1
GATE EE 2013
+2
-0.6
The equation $$\left[ {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] = \left[ {\matrix{ 0 \cr 0 \cr } } \right]$$ has
A
no solution
B
only one solution
C
non-zero unique solution
D
multiple solutions
2
GATE EE 2013
+2
-0.6
A matrix has eigen values $$-1$$ and $$-2.$$ The corresponding eigenvectors are $$\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]$$ and $$\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$ respectively. The matrix is
A
$$\left[ {\matrix{ 1 & 1 \cr { - 1} & { - 2} \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & 2 \cr { - 2} & { - 4} \cr } } \right]$$
C
$$\left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]$$
D
$$\left[ {\matrix{ 0 & 1 \cr { - 2} & { - 3} \cr } } \right]$$
3
GATE EE 2013
+1
-0.3
A function $$y = 5{x^2} + 10x\,\,$$ is defined over an open interval $$x=(1,2).$$ At least at one point in this interval, $${{dy} \over {dx}}$$ is exactly
A
$$20$$
B
$$25$$
C
$$30$$
D
$$35$$
4
GATE EE 2013
+2
-0.6
The curl of the gradient of the scalar field defined by $$\,V = 2{x^2}y + 3{y^2}z + 4{z^2}x$$ is
A
$$4xy{a_x} + 6yz{a_y} + 8zx{a_z}$$
B
$$4{a_x} + 6{a_y} + 8{a_z}$$
C
$$\left( {4xy + 4{z^2}} \right){a_x} + \left( {2{x^2} + 6yz} \right){a_y} + \left( {3{y^2} + 8zx} \right){a_z}$$
D
$$0$$
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