1
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $${M^4} = {\rm I}$$ (where $${\rm I}$$ denotes the identity matrix) and $$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$ and $${M^3} \ne {\rm I}$$. Then, for any natural number $$k, $$ $${M^{ - 1}}$$ equals:
A
$${M^{4k + 1}}$$
B
$${M^{4k + 2}}$$
C
$${M^{4k + 3}}$$
D
$${M^{4k}}$$
2
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The value of $$'x'$$ for which all the eigenvalues of the matrix given below are real is $$\left[ {\matrix{ {10} & {5 + j} & 4 \cr x & {20} & 2 \cr 4 & 2 & { - 10} \cr } } \right]$$
A
$$5+j$$
B
$$5-j$$
C
$$1-5j$$
D
$$1+5j$$
3
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
For $$A = \left[ {\matrix{ 1 & {\tan x} \cr { - \tan x} & 1 \cr } } \right],$$ the determinant of $${A^T}\,{A^{ - 1}}$$ is
A
$${\sec ^2}x$$
B
$$\cos 4x$$
C
$$1$$
D
$$0$$
4
GATE ECE 2015 Set 1
Numerical
+1
-0
Consider system of linear equations : $$$x-2y+3z=-1$$$ $$$x-3y+4z=1$$$ and $$$-2x+4y-6z=k,$$$

The value of $$'k'$$ for which the system has infinitely many solutions is _______.

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