MCQs of Vector Calculus (Mathematics - II - 3110015)

Showing 31 to 40 out of 79 Questions

31.

\nabla f = (y^{2} + 2 y + z) \hat{i} + (2 xy + 2 x) \hat{j} + x \hat{k}

and

ϕ (1, 1, 0) = 5

, then

ϕ

32.

The differential form

M dx + N dy + P dz

is exact on an open simply connected domain if and only if

(a)	$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}, \frac{\partial M}{\partial z} = \frac{\partial P}{\partial y}, \frac{\partial N}{\partial z} = \frac{\partial P}{\partial x}$
(b)	$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}, \frac{\partial P}{\partial x} = \frac{\partial M}{\partial z}, \frac{\partial N}{\partial z} = \frac{\partial P}{\partial y}$
(c)	$\frac{\partial N}{\partial y} = \frac{\partial M}{\partial x}, \frac{\partial M}{\partial z} = \frac{\partial P}{\partial y}, \frac{\partial N}{\partial z} = \frac{\partial P}{\partial x}$
(d)	$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}, \frac{\partial P}{\partial z} = \frac{\partial M}{\partial y}, \frac{\partial N}{\partial z} = \frac{\partial P}{\partial x}$

33.

The parametric representation of a line passing through the points

(x_{1}, y_{1})

(x_{2}, y_{2})

34.

The parametric equations of a circle having centre

(h, k)

and radius

r

, are

35.

x = {at}^{2}

and

y = 2 at

are parametric equations of

36.

Which of the following is a parametric representation of a circle having center

(2, - 3)

and radius

9

37.

A parametric representation of an ellipse

\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1

having center

(h, k)

38.

Which of the following is a parametric representation of an ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{4} = 1

39.

The parametric representation of a circle in

XY

-plane of

3

unit radius and center at

(0, 0, 0)

40.

Let

\bar{r} = (x (t), y (t), z (t))

be the parameterization of the curve

C

. Then the arc length of

C

from

a

b

(a)	$\int_{a}^{b} \sqrt{{(\frac{d x}{d t})}^{2} + {(\frac{d y}{d t})}^{2} + {(\frac{d z}{d t})}^{2}} dt$
(b)	$\int_{a}^{b} \sqrt{(\frac{dx}{dt}) + {(\frac{dy}{dt})}^{2} + {(\frac{dz}{dt})}^{2}} dt$
(c)	$\int_{a}^{b} \sqrt{(\frac{d x}{d t}) + (\frac{d y}{d t}) + (\frac{d z}{d t})} dt$
(d)	$\int_{a}^{b} {(\frac{d x}{d t})}^{2} + {(\frac{d y}{d t})}^{2} + {(\frac{d z}{d t})}^{2} dt$

Showing 31 to 40 out of 79 Questions