WorksheetsELECTROMAGNETICS
Total questions: 53
Worksheet time: 27mins
Name
Class
Date
1.
Identify which of the following quantities is not a vector
a)
Force
b)
Work
c)
Acceleration
d)
Momentum
2.
Which of the following is not a scalar field?
a)
Displacement of a mosquito in space
b)
Atmospheric pressure in a given region
c)
Light intensity in a drawing room
d)
Humidity of a city
3.
Which of the following is correct?
a)
A∙B∙C=B∙C∙A
b)
a_x∙a_y=a_z
c)
A ×A= |A^2 |
d)
A ×B +B ×A= 0
4.
Let F=2a_x-6a_y+10a_z and G=a_x+G_y a_y+5a_z. If F and G have the same unit vector, G_y is __________.
a)
6
b)
-3
c)
0
d)
-6
5.
Which of the following identities is not valid?
a)
a_A∙a_B=〖cosθ〗_AB
b)
A×(B+C)=A×B+A×C
c)
A∙B=B∙A
d)
A(B+C)=AB+BC
6.
Which of the following statements is meaningless?
a)
A∙B+2A=0
b)
A∙(A×B)=-2
c)
A∙B+5=2A
d)
A∙A+B∙B=0
7.
If the distance between points A(2, 10, 4) and B(8, 3, z) is 9.434, what is the value of z?
a)
5
b)
6
c)
3
d)
4
8.
Given that A=a_x+∝a_y+a_z and B=∝a_x+a_y+a_z, if A and B are normal to each other, ∝ is
a)
-1
b)
2
c)
-2
d)
-1/2
9.
If A=3i+2j and B=2i+kj, where ‘k’ is a scalar value, find ‘k’ such that A and B are parallel.
a)
-3
b)
4/3
c)
-2
d)
3
10.
Given the 3-dimensional vectors A = xyi + 2xyzj + 3xzk and B = yzi + 2xzj + 3xyk, determine the scalar product at the point (1, 2, 3).
a)
99
b)
143
c)
138
d)
257
11.
Determine the cross product of the vectors A=i+4j+6k and B=2i+3j+5k.
a)
-2i + 7j + 5k
b)
2i +7j -5k
c)
2i – 7j -5k
d)
2i + 7j + 5k
12.
Given vectors: A=∝a_x+a_y+4a_z; B=3a_x+βa_y-6a_z; C=5a_x-2a_y+γa_z. Determine ∝, β, γ such that vectors are mutually orthogonal.
a)
∝=-4/3,β=8,γ=-17/6
b)
∝=-6/3,β=16,γ=17/6
c)
∝=-8/3,β=16,γ=-17/6
d)
∝=4/3,β=8,γ=17/6
13.
Determine the angle formed between the vectors A and B if A =<1, 2> and B = <3, 4>
a)
10.3⁰
b)
12.5⁰
c)
14.2⁰
d)
8.6⁰
14.
Find the smaller angle of intersection of the planes 5x-14y+2z-8=0 and 10x-11y+2z+15=0.
a)
28.43⁰
b)
22.42⁰
c)
25.72⁰
d)
29.89⁰
15.
The component of 6a_x+2a_y-3a_z along 3a_x-4a_y is
a)
2
b)
30a_x-40a_y
c)
10/7
d)
-12a_x-9a_y-3a_z
16.
Find the vector projection of vector B onto vector A if A=2i+4j+3k and B=i-5j+2k.
a)
0.21i+0.56j+1.55k
b)
-3.15i-0.87j-0.18k
c)
2.18i+0.57j+0.56k
d)
-0.83-1.66j-1.24k
17.
Find the area of the triangle whose vertices are A(-3, 1, 4), B(0, 8, -2), and C(3, 2, -3).
a)
28 sq. units
b)
30 sq. units
c)
32 sq. units
d)
34 sq. units
18.
If the planes 5x-6y-7z=0 and 3mx+2y-nz+1=0 are parallel, find n.
a)
-7/3
b)
8/3
c)
¾
d)
-7/6
19.
Find the equation of the plane parallel to 2x-3y-z-5=0
a)
x-4y-2z+12=0
b)
6x-9+3z+12=0
c)
-x+4y+2z-12=0
d)
-6x+9y+3z+12=0
20.
Find the critical points of the multivariable function f(x,y)=x^2-xy+y^2+3y-1
a)
(-1, -2)
b)
(-1, 2)
c)
(1, -2)
d)
(1, 2)
21.
Calculate the Jacobian of (u, v, w) with respect to (x, y, z) if u=x+2y+z,v=x+2y+3z,and w=2x+3y+5z.
a)
2
b)
3
c)
1
d)
4
22.
If x=u(1+v) and y=v(1+u), find the Jacobian J(x, y).
a)
u + v
b)
-u – v
c)
1 + u + v
d)
1 – u – v
23.
A particle moves along the curve x=t^3+1,y=t^2,z=2t+5, where ‘t’ is the time. Find the component of its velocity at t = 1 in the direction i+j+3k.
a)
√5
b)
√8
c)
√10
d)
√11
24.
A particle moves along the curve x=t^3+1,y=t^2,z=2t+5, where ‘t’ is the time. Find the component of its acceleration at t = 1 in the direction i+j+3k.
a)
5/√11
b)
6/√11
c)
7/√11
d)
8/√11
25.
If f=3x^2y-y^3z^2, find grad f at the point (1, -2, -1).
a)
12i-9j-16k
b)
-12i-9j-16k
c)
12i+9j-16k
d)
12i-9j+16k
26.
Find the maximum directional derivative of the function f(x,y) = 2x^2 + 3xy + 4y^2 at the point P(1,1).
a)
10.21
b)
13.04
c)
11.52
d)
14.56
27.
