Free Printable VCFT: Cat 2

1.

Gauss's theorem of vector calculus connects

a)

volume integral with surface integral

b)

surface integral of divergence of a vector with volm integral of a scalar

c)

surface integral of divergence of a vector with volm integral of the same vector

d)

surface integral of divergence of a vector with volm integral of a different vector

2.

Surface integral of curl of a vector is connected with its line integral through

a)

Green's theorem

b)

Stoke's theorem

c)

Guass's theorem

d)

Laplace's theorem

3.

To move from Green's Theorem to Stoke's Theorem we need to change

a)

from 2 dimensions to 3 dimension

b)

a line integral to a surface integral

c)

the double integral of curlF⋅kcurl⁡F⋅k over a region DD in the plane to a surface integral of curlF⋅ncurl⁡F⋅n over a surface floating in space

d)

the component of the curl to the tangential vector

4.

The surface does not have to be flat inside. True or False

a)

True

b)

False

5.

Does the orientation matter?

a)

Yes

b)

No

6.

When a vector is irrotational, which condition holds good?

a)

a)Stoke’s theorem gives non-zero value

b)

b) Stoke’s theorem gives zero value

c)

c) Divergence theorem is invalid

d)

d) Divergence theorem is valid

7.

The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates. State True/False.

a)

True

b)

False

8.

Determine the integral rule of the given expression:

a)

cosx + c

b)

-cosx + c

c)

½sin²x + C

d)

¹/_√(1-x²) + C

9.

Determine the integral rule of the given expression:

a)

x^-2 + C

b)

^-2/_x³ + C

c)

^-1/_x + C

d)

²/_x + C

10.

Evaluate $\oint_c^{ }\left(7y-e^{\sin x}\right)dx+\left[15x-\sin\left(y^3+8y\right)\right]dy$ where c is the circle with radius 3 centered at (5,-7)

hint: use green's theorem

a)

9 $\pi$

b)

$\pi^2$

c)

$72\pi$

d)

can't be calculated

11.

$\int_A^B\overrightarrow{f\ }.d\ \overrightarrow{r\ }$ is,

a)

Volume integral

b)

Surface integral

c)

Line integral

d)

None of the above

12.

The volume of the parallelepiped formed by the coterminous edges a,b,c is represented by

a)

$a\times\left(b\times c\right)$

b)

$a.\left(b\times c\right)$

c)

$a\times\left(b.c\right)$

d)

$a.\left(b.c\right)$

13.

which is called polar coordinate sytem

a)

Rectangular

b)

cylindrical

c)

spherical

d)

none

14.

$x=r\cos\theta,\ y=r\sin\theta,\ z=z,\ 0<\theta<2\pi$

a)

spherical coordinates

b)

cylindrical coordinates

c)

parametric equations

d)

none

15.

Area of a region enclosed by a closed curve C can be computed using the formula

a)

$\frac{1}{2}\int_{ }^{ }xdy-ydx$

b)

$\frac{1}{2}\int_{ }^{ }xdy+ydx$

c)

$\frac{1}{2}\int_{ }^{ }xdx-ydy$

d)

$\frac{1}{2}\int_{ }^{ }xdx+ydy$

VCFT: Cat 2

Total questions: 15

Worksheet time: 27mins

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