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1
GATE CE 2024 Set 2
MCQ (More than One Correct Answer)
+2
-0.833

Three vectors $\overrightarrow{p}$, $\overrightarrow{q}$, and $\overrightarrow{r}$ are given as

$ \overrightarrow{p} = \hat{i} + \hat{j} + \hat{k}$

$ \overrightarrow{q} = \hat{i} + 2\hat{j} + 3\hat{k}$

$ \overrightarrow{r} = 2\hat{i} + 3\hat{j} + 4\hat{k}$

Which of the following is/are CORRECT?

A

$ \overrightarrow{p} \times (\overrightarrow{q} \times \overrightarrow{r}) + \overrightarrow{q} \times (\overrightarrow{r} \times \overrightarrow{p}) + \overrightarrow{r} \times (\overrightarrow{p} \times \overrightarrow{q}) = \overrightarrow{0}$

B

$ \overrightarrow{p} \times (\overrightarrow{q} \times \overrightarrow{r}) = (\overrightarrow{p} \cdot \overrightarrow{r}) \overrightarrow{q} - (\overrightarrow{p} \cdot \overrightarrow{q}) \overrightarrow{r}$

C

$ \overrightarrow{p} \times (\overrightarrow{q} \times \overrightarrow{r}) = (\overrightarrow{p} \times \overrightarrow{q}) \times \overrightarrow{r}$

D

$ \overrightarrow{r} \cdot (\overrightarrow{p} \times \overrightarrow{q}) = (\overrightarrow{q} \times \overrightarrow{p}) \cdot \overrightarrow{r}$

2
GATE CE 2024 Set 1
MCQ (Single Correct Answer)
+2
-0.833

A vector field $\vec{p}$ and a scalar field $r$ are given by:

$\vec{p} = (2x^2 - 3xy + z^2) \hat{i} + (2y^2 - 3yz + x^2) \hat{j} + (2z^2 - 3xz + x^2) \hat{k}$

$r = 6x^2 + 4y^2 - z^2 - 9xyz - 2xy + 3xz - yz$

Consider the statements P and Q:

P: Curl of the gradient of the scalar field $r$ is a null vector.

Q: Divergence of curl of the vector field $\vec{p}$ is zero.

Which one of the following options is CORRECT?

A

Both P and Q are FALSE

B

P is TRUE and Q is FALSE

C

P is FALSE and Q is TRUE

D

Both P and Q are TRUE

3
GATE CE 2015 Set 1
Numerical
+2
-0
The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\widehat i + \widehat j - 2\widehat k} \right)\,\,$$ at point $$(2, -1, 4)$$ is _______.
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4
GATE CE 2014 Set 1
Numerical
+2
-0
A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$$ $$sin$$ $$(5t),$$ where $$x, y$$ and $$z$$ show variations of the distance covered by the particle (in cm) with time $$t $$ (in $$s$$). The magnitude of the acceleration of the particle (in cm/s2) at $$t=0$$ is _______.
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GATE CE Subjects
Engineering Mechanics
Work Energy Principle and Impulse Momentum Equation Equilibrium of Force Systems
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
Irrigation
Water Requirement of Crops Gravity Dams and Spillways
Geomatics Engineering Or Surveying
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
Environmental Engineering
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
Transportation Engineering
Highway Devolopment and Planning Highway Geometric Design Traffic Engineering Highway Materials Pavement Design Railway, Runway and Taxiway Design
Engineering Mathematics
Probability and Statistics Differential Equations Transform Theory Calculus Complex Variable Linear Algebra Vector Calculus Numerical Methods
General Aptitude
Numerical Ability Logical Reasoning Verbal Ability
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