Manipal University 2010 B.Tech Mathematics and Computing First semester b.e make up - - enggmathematics i (mat – 101) - Question Paper
FIRST SEMESTER B.E DEGREE MAKE UP EXAMINATION- DECEMBER 2010
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Reg.No |
MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL UNIVERSITY, MANIPAL - 576 104
SUB: ENGG. MATHEMATICS I (MAT - 101)
(REVISED CREDIT SYSTEM)
Max.Marks : 50
Time : 3 Hrs.
Note : a) Answer any FIVE full questions.
b) All questions carry equal marks
1A.
1B.
x 1 v 2 z 3
1C. Find the image of the line = - in the plane 2x + y + z = 6.
(4 + 3+3)
. . _i 9 9
2A. If y = sin msin x , show that (1- x )yn+2 = (2n+l) xyn+i + (n -m)yn
/I
2B. Obtain the reduction formula for j*sin"x dx and hence evaluate Jcosnxdx.
0
A variable plane at a constant distance p from the origin meets the coordinate axes at A, B, C. Through A, B, C planes are drawn parallel to coordinate planes.
2C.
_2 _9 _9 _9
Show that locus of their point of intersection is x + y-2 + z-2 = p-2
(4 + 3+ 3)
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3 A. Find the nature of the series n !?n n-l 11 |
(ii) +--+--+--+ ... 1 2 3 2.4 5 2.4.6 7 |
3B. Sketch and find perimeter of the curve r = a ( 1 - cosG), a >0 3C. Find the evolute of y2 = 4ax.
(4 + 3+ 3)
lim x > 0
ax +b* 2
(i)
lim tan x - x x 0 x2 tan x
(ii)
4B. Find the angle between the curves
rm = am cosmG, rm = am sinmG, a >0
Find the centre and the radius of the circle of intersection by the plane
4C.
5A.
5B.
5C.
2 2 2
x+4y+z = 4 and the sphere x + y + z - x - z - 2 = 0 .
(4 + 3+ 3)
Find the first three nonzero terms in the Maclaurins series expansion tan x.
The tangents at two points P, Q on the curve x = a (0 - sin0), y = a ( 1 - cosG) are at right angles. Show that if pi and p2 be the radii of curvature at the points, then show that pf + - 16a2.
Find the volume of the solid generated by revolution of the curve
2/2/2/ x/3 + y/3 = a/3 about the x - axis.
(4 + 3+ 3)
f 3 i 3 A
6A. (i) If u = tan
then show that
v x~y
+ 2xy-+ y 7 = (l-4sin u)sin2u
d2u
ax2
x
dxdy dy
6B. State and prove Lagranges mean value theorem.
6C. Find the maximum possible error in calculating g if T=2n/ , given 1%
\g
and 0.5% errors in I and T respectively.
(4 + 3+ 3)
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Trace the following curve with explanations y (a -x) = x , a > 0
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| Earning: Approval pending. |
