16MA102 – ENGINEERING MATHEMATICS II
a b c
1) Obtain the value of
   dxdydz
0 0 0
a) xyz
b) abz
c) abc
d) xbc
Ans: c
 a
2) Evaluate
  rdrd
Ans:b
0 0

a)
2
b)
a 2
2
a2
c) 0 d)
2
3) Find curl(grad  )=
a) j
b) 1
c) 0
d) k
Ans: c
4) If A and B are irrotational then A  B is
a) irrotational
b) unit vector
c) scalar potential
d) solenoidal
5) Find the constants a and b if f(z)=x+2ay+i(3x+by) is analytic
a) -3/2,1
b) 1,-3/2
7) If f(z)=
c)  3
b) 1,3
Ans:a
c) 1,2 d) ½,2
6) Find the fixed points of the mapping w=
a)3,2
Ans :d
6z  9
z
d) 3,3
Ans: d
1
 2[1  ( z  1)  ( z  1) 2  ...] ,find the residue of f(z) at z=1
z 1
a) -1 b) 1 c)2
8) Evaluate
zdz
d)0
Ans: b
 ( z  1)( z  2)
where c is the circle |z|=1/2
b) -1 c) 2
d)0
c
a) 1
Ans: d
9) If L[f(t)]=F(s),then L[eat f(t)]=
a)F(s-a)
b)F(s+a)
b)F(a-s)
d)0
Ans: a
10)Find L[sin2t]=
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16MA102 – ENGINEERING MATHEMATICS II
a)
2
s  22
b)
2
s
s  22
c)
2
2
s 2
2s
s  22
d)
2
Ans:a
2
4 2
11) The change of order of integration of the integral
  f ( x, y)dxdy
1 0
2 4
4 2
a)
  f ( x, y)dxdy
b)
  f ( x, y)dydx
0 1
1 0
4 2
c)
  f ( x, y)dxdy
4 2
d)
  f ( x, y)dxdy
1 0
Ans:b
1 0
 / 2 sin
  rdrd
12) The value of
a)

2
0
0
b)

4
c)

8
d) 
Ans:d
d)1
Ans: a
13) If  is a constant then  is
a) 0
b)2
c)6
14) Stoke’s theorem relates
a)surface integral to volume integral
b)line integral to surface integral
c)line integral to volume integral
d)None of these
Ans: b
d) u x  v y
Ans: d
15) One of the C-R Equation is
a) u x  v y
b) u y  v x
16) The point at which f(z) =
a) z=1
17) The value of
18)If f(z)=
z
ceases to be analytic
z 1
b) z=0
z
c
a) 6i
c) u xx  v yy
c)z=2
d) z=3
Ans: a
d) 0
Ans:d
zdz
where C is |z|=1/2 is
2
1
b) 18i
c) 4i
sin z
,z=0 is a
z
a)pole
b)simple pole
Ans:c
c)Removable singularity
SNS COLLEGE OF TECHNOLOGY (AUTONOMOUS)
d)Essential singularity
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16MA102 – ENGINEERING MATHEMATICS II

19) If L[f(t)]=F(s),then L 
 is
 t 
f (t )


