MCQOPTIONS
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MCQOPTIONS
This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Vector Calculus knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find a unit vector normal to the surface of the ellipsoid at (2,2,1) if the ellipsoid is defined as f(x,y,z) = x2 + y2 + z2 10. |
| A. | ( frac{2}{3} a_x + frac{2}{3} a_y + frac{1}{3} a_z ) |
| B. | ( frac{1}{3} a_x + frac{1}{3} a_y + frac{1}{3} a_z ) |
| C. | ( frac{2}{3} a_x + frac{2}{3} a_y + frac{2}{3} a_z ) |
| D. | ( frac{2}{3} a_x + frac{1}{3} a_y + frac{1}{3} a_z ) |
| Answer» B. ( frac{1}{3} a_x + frac{1}{3} a_y + frac{1}{3} a_z ) | |
| 2. |
State whether the given equation is a conservative vector.G = (x3y) ax + xy3 ay |
| A. | True |
| B. | False |
| Answer» C. | |
| 3. |
Let F = (xy2) ax + yx2 ay, F is a not a conservative vector. |
| A. | True |
| B. | False |
| Answer» C. | |
| 4. |
Electric field E can be written as _________ |
| A. | -Gradient of V |
| B. | -Laplacian of V |
| C. | Gradient of V |
| D. | Laplacian of V |
| Answer» B. -Laplacian of V | |
| 5. |
If W = xy + yz + z, find directional derivative of W at (1,-2,0) in the direction towards the point (3,6,9). |
| A. | -0.6 |
| B. | -0.7 |
| C. | -0.8 |
| D. | -0.9 |
| Answer» D. -0.9 | |
| 6. |
If W = x2 y2 + xz, the directional derivative ( frac{dW}{dl} ) in the direction 3 ax + 4 ay + 6 az at (1,2,0). |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» C. 7 | |
| 7. |
Find gradient of B if B = r if X is in spherical coordinates. |
| A. | ( , a_r ,a_ + frac{ }{sin( )} a_ ) |
| B. | (r , a_r ,a_ + r frac{ }{sin( )} a_ ) |
| C. | ( , a_r r ,a_ + frac{ }{sin( )} a_ ) |
| D. | ( r , a_r ,a_ + r frac{ }{sin( )} a_ ) |
| Answer» B. (r , a_r ,a_ + r frac{ }{sin( )} a_ ) | |
| 8. |
Find gradient of B if B = ln(r) + r2 if B is in spherical coordinates. |
| A. | ( frac{ }{r}+ 2r ,a_r r a_ + frac{lnr}{rsin( )} a_ ) |
| B. | ( frac{ }{r}+ 2r ,a_r r a_ + frac{lnr}{rsin( )} a_ ) |
| C. | ( frac{ }{r}+ 2r ,a_r r^2 a_ + frac{lnr}{rsin( )} a_ ) |
| D. | ( frac{ }{r}+ 2r ,a_r r^2 a_ + frac{lnr}{rsin( )} a_ ) |
| Answer» B. ( frac{ }{r}+ 2r ,a_r r a_ + frac{lnr}{rsin( )} a_ ) | |
| 9. |
Find the gradient of A if A = 2 + z3 + cos( ) + z and A is in cylindrical coordinates. |
| A. | (2 z^3 , a_ frac{1}{ } sin( ) , a + 3 ^2 z^2 , a_z ) |
| B. | (2 z^3 , a_ frac{1}{ } sin( ) , a + 3 ^2 z^2+1 , a_z ) |
| C. | (2 z^3 , a_ frac{1}{ } sin( ) , a + 3 ^2 z^2+1 , a_z ) |
| D. | (2 z^3 , a_ frac{1}{ } sin( ) , a + 3 ^2 z^2 , a_z ) |
| Answer» C. (2 z^3 , a_ frac{1}{ } sin( ) , a + 3 ^2 z^2+1 , a_z ) | |
| 10. |
Find the gradient of the function W if W = zcos( ) if W is in cylindrical coordinates. |
| A. | zcos( )a<sub> </sub> z sin( ) a<sub> </sub> + cos( ) a<sub>z</sub> |
| B. | zcos( )a<sub> </sub> sin( ) a<sub> </sub> + cos( ) a<sub>z</sub> |
| C. | zcos( )a<sub> </sub> + z sin( ) a<sub> </sub> + cos( ) a<sub>z</sub> |
| D. | zcos( )a<sub> </sub> + z sin( ) a<sub> </sub> + cos( ) a<sub>z</sub> |
| Answer» B. zcos( )a<sub> </sub> sin( ) a<sub> </sub> + cos( ) a<sub>z</sub> | |
| 11. |
Find the gradient of V = x2 sin(y)cos(z). |
| A. | 2x siny cos z a<sub>x</sub> + x<sup>2</sup> cos(y)cos(z) ay x<sup>2</sup> sin(y)sin(z) az |
| B. | 2x siny cos z a<sub>x</sub> + x<sup>2</sup> cos(y)cos(z) ay + x<sup>2</sup> sin(y)sin(z) az |
| C. | 2x sinz cos y a<sub>x</sub> + x<sup>2</sup> cos(y)cos(z) ay x<sup>2</sup> sin(y)sin(z) az |
| D. | x siny cos z a<sub>x</sub> + x<sup>2</sup> cos(y)cos(z) ay x<sup>2</sup> sin(y)sin(z) az |
| Answer» B. 2x siny cos z a<sub>x</sub> + x<sup>2</sup> cos(y)cos(z) ay + x<sup>2</sup> sin(y)sin(z) az | |
| 12. |
Find the gradient of a function V if V= xyz. |
| A. | yz a<sub>x</sub> + xz a<sub>y</sub> + xy a<sub>z</sub> |
| B. | yz a<sub>x</sub> + xy a<sub>y</sub> + xz a<sub>z</sub> |
| C. | yx a<sub>x</sub> + yz a<sub>y</sub> + zx a<sub>z</sub> |
| D. | xyz a<sub>x</sub> + xy a<sub>y</sub> + yz a<sub>z</sub> |
| Answer» B. yz a<sub>x</sub> + xy a<sub>y</sub> + xz a<sub>z</sub> | |
| 13. |
The gradient is taken on a _________ |
| A. | tensor |
| B. | vector |
| C. | scalar |
| D. | anything |
| Answer» D. anything | |
| 14. |
The gradient of a scalar field V is a vector that represents both magnitude and the direction of the maximum space rate of increase of V. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 15. |
Del operator is also known as _________ |
| A. | Divergence operator |
| B. | Gradient operator |
| C. | Curl operator |
| D. | Laplacian operator |
| Answer» C. Curl operator | |