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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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Construction Material and Management
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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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Materials and Specifications Tension Members Riveted Joints and Bolted Joints Welded Connections Eccentric Connections Compression Members Beams Plate Girder
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Water Requirement of Crops Gravity Dams and Spillways
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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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