a)  f (t )dt
b)  F ( s)ds
s
s
20) If L[f(t)]=
1
1−𝑥

c)  F (s)ds

d)
 f (s)ds

s
1
then lim
f(t) is
t 
s( s  a)
a)-a
21.∫0 ∫0
(a) ½
Ans:b
b)a
Ans:c
c)1/a
𝑑𝑥 𝑑𝑦 is
(b) 1-X
d)-1/a
(c) 1-y
𝑥2
(d) 0
Ans: (a)
𝑦2
22.Area of the ellipse 2 + 2 = 1 is
𝑎
𝑏
(a) πa2b
(b) πab2
(c) πab
(d) π2ab
Ans: (c)
⃗⃗ are irrotational then div(𝐴⃗ X 𝐵
⃗⃗) is
23.If 𝐴⃗ and 𝐵
(a) Solenoidal
(b) irrotational
(c) ⃗0⃗ (d) 1
Ans: a
⃗⃗⃗⃗⃗
24.Using Stoke’s theorem, the value of ∫𝑐 𝑟⃗ ∙ 𝑑𝑟
(a) 0
(b) 1
(c) 3
(d) -1
Ans: (a)
25.If u is to be harmonic, then 𝑢𝑥𝑥 + 𝑢𝑦𝑦 is
(a) 1
(b) 2
(c) 3
(d) 0
Ans: (d)
5𝑍+4
26.The fixed points of the mapping 𝑤 =
are
𝑍+5
(a) 2, 2
(b) 2, -2
(c) -2, -2
(d)-4/5, 5
27.The value of ∫𝑐
(a) 2πi
(b) 0
3𝑧 2 +7𝑧+1
Ans: (b)
1
𝑑𝑧 where C is |𝑧| = is
𝑧+1
2
(c) πi
(d) πi/2
Ans: (b)
1
28.Residue of 𝑒 𝑧 at z=0 is
(a) 0
(b) 1
(c) ∞
(d) -1
SNS COLLEGE OF TECHNOLOGY (AUTONOMOUS)
Ans: b
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16MA102 – ENGINEERING MATHEMATICS II
29.𝐿−1 [
1
] is
𝑠(𝑠 2 +1)
(a) 1+sint
(b) 1- sint
(c)1+cost
(d)1-cost
Ans: d
30.If L[f(t)] = F(s) then L[tn f(t)] =
𝑛−1
n-1 𝑑
(a) (-1)
𝑑𝑠 𝑛−1
𝐹(𝑠)
(b)
𝑑𝑛
𝑑𝑠 𝑛
Ans: (c)
𝑛
n𝑑
𝐹(𝑠)
(c) (-1)
𝑑𝑠 𝑛
𝐹(𝑠)
(d)
𝑑 𝑛−1
𝑑𝑠 𝑛−1
𝐹(𝑠)
𝑡
31.If L[f(t)] = F(s) then L[f( )] =
2
(a) ½ F[2s]
(b) ½ F[s/2]
(c) 2F[2/s]
(d) 2F[2s]
Ans: (d)
𝑒𝑧
32.The order of the pole z = 0 of the function 3 is
𝑧
(a) 0
(b) 3
(c) 1
(d) 2
Ans: (b)
33.The transformation w = c+ z where c is real is known as
(a) Rotation (b) magnification (c) reflection
(d) translation
Ans: (d)
34.The value of ∫𝑐
(a) 0
(b) πi
𝑧2
𝑧−3
𝑑𝑧 where C is |𝑧| = 1 is
(c) 2πi
35.If 𝐹⃗ is a conservative, then ∇ 𝑋 𝐹⃗ =
(a) 2
(b) 3
(c) 1
(d) 3πi
Ans: (a)
(d) 0
Ans: (d)
36. The analytic function with constant imaginary part is
(a) Need not to be a constant
(b) constant
(b) Conformal mapping
(d) bilinear transformation
1
𝑥
37. Change of order of integration ∫0 ∫0 𝑥𝑦𝑑𝑦𝑑𝑥 is
0
1
1
𝑦
Ans: (b)
(a) ∫1 ∫𝑦 𝑥𝑦𝑑𝑥𝑑𝑦
1
1
0
𝑦
(b) ∫0 ∫𝑦 𝑥𝑦𝑑𝑥𝑑𝑦
(c) ∫0 ∫1 𝑥𝑦𝑑𝑥𝑑𝑦
(d) ∫1 ∫1 𝑥𝑦𝑑𝑥𝑑𝑦
Ans: (c)
⃗⃗
(d) 𝑖⃗ + 𝑗⃗ + 𝑘
Ans: (c)
38. If 𝜑 = 𝑥𝑦𝑧, then grad𝜑 at (1, 1, 1) =
⃗⃗ (b) 𝑖⃗ − 𝑗⃗ + 𝑘
⃗⃗
(a) 𝑖⃗ + 𝑗⃗ − 𝑘
⃗⃗
(c) 𝑖⃗ + 𝑗⃗ + 𝑘
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16MA102 – ENGINEERING MATHEMATICS II
