MCQs of Vector Calculus (Mathematics - II - 3110015)

Showing 71 to 79 out of 79 Questions

71.

The path traversal in calculating the Green’s theorem is

72.

Let

C

be the boundary of the triangle whose vertices are

(0, 0)

(1, 0)

and

(1, 1)

. Then

\oint_{C} \{x^{2} y dx + x^{2} dy\} =

____________.

73.

Let

C

be the boundary of the region bounded by

y = 0

y = 2 x

and

x + y = 3

. Then

\oint_{C} \{(x^{2} + 2 y) dx + (4 x + y^{2}) dy\} =

74.

Let

‘ A ’

be the area of the plane region

R

bounded by closed curve

C

. Then by Green’s theorem

2 A =

_________.

75.

By using Green’s theorem, the area of an ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{289} = 1

76.

The form

\oint_{c} (M dy - N dx) = \iint_{R} \{\frac{\partial M}{\partial x} + \frac{\partial N}{\partial y}\} dxdy

represents ______________ form of Green’s theorem.

77.

What is the outward flux of a vector field

F = (x^{2} + 2 xy) \hat{i} + (y^{2} - 2 xy) \hat{j}

across the curve bounded by

y = x

and

y = x^{2}

78.

The form

\oint_{c} (M dx + N dy) = \iint_{R} \{\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}\} dxdy

represents ______________ form of Green’s theorem.

79.

The circulation of

\oint_{C} \{(x + siny) dx + (x + cosy) dy\}

around and over the region bounded by the lines

y = 0, x = 1, y = π

and

x = 0

Showing 71 to 79 out of 79 Questions