1
GATE CE 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are

A
(1, 0, $$\sqrt 2 $$)
B
(1, 0, $$-$$$$\sqrt 2 $$)
C
($$-$$1, 0, $$\sqrt 2 $$)
D
($$-$$1, 0, $$-$$$$\sqrt 2 $$)
2
GATE CE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

A
$${\lambda ^2} - 4\lambda - 5 = 0$$
B
$${\lambda ^2} 4\lambda + 5 = 0$$
C
$${\lambda ^2} + 4\lambda - 5 = 0$$
D
$${\lambda ^2} + 4\lambda + 5 = 0$$
3
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?
A
$$PQ = {\rm I}\,\,\,but\,\,\,QP \ne {\rm I}$$
B
$$QP = {\rm I}\,\,\,but\,\,\,PQ \ne {\rm I}$$
C
$$PQ = {\rm I}\,\,\,and\,\,\,QP = {\rm I}$$
D
$$PQ - QP = {\rm I}$$
4
GATE CE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is
A
$$4$$
B
$$3$$
C
$$2$$
D
$$1$$
GATE CE Subjects
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