39. Laplace transform of t4 e-at is
4!
(a)
(b)
(𝑠+𝑎)4
5!
4!
(c)
(𝑠+𝑎)5
(d)
(𝑠+𝑎)5
5!
(𝑠−𝑎)5
Ans: (c)
40. 𝑑𝑖𝑣 𝑟̅ = _____
a.0
b)1
c)3
d)2
Ans. c
41. The fixed points of the mappings of 𝑤 =
a)+i and –i
b) +1 and -1
b)0
1−𝑧
are
c) 0 and 1
42. If z=a is a point outside C, then ∫𝑐
a)1
1+𝑧
𝑑𝑧
Ans. a
= ______
𝑧−𝑎
c) -1
d) 0 and i
d)2
Ans. b
43. The Laplace L[cos at]=
a)
1
b)
𝑠 2 +𝑎2
𝑠
𝑠 2 +𝑎2
c)
𝑎
d)1
𝑠 2 +𝑎2
Ans. b
44. The Cauchy-Riemann equations are
a)
𝜕𝑢
𝜕𝑥
c)
𝜕𝑣
=
𝜕𝑢
𝜕𝑥
𝜕𝑦
=−
;
𝜕𝑢
𝜕𝑦
𝜕𝑣
𝜕𝑦
;
=−
𝜕𝑢
𝜕𝑦
𝜕𝑣
b)
𝜕𝑥
=−
𝜕𝑣
𝜕𝑢
𝜕𝑥
d)
𝜕𝑥
3
=
𝜕𝑢
𝜕𝑥
𝜕𝑣
𝜕𝑦
=−
;
𝜕𝑢
𝜕𝑦
𝜕𝑣
𝜕𝑦
;
=
𝜕𝑢
𝜕𝑦
2
45. Change the order of integration in ∫0 ∫1 𝑥𝑦(𝑥 + 𝑦)𝑑𝑦𝑑𝑥
2
3
a) ∫1 ∫0 𝑥𝑦(𝑥 + 𝑦)𝑑𝑥𝑑𝑦
2
3
2
3
2
3
𝜕𝑣
𝜕𝑥
=
𝜕𝑣
𝜕𝑥
Ans. a
Ans:a
b) ∫1 ∫0 𝑥𝑦(𝑥 + 𝑦)𝑑𝑦𝑑𝑥
d) ∫1 ∫0 (𝑥 + 𝑦)𝑑𝑥𝑑𝑦
c) ∫1 ∫0 𝑥𝑑𝑥𝑑𝑦
2
5
46. The value of ∫1 ∫2 𝑥𝑦𝑑𝑥𝑑𝑦 is
a)6
b)12.35
c)15
d)15.75
Ans. d
47. If 𝐴̅ = 𝑐𝑢𝑟𝑙𝐹̅ , the value of ∬𝑠 𝐴̅ . 𝑛̅𝑑𝑠 is ______
a)2
b)0 c)3
d)1
48. The inverse Laplace transform of
a)1 b)0 c)3𝑒 −2𝑡
3
𝑠+2
Ans:c
d) 3𝑒 𝑡
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16MA102 – ENGINEERING MATHEMATICS II
49. The Singularities of the function f(z)=
a)-2 and -1
b)2 and -1
𝑧+2
(𝑧−2)(𝑧+1)2
c)2 and 1
d)0 and 1
Ans. b
50. Express the volume bounded by x=0, y=0, z=0, x+y+z=1 in triple intergration
𝑥
𝑦
𝑧
𝑥
a)∫0 ∫0 ∫0 (𝑥 + 𝑦 + 𝑧)𝑑𝑥𝑑𝑦𝑑𝑧
𝑥
1−𝑥
c) ∫0 ∫0
1−𝑥−𝑦
𝑥
𝑦
1−𝑥−𝑦
∫0
𝑑𝑧𝑑𝑦𝑑𝑥
𝑧
d) ∫0 ∫0 ∫0 (𝑥 + 𝑦 + 𝑧)𝑑𝑧𝑑𝑦𝑑𝑥
𝑑𝑥𝑑𝑦𝑑𝑧
∫0
1−𝑥
b) ∫0 ∫0
Ans. b
51. If 𝑐𝑢𝑟𝑙𝐹̅ = 0 then 𝐹̅ is called an
a)Solenoidal b)Irrotational c)Unit vector d)Directive derivative
Ans. b
𝑟̅
52. ∇. ( ) = _____
𝑟
a)2r
b)
𝑟
c)
2
2
4
d)
𝑟
Ans:c
𝑟
53. If u(x,y)=2x+x2-my2 is harmonic, then the value of m is
a)1
b)0
c)4
d)2
Ans. a
54. The image of |z|=1 under the mapping w=1/z is
a)𝑢2 + 𝑣 2 = 1
b) 𝑢2 + 𝑣 2 > 1
55. The value of ∫𝑐
𝑧
𝑑𝑧 where c is |z|= is
2
b) 18𝜋𝑖
56. If f(z)=
a)Zero
sin 𝑧
𝑧
Ans. a
1
𝑧 2 −1
a)6𝜋𝑖
c) 𝑢2 + 𝑣 2 < 1 d) 𝑢2 + 𝑣 2 = 0
c) 4𝜋𝑖
d)0
Ans. d
then z=0 is
Ans:c
b) Essential singularity
c)Removable singularity
d)Isolated singularity
57. L[𝑒 𝑎𝑡 ]= _____
a)
1
b)
𝑠−𝑎
1
c)s-a
𝑠+𝑎
d)s+a
Ans. a
58. L[cos3t]=
a)
𝑠
𝑠 2 −32
b)
𝑠
𝑠 2 +32
c)
𝑎
𝑠 2 −32
SNS COLLEGE OF TECHNOLOGY (AUTONOMOUS)
d)
𝑎
𝑠 2 +32
Ans. b
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