Download VTU ((Visvesvaraya Technological University) B.E/B-Tech 2019 July ( Bachelor of Engineering) First & Second Semester (1st Semester & 2nd Semester) 2018 Jan 2017 Dec 17MAT11 Engineering Mathematics I Question Paper
>7,
13,
Y
USN
17MAT11
OR
?
b. With usual notations prove that the pedkl'ailiition in the for
ik
m
1
n
2
+1)y
n
= 0
de
I ( dr
r
4
2 a. If y = a cos(log x) + bsin(log x) pio4that + (2n +1)xy,, +
C ?
4
a
.
0 ?
bo ?
Q.)
8
0
ry
2
4
5
a.
b.
c.
a.
b.
c.
OR
+ex '
x
Evaluate lim
)
+II'
?
az
ax
)2
+
(
?
az
j+(8t
2
-3t
3
)i
t = 2.
3
Find al' ,
,
M*laurin's expansion of log(secx) upto x
4
terms.
f(x, y) , where x = r cost) , y = r sin 0 , prove that
-
Module-3
A particle moves along the curve f = (t
3
-44)1+ (t
2
+40
and acceleration vectors at time t and their magnitudes at
If f = (x + y +1)i +I ? (x + y)ic
-
, prove that f.curl = 0 .
Prove that div(curl A) =0 .
(06 Marks)
(07 Marks)
i ? I az )
2
(07 !Marks)
Find the velocity
(06 Marks)
(07 Marks)
(07 Marks)
- ,Semester B.E. Degree Examination, Dec.2017/Jan.2018
Engineering Mathematics - 1
Time: 3 hrs. Max. Marks: 100
Note: Answer a full questions, choosing one full question from each module.
Module-I
1 a. Find the n
th
derivative, Of
,
,cosx cos2x.
b. Find the angle betweerill*(/eurves r = a log , r =
log e
s
c. Find the radius of curvature Of * curve r = a(1 + cos()) .
a
(06 Marks)
(07 Marks)
(07 Marks)
(07 Marks)
c. Find the radius of curvatu
a ? x)
=. at the point (a, 0). (07 Marks)
,
Module-2
3 a. Find the Taylor's serisivof log,x. n powers of (x ? I) upto fourth degree terms. (06 Marks)
x
y
;
' au au
x + y
( b. If U = tan l
I
- , prove:
ax
that x + y?
ay
= sin 2U by
,
using Euler s theorem. (07 Marks)
'
a(u,V, w)
c. If U = x +3y
2
, V = , W 2z
2
? xy , evaluate at the point (1, 0).
a(x, y,
(07 Marks)
I oft
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-7,-
>7,
13,
Y
USN
17MAT11
OR
?
b. With usual notations prove that the pedkl'ailiition in the for
ik
m
1
n
2
+1)y
n
= 0
de
I ( dr
r
4
2 a. If y = a cos(log x) + bsin(log x) pio4that + (2n +1)xy,, +
C ?
4
a
.
0 ?
bo ?
Q.)
8
0
ry
2
4
5
a.
b.
c.
a.
b.
c.
OR
+ex '
x
Evaluate lim
)
+II'
?
az
ax
)2
+
(
?
az
j+(8t
2
-3t
3
)i
t = 2.
3
Find al' ,
,
M*laurin's expansion of log(secx) upto x
4
terms.
f(x, y) , where x = r cost) , y = r sin 0 , prove that
-
Module-3
A particle moves along the curve f = (t
3
-44)1+ (t
2
+40
and acceleration vectors at time t and their magnitudes at
If f = (x + y +1)i +I ? (x + y)ic
-
, prove that f.curl = 0 .
Prove that div(curl A) =0 .
(06 Marks)
(07 Marks)
i ? I az )
2
(07 !Marks)
Find the velocity
(06 Marks)
(07 Marks)
(07 Marks)
- ,Semester B.E. Degree Examination, Dec.2017/Jan.2018
Engineering Mathematics - 1
Time: 3 hrs. Max. Marks: 100
Note: Answer a full questions, choosing one full question from each module.
Module-I
1 a. Find the n
th
derivative, Of
,
,cosx cos2x.
b. Find the angle betweerill*(/eurves r = a log , r =
log e
s
c. Find the radius of curvature Of * curve r = a(1 + cos()) .
a
(06 Marks)
(07 Marks)
(07 Marks)
(07 Marks)
c. Find the radius of curvatu
a ? x)
=. at the point (a, 0). (07 Marks)
,
Module-2
3 a. Find the Taylor's serisivof log,x. n powers of (x ? I) upto fourth degree terms. (06 Marks)
x
y
;
' au au
x + y
( b. If U = tan l
I
- , prove:
ax
that x + y?
ay
= sin 2U by
,
using Euler s theorem. (07 Marks)
'
a(u,V, w)
c. If U = x +3y
2
, V = , W 2z
2
? xy , evaluate at the point (1, 0).
a(x, y,
(07 Marks)
I oft
11/2
8 a. Find the reduction formula for icoex dx and hence evaluate cos" x dx .
0
dy ycosx+siny+y
b. Solve = 0
dx sinx+xcosy+x
c.
A body originally at 80?C cools down to 60?Cri
temperature 40?C. Find the temperate of the bod
instant.
9 a. Find the ranleft
(
2
4 2
8 4 7 13
4 -3 --1
by reducing it to echelon form.
? /
s m the surroundings of
minutes from the original
(07 Marks)
(06 Marks)
17TIA711
OR
6 a.
- 5)k . Find the (components of
(06 Marks)
(07 Marks)
(07 Marks)
A particle moves along the curve I' = 2t
2
I+(t
2
-4t)j+(3t
velocity and acceleration along T-31+ 2k at t = 2.
b. If ?grad(x y + y
3
z + z
3
x - x
2
y
2
z
2
) , find div f and curi f.
c.
Prove that curl(grad (0) = 0 .
7 a.
Module-4
2a ?
Evaluate dx
2ax x
-,
Solve ?+ y tan x = y
3
-sdc x
dx
Find the orthogonal trajec,tories of r" = cosn9 .
dy
f -
b.
C.
(06 Marks)
(07 Marks)
(07 Marks)
OR
b. Using the power method find the largest eigenvalue and the corresponding eigenvector of
?
6 --2 2
, 3 -
matrix A -
taking (1, 1, 1)
T
as the initial eigenvector. Petthrm five iterations.
(07 Marks)
3 )
c. Show that the transformation y
1
= x
i
+ 2x
2
+ 5x,
regular. Also, find the inverse transformation.
y, = 2x, + 4x
2
+11x, ; +2x, is
=
>
(97 Marks)
(06 Marks)
(07 Marks)
10 a.
b.
C. using orthogonal
(07 Marks)
OR
Solve the following system of equations by using Gauss-Jordan method:
x+y+z=9, x-2y+3z=8, 2x+y-z=3
(-1 2
Diagnolize the matrix A = I
2 -1
Obtain the canonical form of 3x
2
+ 5y
2
+3z
2
-2yz + 2zx - 2xy
transformation.
2 of 2
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This post was last modified on 01 January 2020