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1
GATE CE 2022 Set 2
MCQ (More than One Correct Answer)
+1
-0

P and Q are two square matrices of the same order. Which of the following statements is/are correct?

A
If P and Q are invertible, then$${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.
B
If P and Q are invertible, then $${[PQ]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.
C
If P and Q are invertible, then $${[QP]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.
D
If P and Q are not invertible, then $${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.
2
GATE CE 2022 Set 1
MCQ (More than One Correct Answer)
+1
-0

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M3 $$-$$ 4M2 $$-$$ 2M

Which of the following is/are the eigenvalue(s) of matrix Q?

A
15
B
25
C
$$-$$20
D
$$-$$30
3
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, $$-$$$$\sqrt 2 $$)
4
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
$${\lambda ^2} + 4\lambda + 5 = 0$$
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Levelling Traversing Theodolites and Plane Table Surveying Measurement of Area, Volume and Theory of Errors and Survey Adjustment Field Astronomy and Photogrammetric Surveying Basics of GIS, GPS and Remote Sensing Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey
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Irrigation
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Sources and Coveyances Water Quality Control of Water Treatment of Water Water Demand Waste Water Characteristics Treatment of Sewage Disposal of Sewage Effluent Solid Waste Management Air Pollution Noise Pollution
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