Periyar University 2005 B.Sc Electronics Allied — II — MATHEMATICS — II - Question Paper
Sunday, 27 January 2013 01:20Web
Second Semester
Electronics
Allied — II — MATHEMATICS — II
Time : 3 hours Maximum : 100 marks
ans ALL ques. in part A, part B and part C.
part A — (10 x two = 20 marks) select the accurate ans :
(a) -r-r + c (b) log f(x) + c
fix)
(c) eflx)+c (d) logf-JLl + c
Kf(x)J
2. The value of the integral / = \e xdx is
o
(a) zero (b) -1
(c) 1 . (d) infinity.
3. ex is
(a) odd function
(b) even function
(c) neither odd or even
(d) sine function.
4. The smallest period of the function sin 2x is
(a) 0 (b) |
(c) n (d) 2/r.
5. The solution of y = px+alp is
(a) y=cx+a/c (b) y = pc+a/p
(c) y2 -2xc+c2 (d) None of the above.
6. The solution of (D2 + 5D - 6)y = 0 is
(a) y=Ae2x+Be3x (b) y = Ae'2x+BeZx (c) y^Ae^+Bc* (d) y=Ae6x+£e-\
7. If /"(*) = 1, L{f(t)) is equal to
(a) i (b) i
(c) i (d) !¦•
S£ S
8. L"1 is provided by
\s-aj
(a) cos at (b) sin a*
(c) t (d) eat.
9. Shortest distance ranging from the lines rsc^+J/J,
r - a2 +tf2 is provided by
| [a!+a2,/i,^] |
(a) J —-__ L
(b) 1 K-g2>A>/2) |
\fi*f2 I
, x I [«! a2, /i, /2] I
(C) J __ _ L
I AX/2 I
(d) None of the above.
10. The radius of the sphere 3x2 +Sy2 +3z2 -Gx +
9y-3z~7 =0 is
, ^ 7 ru\ [35"
(a) -« (b) J-—
V2 V 6
(c) I (d) #.
4 6
part B — (5 x six = 30 marks)
11. (a) Evaluate :
rs r 2x+l ,
(l) -2 -dx
(ii) \logxdx.
Or
(b) obtain the reduction formula for In = jxneaxdx.
12. (a) discuss how fourier coefficients a0,an and
bn are evaluated for a function to be expanded as a
Fourier series.
Or
(b) Show that if fix) is an odd function, then its Fourier series expansion contains no cosine terms.
13. (a) Solve xyp2 + p(3x2 - 2y2) - 6xy = 0 .
Or
(b) Solve & + 8&-0. ax CLX
14. (a) If F(s) is the Laplace Transform of fit),
show that the Laplace transform of fiat) is —fis/a).
a
Or (b) obtain the Laplace transform of e'at.
15. (a) obtain the condition for the lines r=a+tf
and r =b+sg to be coplanar.
Or
(b) obtain the formula of a sphere which touches the sphere x2 +y2 +z2 -6x + 2z +1 = 0 at the point (2, -2, 1) and passes through the origin.
part C — (5 x 10 = 50 marks)
16. (a) Evaluate f ^^ dx.
J(*-l)2(*+3)
Or
(b) By changing the order of integration,
evaluate J J dxdy .
o x y
17. (a) find the Fourier series expansion of the
function f(x) = x of period 2n with -n
(b) obtain a sine series for fix) = c in the range 0 to n.
18. (a) Solve y=xp+x(l + p2)2.
Or (b) Solve (D2 -SD + 2)Y = sin 3x .
19. (a) obtain L~l two a + two .
_(s2+4s + 5)_
Or
(b) Solve ^-2^-y « 3sin* if y(0) = two and dt2 dt
y'(Q) - 0 using Laplace Transform
20. (a) obtain the length of the common perpendicular
, ,, ,. x+2 y + six z-Sy ,
drawn to the lines = = — and
2 three -10
x+6 y-1 z-1 . ., ,
= = using vector method.
4-3-2 5
Or
(b) obtain the formula of the sphere passing through the 3 points (0, 2, 3), (1, 1, -1), (-5, 4, 2) and having its centre on the plane 3x + 4y + 2z = six .
| Earning: Approval pending. |
