MCQs of Vector Calculus (Mathematics - II - 3110015)

Showing 11 to 20 out of 79 Questions

11.

r = x \hat{i} + y \hat{j} + z \hat{k}

, then

\nabla \cdot r =

12.

Let

r = x \hat{i} + y \hat{j} + z \hat{k}

and

r = |r|

. Then div(grad

r^{3}

)

=

13.

Let

r = x \hat{i} + y \hat{j} + z \hat{k}

and

r = |r|

. Then

\nabla \cdot (r^{n} \bar{r}) =

14.

The vector field

F

is solenoidal if

15.

If vector field

\bar{A} = (x + 3 y) \hat{i} + (y - 2 z) \hat{j} + (x + mz) \hat{k}

is solenoidal, then the value of

m

16.

For what value of

λ

the vector field

V = (2 x^{2} y^{2} + z^{2}) \hat{i} + (3 {xy}^{3} - x^{2} z) \hat{j} + ({λxy}^{2} z + xy) \hat{k}

is solenoidal?

17.

The vector

U = \frac{x \hat{i} + y \hat{j}}{x^{2} + y^{2}}

is solenoidal at

18.

Divergence and curl of a vector field are respectively

19.

The curl of a vector function

F = x^{2} \hat{i} + 2 z \hat{j} - y \hat{k}

20.

A = {ze}^{2 xy} \hat{i} + 2 xycos (y) \hat{j} + (x + 2 y) \hat{k}

, then the value of

\nabla \times A

at the point

(2, 0, 3)

Showing 11 to 20 out of 79 Questions