Download VTU BE 2020 Jan CSE Question Paper 17 Scheme 3rd Sem MATD1P301 Advanced Mathematics I

USN

MATD1P301

Third Semester B.E. Degree Examination, Dec.2019/Jan.2020

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Advanced Mathematics - I
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions.
(2 + 30
2

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a.

1 Express
+

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in the form of complex number a + ib. (06 Marks)
b. Prove that (1 + + (1 ? = ?8.
(07 Marks)
c. Find the cube root of - 0 . (07 Marks)
2 a.

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Find n
th
derivative of sin(ax + b). (06 Marks)
b. Iffy = a cos(log x) + bsin(log x) . Show that + (2n + 1)xy? + (n
2

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+ 1)y,, = 0 . (07 Marks) ,
1
c. Find n
th
derivative ?flog(

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2x + 3
(07 Marks)
)10
e
t

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2-3x
3 a. Find the angle between the curves. r = a(sin 0 + cos0) and r = 2a cos 0
b. Find the pedal equation for the curve r
2
= a

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2
see(20)
c. Expand y --- - Log (cos x) using Maclaurin's series upto 4
th
degree term.

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show that xu, + yu ? + zy, = 2 tanu
_ . , a au
b. If u = RI
-
, s, t) where r=

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x
? s=
Y
?, t = z Fi ?. no x ?
u

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+ y--- + z
a
u
-- .
y

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z x Ox cry ez
c. Ifu=x+y+z,v=y+z,w?zfind
a(uvw)

a(x

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y
z)
5 a.
Obtain reduction formula for f sin" x dx where n is a positive integer.
Evaluate x

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9
VI ? x
2
dx .
rl

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I 2
c. Evaluate : Si( + y
-
)dxdy
0

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4 a. if
u s
i
n

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x
3
y
-
+ z

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ax + by + ez

(06 Marks)
(07 Marks)
(07 Marks)

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(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)

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(07 Marks)
Important Note
1 2 2
6 a. Evaluate : dx dy dz .
0 0 1

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b. Prove that 13(m, n) = r3(n, m)
c. Evaluate : ,
x2
dx .
V2 x

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0
(06 Marks)
(07 Marks)
(07 Marks)
1 of 2

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USN

MATD1P301

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Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Advanced Mathematics - I
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions.
(2 + 30

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2

a.

1 Express

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+
in the form of complex number a + ib. (06 Marks)
b. Prove that (1 + + (1 ? = ?8.
(07 Marks)
c. Find the cube root of - 0 . (07 Marks)

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2 a.
Find n
th
derivative of sin(ax + b). (06 Marks)
b. Iffy = a cos(log x) + bsin(log x) . Show that + (2n + 1)xy? + (n

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2
+ 1)y,, = 0 . (07 Marks) ,
1
c. Find n
th

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derivative ?flog(
2x + 3
(07 Marks)
)10
e

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t
2-3x
3 a. Find the angle between the curves. r = a(sin 0 + cos0) and r = 2a cos 0
b. Find the pedal equation for the curve r
2

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= a
2
see(20)
c. Expand y --- - Log (cos x) using Maclaurin's series upto 4
th

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degree term.
show that xu, + yu ? + zy, = 2 tanu
_ . , a au
b. If u = RI
-

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, s, t) where r=
x
? s=
Y
?, t = z Fi ?. no x ?

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u
+ y--- + z
a
u
-- .

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y
z x Ox cry ez
c. Ifu=x+y+z,v=y+z,w?zfind
a(uvw)

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a(x
y
z)
5 a.
Obtain reduction formula for f sin" x dx where n is a positive integer.

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Evaluate x
9
VI ? x
2
dx .

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rl
I 2
c. Evaluate : Si( + y
-
)dxdy

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0
4 a. if
u s
i
n

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x
3
y
-

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+ z
ax + by + ez

(06 Marks)
(07 Marks)

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(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)

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(07 Marks)
(07 Marks)
Important Note
1 2 2
6 a. Evaluate : dx dy dz .

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0 0 1
b. Prove that 13(m, n) = r3(n, m)
c. Evaluate : ,
x2
dx .

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V2 x
0
(06 Marks)
(07 Marks)
(07 Marks)

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1 of 2
MATDIP301
Solve
1
-

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d
= e (ex + x
2
) .
dx

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Solve (x
2
+ y
2
)dx= 2xy dy

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Solve ?
dx
= ?
x
+ 2y

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2
.
dy y
dy
8 a. Solve d

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2
,
y
+ 5? + 6y = .
dx

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-
dx
2

b. Solve

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d
,
y dy
+ 4 + 4y = cos x .
dx

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-
dx
2
y
c. Solve

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d
? + 3
dy
+ 2y = 12x
2

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dx
2
dx
7

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a.
b.
C.
(06 Marks)
(07 Marks)

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(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
2 of 2

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