Engineering Mathematics
Linear Algebra
Marks 1Marks 2
Differential Equations
Marks 1Marks 2
Probability and Statistics
Marks 1Marks 2
Numerical Methods
Marks 1Marks 2
Vector Calculus
Marks 1Marks 2
Transform Theory
Marks 1Marks 2
Complex Variable
Marks 1Marks 2
1
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
Let $$P$$ be $$2x2$$ real orthogonal matrix and $$\overline x $$ is a real vector $${\left[ {\matrix{ {{x_1}} & {{x_2}} \cr } } \right]^T}$$ with length $$\left| {\left| {\overline x } \right|} \right| = {\left( {{x_1}^2 + {x_2}^2} \right)^{1/2}}.$$ Then which one of the following statement is correct?
A
$$\left| {\left| {P\overline x } \right|} \right| \le \left| {\left| {\overline x } \right|} \right|$$ where at least one vector satisfies $$\left| {\left| {P\overline x } \right|} \right| < \left| {\left| {\overline x } \right|} \right|$$
B
$$\left| {\left| {P\overline x } \right|} \right| = \left| {\left| {\overline x } \right|} \right|$$ for all vectors $${\overline x }$$
C
$$\left| {\left| {P\overline x } \right|} \right| \ge \left| {\left| {\overline x } \right|} \right|$$ where at least one vector satisfies $$\left| {\left| {P\overline x } \right|} \right| > \left| {\left| {\overline x } \right|} \right|$$
D
No relationship can be established between $$\left| {\left| {\overline x } \right|} \right|$$ and $$\left| {\left| {P\overline x } \right|} \right|$$
2
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
$${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m < n.$$ This set of vectors is linearly dependent. $$Q$$ is the matrix with $${q_1},\,{q_2},{q_3},.......{q_m}$$ as the columns. The rank of $$Q$$ is
A
less than $$m$$
B
$$m$$
C
between $$m$$ and $$n$$
D
$$n$$
3
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
If $$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]\,$$ then $${A^9}$$ equals
A
$$511\,\,A + 510\,\,I$$
B
$$309\,\,A + 104\,\,I$$
C
$$154\,\,A + 155\,\,I$$
D
$${e^{9A}}$$
4
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
If $$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]$$ then $$A$$ satisfies the relation
A
$$A - 31 + 2\,{A^{ - 1}} = 0$$
B
$${A^2} + 2A + 2I = 0$$
C
$$\left( {A + I} \right)\left( {A + 2I} \right) = 0$$
D
$${e^A} = 0$$
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement