Download OU B.Sc 2016 April 1st Year 2017E Mathematics Question Paper

Download OU (Osmania University) B.Sc (Bachelor of Science) 2016 April 1st Year 2017E Mathematics Previous Question Paper

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x Code No. 2017 I E
FACULTIES OF ARTS AND SCIENCE
B.A. I B.Sc. I? Year Examination, March I April 2016
Subject : MATHEMATICS
Paper? I : Differential Equations and Soiid Geometry
Time : 3 hours Max. Marks : 100
Note: Answer Six questions from Part-A 8. Four questions from Part-B.
Choosing at least one from each Unit. Each question in Part-A carries
6 marks and' In Part-B carries 16 marks.
A Part? A (6 X 6 = 36 Marks)
Unit ?I
dy
1 Solve seczyd?+2xtany = x3.
x
Unit -? 1|
3 Solve y"+3y'+2y=126X
4 Solve (D2 ? 3D + 2)y = 3 sin 2x.
Unit- III
5 Find the equation of the pian?ggg?
1, 1)and (1 1, ?1).
asses through the points (?1, 1, 1), (1, -
6 Find the point where th?Me Waning (2 -3, 1), (3, -4, -5) cuts the plane 2x +
y + Z: 7
Unit'- Iv
7 fiat the cone whose vertex is at the origin and the direction cosines
rafors satisfy the relation 362 ?4m +Sn - 0.
8
3%: y?2= : and whose guiding curve is the ellipse x2 + 2y2 = 1, 2= 0.
Part ? B (4 X 16 = 64 Marks)
Un?-I
9 a) Prove that the integrating factor of non-exact differential equation de+Ndy=0
is 1/Mx+Ny2 if the differ1entiai equation is homogeneous and Mx + Ny ? 0.
b) Solve (1+y2 )dx= (tan y? x)dy.
10 a) Explain the mzethod of solving Clairaut? 3 equation y= px + f(p)
b) Solve (x2 +y2 +2x) dx+2y dy= 0

_ 2 -
Unit ? Ii
11 a) Explain the method of solving second order Cauc
azx2 $321+ a1X?+ aoy = Q(x) where ao, a1 and
non?zero. X
b) Solve (D2 ? 3D + 2)y = xe2x + sinx.
12 a) Solve (D2 + 40+4) y = 4x2 + 6ex by undeterminec
b) Apply method of variation of parameters to solve
Unit - iii
13 a) A variable plane is at a constant distance 3p fror
in A, B and C. Show that the locus of the centroic
X-2 + y-z +Z'2 = p'2
b) Find the shortest distance between the lines
?1_y?2_z?3 x~2-y?3_z?4
and
2 3 3 3 4 5 E9
Codie No. 2017 I E
hy Euler equation
a2 are constants which are
i coefficients.
D2 ? 2D) y = ex einx.
n the origi, _
d" .1 eets the axes
i of the t
14 23) Find the equation of the sphere which pg
12,,,.0)and(123)
b) Find the equation of the sphere which
tag,?
agrou h the points (00 0). (0?11 1) (?
Ktagssghrou h the circle
x2 +y +z2 =5, x+2y+3z= 3?andtouchthepl ne4x+3y=15
Unit IV
15 a) Prove that 2x +2y2 +722
vertex at (2,2 ,1).
b) Find the angle betwee
8yz+32x- 5xy= 0
Mm]?
lines of intersecti
16 a) Find the equatiori?ef the cylinder whose generator
? m
b) Fin :2; the ?quation of the right circular cylinder of r:
x 12y? 3 __5__? z
2 2 7
. X
a2 and are parallel to the ?he ?
35?
-::.OZX +2x +2y +26 -17 = 0 represents a cone with
n of 4x -y? 5z=0 and
s touch the sphere
y?Z
E n
adius 3 and whose axis is