MATD1P301
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
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Advanced Mathematics - ITime: 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 nth
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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2-3x3 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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2see(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--- + za
u
-- .
y
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z x Ox cry ezc. Ifu=x+y+z,v=y+z,w?zfind
a(uvw)
a(x
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yz)
5 a.
Obtain reduction formula for f sin" x dx where n is a positive integer.
Evaluate x
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9VI ? x
2
dx .
rl
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I 2c. Evaluate : Si( + y
-
)dxdy
0
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4 a. ifu s
i
n
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x3
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)
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MATD1P301
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Third Semester B.E. Degree Examination, Dec.2019/Jan.2020Advanced Mathematics - I
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions.
(2 + 30
--- Content provided by FirstRanker.com ---
2a.
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)
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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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t2-3x
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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= a2
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
-
--- Content provided by FirstRanker.com ---
, 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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yz x Ox cry ez
c. Ifu=x+y+z,v=y+z,w?zfind
a(uvw)
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a(xy
z)
5 a.
Obtain reduction formula for f sin" x dx where n is a positive integer.
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Evaluate x9
VI ? x
2
dx .
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rlI 2
c. Evaluate : Si( + y
-
)dxdy
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04 a. if
u s
i
n
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x
3
y
-
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+ zax + 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 1b. Prove that 13(m, n) = r3(n, m)
c. Evaluate : ,
x2
dx .
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V2 x0
(06 Marks)
(07 Marks)
(07 Marks)
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1 of 2MATDIP301
Solve
1
-
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d= e (ex + x
2
) .
dx
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Solve (x2
+ 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)
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