1} & 0 \cr 2 & { - 2} & 0 \cr } } \right]\,\,\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = 0$$ is equal to
A
$$1$$
B
$$2$$
C
$$3$$
D
$$0$$
2
GATE EE 1994
+1
-0.3
The integration of $$\int {{\mathop{\rm logx}\nolimits} \,dx}$$ has the value
A
$$\left( {x\log x - 1} \right)$$
B
$${\log x - x}$$
C
$$x\left( {\log x - 1} \right)$$
D
None of the above
3
GATE EE 1994
+1
-0.3
The volume generated by revolving the area bounded by the parabola $${y^2} = 8x$$ and the line $$x=2$$ about $$y$$-axis is
A
$${{128\pi } \over 5}$$
B
$${5 \over {128\pi }}$$
C
$${{127} \over {5\pi }}$$
D
None of the above
4
GATE EE 1994
+1
-0.3
The directional derivative of $$f\left( {x,y} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at point $$P\left( {2,1,3} \right)\,\,$$ in the direction of the vector $$\,\,a = \overrightarrow i - 2\overrightarrow k \,\,$$ is
A
$$4/\sqrt 5$$
B
$$-$$ $$4/\sqrt 5$$
C
$$\sqrt 5 /4$$
D
$$-$$ $$\sqrt 5 /4$$
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