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1
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+2
-0

For the matrix

$[A]= \begin{bmatrix}1&2&3\\\ 3&2&1\\\ 3&1&2 \end{bmatrix} $

which of the following statements is/are TRUE?

A
The eigenvalues of [A]T are same as the eigenvalues of [A] 
B
The eigenvalues of [A]-1 are the reciprocals of the eigenvalues of [A]
C
The eigenvectors of [A]T are same as the eigenvectors of [A] 
D
The eigenvectors of [A]-1 are same as the eigenvectors of [A]
2
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the matrix $$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?
A
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and only one independent eigenvector exists.
B
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and two independent eigen vectors exist.
C
Eigenvalue $$3$$ has a multiplicity of $$2,$$ and no independent eigen vector exists
D
Eigenvalues are $$3$$ and $$-3,$$ and two independent eigenvectors exist
3
GATE CE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
If $$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8 & 4 \cr } } \right]A{B^T}$$ is equal to
A
$$\left[ {\matrix{ {38} & {28} \cr {32} & {56} \cr } } \right]$$
B
$$\left[ {\matrix{ 3 & {40} \cr {42} & 8 \cr } } \right]$$
C
$$\left[ {\matrix{ {43} & {27} \cr {34} & {50} \cr } } \right]$$
D
$$\left[ {\matrix{ {38} & {32} \cr {28} & {56} \cr } } \right]$$
4
GATE CE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider the following linear system $$$x+2y-3z=a$$$ $$$2x+3y+3z=b$$$ $$$5x+9y-6z=c$$$
This system is consistent if $$a,b$$ and $$c$$ satisfy the equation
A
$$7a - b - c = 0$$
B
$$3a + b - c = 0$$
C
$$3a - b + c = 0$$
D
$$7a - b + c = 0$$
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GATE CE Subjects
Engineering Mechanics
Equilibrium of Force Systems Work Energy Principle and Impulse Momentum Equation
Strength of Materials Or Solid Mechanics
Centroid and Moment of Inertia Torsion Pure Bending Shear Stress In Beams Strain Energy Method Columns and Struts Complex Stress Deflection of Beams Thin Cylinder Simple Stresses Shear Force and Bending Moment Propped Cantilever Beam
Structural Analysis
Energy Principle Truss Stability and Static Indeterminacy Methods of Analysis Indeterminacy Arches and Cable Slope Deflection Method Matrix Method Moment Distribution Method Influence Line Diagram Plastic Analysis
Construction Material and Management
Critical Path Method Construction Materials Program Evolution Review Technique
Reinforced Cement Concrete
Doubly Reinforced Sections Limit State of Collapse Shear Footings Bond Slabs Limit State of Collapse Torsion Limit State of Serviceability Prestressed Concrete Singly Reinforced Sections Workmenship and Fundamentals Flanged Beams Limit State of Collapse Compression
Steel Structures
Eccentric Connections Plate Girder Tension Members Welded Connections Materials and Specifications Riveted Joints and Bolted Joints Beams Compression Members
Geotechnical Engineering
Origin of Soils Definitions and Properties of Soils Classification of Soils and Clay Mineralogy Effective Stress and Permeability Seepage Analysis Compaction of Soil Compressibility and Consolidation Shear Strength of Soil Stress Distribution of Soil Retaining Wall and Earth Pressure Stability of Slopes Shallow Foundation Pile Foundation Soil Stabilization
Fluid Mechanics and Hydraulic Machines
Fluid Pressure and Measurement Fluid Dynamics Boundary Layer Theory Drag and Lift Flow Through Pipes Open Channel Flow Hydraulic Machines Properties of Fluids Fluid Statics
Hydrology
Precipitation and Frequency of Rainfall Data Evaporation and Transpiration Infiltration Hydrograph Flood Estimation and Flood Routing
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Gravity Dams and Spillways Water Requirement of Crops
Geomatics Engineering Or Surveying
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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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Engineering Mathematics
Probability and Statistics Calculus Complex Variable Differential Equations Linear Algebra Numerical Methods Vector Calculus Transform Theory
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