Find the directional derivative of f=x^2 yz+4xz^2 at (1, -2, -1) in the direction 2i-j-2k.
a)
11/5
b)
23/4
c)
37/3
d)
45/2
28.
What is the greatest rate of increase of u=xyz^2at the point (1, 0, 3)?
a)
9
b)
11
c)
13
d)
15
29.
Compute the divergence of the vector field F=x^2 yi+xyzk-x^2 y^2 k.
a)
2xy – 3xy
b)
2xy – xz
c)
2yz + xy
d)
2xy + xz
30.
If f=xy^2 i+2x^2 yzj-3yz^2 k then find div f at the point (1, -1, 1).
a)
7
b)
9
c)
11
d)
13
31.
Determine ∆∙r where r is a position vector
a)
1
b)
2
c)
3
d)
0
32.
Find the curl of the function f=xy^2 i+2x^2 yzj-3yz^2 k at the point (1, -1, 1).
a)
-i + 2k
b)
-i – 2k
c)
i + 2k
d)
i – 2k
33.
Find the curl of the vector (x^2-y^2 )i+2xyj+(y^2-xy)k.
a)
(4y + x)i + yj – 4yk
b)
(2y + x)i – yj + 4yk
c)
(2y - x)i + yj + 4yk
d)
(y - 2x)i + yj + 3yk
34.
The curl of f(x,y,z)=2xyi+(x^2+z^2 )j+2zyk is _____________________.
a)
0 & irrotational
b)
xy^2 i-2xyzk & irrotational
c)
xy^2 i-2xyzk & rotational
d)
Option 4
35.
A vector field which has a vanishing divergence s called as ___________________.
a)
Solenoidal field
b)
Rotational field
c)
Hemispheroidal field
d)
Irrotational field
36.
A vector field with a vanishing curl is called as __________.
a)
Solenoidal
b)
Irrotational
c)
Rotational
d)
Cycloidal
37.
Given the field A=3x^2 yza_x+x^3 za_y+(x^3 y-2z) a_z, it can be classified that field A is _________.
a)
Divergenceless
b)
Solenoidal
c)
Conservative
d)
Rotational
38.
Find the derivative of the vector function f(t)= t sint i+ t^2 j+tcos2t k at t=π/4
a)
√2/2 (1+π/4)i+π/2 j-π/2 k
b)
√2/2 (1-π/4)i-π/4 j+π/2 k
c)
π/4 i-π/2 j+π/2 k
d)
√2/2 πi+(√2 π)/4 j-π/2 k
39.
Evaluate: ∫_0^(π/2)▒(3 sin^2t cost i+3sintcos^2 t j+2 sintcost k)dt
a)
i-j-k
b)
i+j-k
c)
i+j+k
d)
i-j+k
40.
Find the arc length of the vector function: v(t)=√2 t i+e^t j+e^(-t) k at interval 0≤t≤1.
a)
1.52
b)
4.55
c)
3.41
d)
2.35
41.
If C is the line segment from (0, 0, 0) to (1, 2, 3), find ∫▒〖xe^yz ds〗
a)
125.48
b)
250.87
c)
110.32
d)
310.43
42.
Evaluate the line integral ∫▒〖F∙dr〗 where F=x^2 y^2 i+y j and the curve C_1 is y^2=4x in the xy-plane from (0, 0) to (4, 4).
a)
187
b)
264
c)
342
d)
812
43.
Evaluate ∮▒〖xydx+x^2 y^3 dy〗 where C is the triangle with vertices (0,0), (1,0), (1,2) with positive orientation.
a)
2/3
b)
1/3
c)
3/2
d)
1
44.
If r=xa_x+ya_y+za_z, the position vector of point (x, y, z) and r=|r|, which of the following is incorrect?
a)
∇r=□(→┬r/r)
b)
∇^2 (→┬r∙→┬r )=6
c)
∇∙→┬r=1
d)
∇×r=0
45.
Which of the following is zero?
a)
Grad div
b)
Curl curl
c)
Div curl
d)
Div grad
46.
Which of the following is zero?
a)
Grad div
b)
Curl curl
c)
Curl gad
d)
Div grad
47.
If a vector field Q is solenoidal, which of these is true?
a)
∮▒〖Q∙dS〗=0
b)
∮▒〖Q∙dl〗=0
c)
∇×Q=0
d)
∇^2 Q=0
48.
Find the potential function for the vector field F=2xy^3 z^4 i+3x^2 y^2 z^4 j+4x^2 y^2 z^3 k.
a)
f=x^3 y^4 z^2+C
b)
f=x^4 y^3 z^2+C
c)
f=x^2 y^3 z^4+C
d)
f=x^3 y^4 z^2+ C
49.
In cylindrical coordinates, the equation (∂^2 u)/(∂p^2 )+1∂u/p∂p+(∂^2 u)/(∂z^2 )+10=0 is called _____________.
a)
Poisson’s equation
b)
Laplace’s equation
c)
Maxwell’s equation
d)
Lorentz's equation
50.
The flow integral along the closed curve C is called ________________.
a)
Flow integral
b)
Flux
c)
Circulation
d)
None of the choices
51.
The necessary and sufficient condition that ∫_A^B▒〖→┬F∙dr〗 be independent of path is
a)
div(F) = 0
b)
div(F) = 1
c)
curl(F) = 1
d)
curl(F) = 0
52.
Green’s theorem is useful for changing a line integral around a closed curve C into ___________ over the region R enclosed by C.
a)
Double Integral
b)
Triple Integral
c)
Volume Integral
d)
Line Integral
53.
The path traversal in calculating the Green’s theorem is ___________.
a)
Inwards
b)
Clockwise
c)
Counterclockwise
d)
Outwards
100 %
