RTU 2016 Question Paper Semester I Engineering Mathematics I

Roll No. Total No ot Pages: lll
N
o
c LF,2002
B. Tech I Sem. (Main/Back) Exam. Jan.20l6
N
H 102 Engineering Mathematics-I
F{ Common to all Branches

Time: 3 Hours Maximum Marks: 80
Min. Passing Marks: 24
Instructions to Candidates :
Attempt any five questions, selecting one question.frotn each unit. All questions
carry equal marks. Schematic diagrams must be shown wherever necessary. Any
data you feel missing suitably be assumed and stated clearly.
Units oJ quantities usetl/calculated must be stated clearly.
Use of following supporting rnaterial is pemitted during exarnination.
I. NIL 2. NIL

Q.l (a) Find the asymptotes of the curve
*3 - 5x'y + 8xy2 - 4y3 + 2y2 + xz -3xy - l= 0. t8l
O) Show that the radius of curvature at any point P on the parabola y2 = 4ax, is
-f,
zrsPt%
where S is the focus of the parabola. t8l

OR
Q.l (a) Prove that the curve x3 + y3 = a3 has point of inflexion at the point of inflexion at
the points where it crosses the co-ordinate axes. t8l
(b) Trace the curve r=a (l +cosO). (Cardioid). t8i

[1E2002] Page 1of3 Is444o1

UNIT.II
l,\
x' + v'
e.2 (a) I1 u =,ur',I l, then show that
[ *+Y,/
0'u+zxY
- 3'u + y'd',tf dy' =sin2u(1-4sin'?u)
x-" *
dx' *dxdy t8l

(b) If measurements of radius of base and height of a right circular cone are incorrect
by -l%o & 2Vo respectively, find the error in its volume. t8I
OR
Q.2 (a) Find the minimum value of x2+y2+22, given that ax + by + cz = p t8l
(b) Find the volume of the greatest rectangular parallelopiped inscribed in the
ellipsoid whose equarion i, {*}*'] =r t81

UNIT.III
Q.3 (a) Find the surface area of the solid formed by revolving the ellipse

{-+
a'
= I , about the major axis. t81

(b) Find the volume of the solid generated by revolving the curve (a-x) y2 = aX' 2

about its asymptote. I8l
OR

I rz-' zll,*y
Q.3 (a) Change the order of integration in the integral J" [ ,**" ax ayand then
' l-p -71'
evaluate it. t81

(b) Show that .rni- x'zdx - - 5nr'[ t81
1l + x. ). l2g

[1E2002] Page 2 of 3 as444ol

UNIT.IV

-t,,-rv) dy =0. tsl
)dx
dv
(tr) xr+v=v.losx. t5l
dx
(b) (D2+ l)2y = 24x cosx ; D = d/dx, Solve it. t6t
OR
Q.4 (a) Solve:
(i) (3x2y + y/x) dx + (x3+ log x) dy = g I5l
(ii) (xy sin xy + cos xy) ydx + (xy sin xy - cos xy) xdy = Q. tsl
(b) Solve:
d2x ^ cosa:-:+n'x
dx
*+2n
dt' dr
=acosnt, such that x = 0 and dx/dt = 0 at t = 0. t61

UNIT.V
Q.5 (a) Solve:
tl + x)'d'!/o*,+ tl+ xtdv/o*+y =4 cos (log ( I + x)). t8l
(b) Solve:
-)
91+ (3sinx -cotx)9 + 2sin 2x )v = 51n2*
t t8I
dxz dx "-cosx
OR
Q.5 (a) Solve:
(2x'z + 3x) d'v/*, + <a* * l)dfi+ 2y = (x + t)e'. t8l
(b) Solve by the method of variation of parameters-
, dzv dv
x- x:_v x-e... t8l
dx' dx ' =
-+

lLE2O02l Page 3 of3 Is44401