Punjab Technical University 2008-1st Sem B.Tech <>EnggMathematics -I (AMA-101) (_ 2nd) << >> - Question Paper
Roll No.......................
Total No. of Questions : 9) [Total No. of Pages : 03
ENGINEERING MATHEMATICS -1 SUBJECT CODE : AM - 101 (2K4 & ONWARDS)
Paper ID : [A0111]
jNote : Please fill subject code and paper ID on OMR[
Time : 03 Hours Maximum Marks : 60
Instruction to Candidates:
1) Section - A is Compulsory.
2) Attempt any Five questions from Section - B & C.
3) Select atleast two questions from Section - B & C.
Section - A
QO . [Marks: 2 eachJ
vi ( n
a) Test for the convergence of the series 2
n + lj '
b) Using double integration, find area enclosed between the curves y2 = x3 and x = y.
c) If u = x3 + xy and v = xy. Find .
d) Prove T( + 1) = r(n), where n > 0.
e) Find the curvature of curve y2 = x3 + 8 at the point (1,3).
f) Find the cube roots of unity.
g) Evaluate U xyz dxdydz.
h) Define homogeneous function with an example.
i) Find the centre and the radius ofthe sphere x2+y2 + z2-6x + 8y-10z + 1 =0. j) Expand tan x in powers of x upto x3.
Q3) (a) Trace the curve a2y2 = x2(a2 - x2).
Q2) (a) State and prove Eulers theorem.
(b) If pl ,p2 be the radii of curvature at the extremities of the chord of the cardioid r = a(l + cos0) which pass through the pole, show that
Q4) (a) Expand x2y + 3_y - 2 in powers of (x - 1) and (y + 2) using Taylors theorem.
(b) Discuss maxima and minima of x3>(l - x -y).
Q 5) (a) F ind the moment, about x-axis of arc of parabola y - -Jx, lying between
(0, 0) & (4, 2). .
(b) Find root mean square of sin x over the range x = 0 to njl.
Section - C
[Marks: 8 Each]
Q6) (a) Show that the two circles
x2+y2 + z2-2x + 3y + 4z-5 = 0,5y + 6z+ 1 =0 x2 + y1 + z2 - 3x - 4y + 5z - 6 = 0, x + 2y - Iz = 0 lie on the same sphere and find its equations.
(b) Find the equation of cone whose vertex is at the points (1, 1,3) and which passes through the ellipse 4x2 + z2 = \ ,y = 4.
Q7) (a) Change the order of integration j J , xy dxdy and hence evaluate the
integral.
(b)
1 3 5
Q8) (a) Test the convergence of the series - + - +..........
X. * W 4 ij fc1 4 ij * ' 4 D
sin(x2 + nx)
=1 n(n + 2)
Q9) (a) Separate tan '(x + (y) into real and imaginary parts.
(b) Solve the equation jc4-x3 + x2-jc+1=0} using De Moivres theorem.
|
Attachment: |
| Earning: Approval pending. |
