Bharati Vidyapeeth 2007 B.E Biotechnology maths - Question Paper

Frequency six 27 72 112 71 32
Test the hypothesis that the data follow a binomial distribution.
(c) A certain stimulus administered to every of 12 patients resulted in the subsequent
change in blood pressure, 5, 2, 8, -1, 3, 0, -2, 1, 5, 0, 4, 6. Can it be
concluded that the stimulus will increase the blood pressure? (6+7+7)
6. (a) discuss the one-way and Two-way classification of ANOVA.
(b) 3 varieties A, B, C of a crop are tested in randomized block design with four
replications as follows:
Variety one two three 4
A six four eight 6
B seven six 6 9
C eight five 10 9
Analyze the experimental outcomes and state your conclusion.
(c) discuss the limitation of designs of experiments. (8+6+6)
7. (a) discuss the Lung Cancer and elaborate the causes for Lung Cancer?
(b) describe : (i) commensalisms
(ii) Mutualism
(iii) Growth equations of microbial populations. (10+10)
8. (a) discuss the Microbial Growth in chemostat.
(b) define the Genetic inbreeding models. (10+10)
Visvesvaraya Technological University
Model ques. paper-I
THIRD SEMESTER B.E. exam
ENGINEERING MATHEMATICS-III (06 MAT 31)
(Common to all Branches)
Time: 03 hours Max. Marks: 100
Note: ans any 5 ques. choosing atleast 2 from every part
PART-A
1. (a) obtain the Fourier series for the function ( ) (2 ) in (0,2 ) f x x x p p = - .
(b) find the cosine half range Fourier series for two ( ) ( 1) in 0 one f x x x = - < < .
(c) obtain the complex form of the Fourier series for () in ( 1,1) x f x e- = - .
(7+7+6)marks
2. (a) find the finite Fourier transforms of
1 0 one 2
( )
1, ,1/2 1
x
f x
x
- < < ì
= í < < î
(b) obtain the Fourier sine transforms of . x e- Hence show that
2 0
sin
, 0
2 1
m x mx e
dx m
x
p - ¥ = >
+ ò .
(c) obtain the inverse Fourier sine transform of , 0
au e
a
u
-
> .
(7+7+6)marks
3. (a) Form the P.D.E by eliminating the arbitrary functions from
1 two ( ) ( ) z x f x t f x t = + + + .
(b) Use the separation of variables technique to solve three two 0 x y u u + = with
- x u(x, 0)=4e .
(c) Solve: two 2 two ( ) ( ) ( ) x y z p y z xq z x y - + - = - .
(7+7+6) marks
4. (a) Derive the 1 dimensional heat formula in the standard form.
(b) Determine the displacement ( , ) u x t of string if
2 3
0 , (0, ) 0, ( , ) 0, ( , 0) 0 and ( ,0) sin tt xx t
x
u c u u t u t ux ux u
p æ ö = = = = = ç ÷
è ø
l
l
.
(c) find the different possible solutions of the Laplace’s formula 0 xx yy u u + = by
the method of separation of variables.
(7+7+6) marks
PART-B
5. (a) obtain the approximate value of the real root the formula 10 two log seven x x - = by
Newton-Raphson method.
(b) Solve the subsequent system of equations by Gauss-Seidel iteration method:
20 two 17
3 20 18
2 three 20 25
x y z
x y z
x y z
+ - =
+ - = -
- + =
Carry out three iterations.
(c) obtain the largest eigen value and the corresponding eigen vector of the subsequent
matrix by using power method
2 0 1
0 two 0
1 0 2
A
é ù
ê ú =ê ú
ê ú ë û
. Take [1 0 0]T as the initial eigen vector.
(7+7+6) marks
6. (a) From the subsequent table, estimate the number of students who found marks
ranging from 40 and 45.
Marks 30-40 40-50 50-60 60-70 70-80
No. of students 31 42 51 35 31
(b) Use Newton’s divided difference formula to calculate y at x = nine for the
subsequent data
x five seven 11 13 17
y 150 392 1452 2366 5202
(c) Using Simpson’s one-third rule, evaluate 1
0
1
1
dx
x + ò by taking seven ordinates and
hence obtain the value of log two e .
(7+7+6) marks
7. (a) Derive the Euler’s formula in the form 0
f d f
y dx y
æ ö ¶ ¶
- = ç ÷¢ ¶ ¶è ø
.
(b) obtain the extremal of the functional 2
1
2 two ( two sec ) x
x
y y y x dx ¢ - + ò .
(c) Show that the geodesics on a plane are straight lines.
(7+7+6) marks
8. (a) obtain the Z- transforms of two ( ) cos (a)n b nq .
(b) obtain the inverse Z-transform of
3
3
8
(4 )
z z
z
-
-
.
(c) Solve the difference equations of two one three two one n n n u u u + + - + = by using Z-transforms.
(7+7+6) marks

Earning:   Approval pending.