Download VTU BE 2020 Jan ME Question Paper 15 Scheme 3rd Sem MATD1P301 Advanced Mathematics I

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

a.

1 Express
+

--- Content provided by⁠ FirstRanker.com ---

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.

--- Content provided by FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by‌ FirstRanker.com ---

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

a(x

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by‌ FirstRanker.com ---

9
VI ? x
2
dx .
rl

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

4 a. if
u s
i
n

--- Content provided by​ FirstRanker.com ---

x
3
y
-
+ z

--- Content provided by‌ FirstRanker.com ---

ax + by + ez

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

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

FirstRanker.com - FirstRanker's Choice
USN

MATD1P301

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

2

a.

1 Express

--- Content provided by⁠ FirstRanker.com ---

+
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)

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by‍ FirstRanker.com ---

Evaluate x
9
VI ? x
2
dx .

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

0
4 a. if
u s
i
n

--- Content provided by⁠ FirstRanker.com ---

x
3
y
-

--- Content provided by⁠ FirstRanker.com ---

+ z
ax + by + ez

(06 Marks)
(07 Marks)

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

1 of 2
MATDIP301
Solve
1
-

--- Content provided by​ FirstRanker.com ---

d
= e (ex + x
2
) .
dx

--- Content provided by​ FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

Solve ?
dx
= ?
x
+ 2y

--- Content provided by​ FirstRanker.com ---

2
.
dy y
dy
8 a. Solve d

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

-
dx
2

b. Solve

--- Content provided by‍ FirstRanker.com ---

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

--- Content provided by​ FirstRanker.com ---

-
dx
2
y
c. Solve

--- Content provided by FirstRanker.com ---

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

--- Content provided by FirstRanker.com ---

dx
2
dx
7

--- Content provided by‌ FirstRanker.com ---

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

--- Content provided by⁠ FirstRanker.com ---

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

--- Content provided by‌ FirstRanker.com ---

FirstRanker.com - FirstRanker's Choice