ExamSIDE
Questions (Powered by ExamGOAL)
Engineering Mathematics
Probability and Statistics
Marks 1Marks 2
Differential Equations
Marks 1Marks 2
Transform Theory
Marks 1Marks 2
Calculus
Marks 1Marks 2
Complex Variable
Marks 1Marks 2
Linear Algebra
Marks 1Marks 2
Vector Calculus
Marks 1Marks 2
Numerical Methods
Marks 1Marks 2
Next
1
GATE CE 2024 Set 2
MCQ (More than One Correct Answer)
+2
-0

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 _______.
Your input ____
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 _______.
Your input ____
Next
Questions Asked from Marks 2
GATE CE 2024 Set 2 (1) GATE CE 2024 Set 1 (1) GATE CE 2015 Set 1 (1) GATE CE 2014 Set 1 (1) GATE CE 2009 (1) GATE CE 2007 (1) GATE CE 2006 (1) GATE CE 2005 (2) GATE CE 2002 (1)
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude