1
GATE PI 2009
+2
-0.6
The value of $${x_3}$$ obtained by solving the following system of linear equations is $${x_1} + 2{x_2} - 2{x_3} = 4$$$$$2{x_1} + {x_2} + {x_3} = - 2$$$ $$- {x_1} + {x_2} - {x_3} = 2$$\$
A
$$-12$$
B
$$-2$$
C
$$0$$
D
$$12$$
2
GATE PI 2009
+1
-0.3
The total derivative of the function $$'xy'$$ is
A
$$x$$ $$dy+y$$ $$dx$$
B
$$x$$ $$dx+y$$ $$dy$$
C
$$dx+dy$$
D
$$dx$$ $$dy$$
3
GATE PI 2009
+1
-0.3
The line integral of the vector function $$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$ along the $$x$$ - axis from $$x=1$$ to $$x=2$$ is
A
$$0$$
B
$$2.33$$
C
$$3$$
D
$$5.33$$
4
GATE PI 2009
+2
-0.6
The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions
(i) $${{dy} \over {dx}} = 1$$ at $$x=0$$
(ii) $${{dy} \over {dx}} = 1$$ at $$x=1$$
A
$$y=1$$
B
$$y=x$$
C
$$y=x+c$$ where $$c$$ is an arbitrary constant.
D
$$\,y = {C_1}x + {C_2}$$ where $${C_1},\,{C_2}$$ are arbitrary constants
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