Guru Nanak Dev University 2007-3rd Sem B.Sc Chemistry MATHEMATICS (CHEM-305) (, 2k7) - Question Paper
2117
B.Sc. (H.S.) 3rd Semester
CHEMISTRY
Paper - Chem-305
(Mathematics)
Time Allowed : 3 Hours
Maximum Marks : 75
NOTE : SECTION-A is compulsory. Attempt any eight ques. from SECTION-B. Attempt any two ques. from SECTION-C.
(Refer to the attachment for the ques. paper.)
I v "1 I u
54152117
B.Sc. (H.S.) Third Semester CHEMISTRY PaperChem-305 (Mathematics)
Time allowedThree Hours] [Maximum Marks75
Note :Section A is compulsory. Attempt any 8 questions from Section B. Attempt any 2 questions from Section C.
SECTIONA
(each IV2 marks)
1. (($'' Define order and degree of the differential equations.
(pf Form the differential equation, if
y = ex(A cos x + B sin x).
j#f Form the partial differential equation from
z = f(x2 - y2).
Solve :
r + 6s + 9t = 0.
J<) Write the formula of Trapezoidal rule. Give its order of error also.
(f)/t)escribe the Homers method to find the roots of f(x) = 0.
What are Dirichlets conditions ?
fK) Write the Fourier integral of f(x).
Find the Laplace transform of (eat + e~at).
Xff If f(t) is a periodic function with period T, then give L{f(t)}.
SECTIONB
Solve :
(x2 - y2)dx - xydy = 0. jyy Find particular integral of
(D2 - 2D + 4)y = ex cos x.
4. The number N of bacteria in a culture grew at a rate proportional to N. The value of N was initially 100 and increased to 332 in one hour. What would be the value of N after 1 lA hours ?
(sT) Solve the equation y2z p + x2z q = y2x.
6. Solve the partial differential equation
d2y 2 d2y r .
r--a - = Esmpt. at2 5x2
Tf' Evaluate :
1 z x+z
JJ J (x + y + z) dx dy dz.
-1 0 x-z
8. Find a negative root ofx3 -21x + 3500 = 0 correct to 2 decimal places using Newton Raphson method.
i |
Evaluate J --dx taking 6 subintervals by using
1
Simpsons rule.
Express f(x) = ex as a Fourier series in the interval
0 < x < 27i.
(cos 2t - cos 3t)
_JFind the Laplace transform of
t
Using Convolution theorem, evaluate
L-1
(s2 +a2)2
Jf3r Solve the differential equation
1 2
- + 2 + 5y = el sint, where y(0) = 0 and dr dt
y'(0) = 1, using Laplace transforms. SECTIONC
14. (a)Solve :
d2y . ,
- 4y = x sin hx.
dx
(b) Solve 2z + p2 + qy + 2y2 = 0, using Charpits method.
15. (a) Show using double integrals that the area between
2 2 3
the parabolas y = 4ax and x = 4ay is a .
(b) Find the centre of gravity of the cardioid r = a(l + cos 9).
16. Obtain a half range cosine series for f(x) given by :
f kx for -7t<x<0;
f(x) = i . , . 8 x + 1 for 0<x<n.
1 1 1
Also deduce the sum of the series + "T +......
I2 5l
4
17. (a) Solve the simultaneous equations
-y = et, + x = sint given that x(0) = 1, dt dt
y(0) = o.
x2 x4 x6
(b) If J0(x) = l-+
22 22-42 22-42-62 then find the Laplace transform of J0(x).
5415 4 100
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