Sir I want the organic chemistry questions set for the semester 5...plz any one provide

 [4317] – 404
T.Y. B.Sc. (Semester – IV) Examination, 2013
MATHEMATICS (Paper – IV)
MT-344 : Ring Theory
(2008 Pattern) (New Course)
Time : 2 Hours Max. Marks : 40
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
1. Attempt any five of the following : 10
a) Let a belong to a ring R. Let = ∈ |Rx{S ax = }0 . Show that S is a subring
of R.
b) List all zero-divisors in 13.
c) Find all maximal ideals in 12.
d) Show that the function f :5 →10 given by f(x) = 3x is not a homomorphism.
e) Find zeros of x2 + 3x + 2 in 6.
f) Determine whether the polynomial x4 + 3x + 3 is irreducible over . Justify.
g) Show that in the ring [i]; 13 is reducible element.
2. Attempt any two of the following : 10
a) Prove that a finite integral domain is a field.
b) Let R = {0, 2, 4, 6, 8} under addition and multiplication modulo 10. Write
addition and multiplication table for R. Is R is a field ? Explain.
c) Prove that the only ideals of a field F are {0} and F itself.
Seat
No.
[4317] – 404 
B/I/13/1,825
3. Attempt any two of the following : 10
a) Let R be a ring with unity e. Then show that the mapping φ :→R given by
n →ne is a ring homomorphism.
b) Let φ be a ring homomorphism from a commutative ring R onto a cummutative
ring S and let A be a prime ideal of S. Then show that }A)x(/Rx{)A(1 ∈φ∈=φ −
is a prime ideal in R.
c) Let F be a field. Then show that F[x] is a principal ideal domain.
4. Attempt any one of the following :
a) i) In a principal ideal domain prove that an element is an irreducible if and
only if it is a prime. 7
ii) If a, b are associates in an integral domain D. Then prove that <a> = <b>,
where <a> denotes the ideal generated by a. 3
b) i) Prove that in a principal ideal domain, any strictly increasing chain of
ideals II .... 21 ⊂⊂ must be finite in length. 5
ii) Show that the polynomial xp–1+ xp–2+...+1 is irreducible over . 5
———————
 [4317] – 407
T.Y. B.Sc. (Semester – IV) Examination, 2013
MATHEMATICS (Paper – VII) (Ele. – II)
MT – 347 : Computational Geometry
(2008 Pattern)
Time : 2 Hours Max. Marks : 40
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
1. Attempt any five of the following : 10
i) An object is rotated through angle 90° about the point [4 3]. Obtain the
transformation matrix.
ii) Write any two properties of Bezier curve.
iii) If we apply transformation matrix T = ⎥
⎦
⎤
⎢
⎣
⎡
22
13 on a square, then we get a
parallelogram of area 64 cm2. Find the length of each side of the original
square.
iv) Find the angle δθ to generate 11 equidistant points on the parabolic segment
y2 = 4x, 2 < y < 4.
v) Define Dimetric projection. Find the angle θ about X axis if fz = . 2
1
vi) Write down the transformation matrix T if we want to expand the size of the
cube four times the unit cube.
vii) Obtain the transformation matrix to create the top view of the object.
2. Attempt any two of the following : 10
i) If the line y = mx + h is transformed onto the line ∗∗∗∗ += hxmy under the
matrix T = ⎥
⎦
⎤
⎢
⎣
⎡
dc
ba then prove that a cm
b dm m
+
+ =∗ and . a cm
bcad hh ⎟
⎠
⎞ ⎜
⎝
⎛
+
− =∗
Seat
No.
P.T.O.
[4317] – 407 -2- 
ii) Reflect the triangle ABC through the line y = 5 where A[13], B[2 4] and C[3 5].
iii) Obtain the concatenated matrix of the following transformations. Translate in x,
y and z directions by – 1, 2, 1 units respectively. Rotate about z-axis by 90°.
Reflect in XY plane. Apply the concatenated matrix on the point A[3 2 1].
3. Attempt any two of the following : 10
i) Obtain the transformation matrix for the trimetric projection formed by rotation
about Y-axis through an angle 30°=φ followed by rotation about X-axis
through 45°=θ and then orthographic projection on Z = 0 plane. Also determine
the principal foreshortening factors.
ii) Obtain an algorithm to generate uniformly spaced n points on the ellipse
.1
b
y
a
x
2
2
2
2
=+
iii) Obtain the combined transformation matrix of the following transformations.
Reflection through the line y = – x, shearing in X and Y directions by 3, – 4
units resp. Translation in X and Y directions by – 1, 2 units respectively.
Apply on point P[3 – 8].
4. Attempt any one of the following : (10)
i) a) Generate 8 points on the circle (x – 2)2 + (y – 4)2 = 25. 6
b) Perform the perspective projection onto the z = 0 plane of the standard
unit cube from the center of projection at zc = 10 on z-axis. 4
ii) a) Find the cabinet projection of the object represented by matrix X with a
horizontal inclination 25°=α .
X =
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−−
−
112
121
143
121
5
b) Write the parametric equation of a Bezier curve determined by control
points B0[1 1], B1[2 3], B2[4 3] and B3[3 1]. Find the position vector of a
point corresponding to t = . 2
1 5
–––––––––––––––––
B/I/13/630
P.T.O.
 [4317] – 408
T.Y.B.Sc. (Semester – IV) Examination, 2013
MATHEMATICS (Paper – VII) (Ele. – II)
MT-347 : Optimization Techniques
(New Course) (2008 Pattern)
Time : 2 Hours Max. Marks : 40
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
1. Attempt any five of the following : 10
i) State the ‘No Passing Rule’ in a sequencing problem.
ii) Explain the three time estimates used in the context of PERT.
iii) What is a float ? What are the different types of floats ?
iv) Player A and player B play a game in which each has 3 coins – a 5p, a 10 p
and a 20p. Each selects a coin without the knowledge of the other’s choice.
If the sum of the coins is an odd amount, then A wins B’s coin; but if the sum
is even then B wins A’s coin. Determine the payoff matrix for player A.
v) Write any two assumptions of a sequencing problem.
vi) Consider the function f(x) = x1 + 2x2 + x1x2 – x1
2 – x2
2. Determine the
maxima and minima of the function (if any)
vii) Define :
a) Saddle Point
b) Optimal strategies.
Seat
No.
[4317] – 408 -2- 
2. Attempt any two of the following : 10
i) Machine A costs Rs. 45,000/- and the operating costs are estimated at
Rs. 1,000/- for the first year increasing by Rs. 10,000/- per year in the
second and subsequent years. Machine B costs Rs. 50,000/- and operating
costs are Rs. 2,000/- for the first year, increasing by Rd. 4,000/- in the
second and subsequent years. If we now have a machine of type A, should
we replace it with B ? If so when ? Assume that both machines have no
resale value and future costs are not discounted.
ii) Using graphical method, obtain the optimal strategies for both players and
the value of the game for two-person zero-sum game whose payoff matrix
is given as follows :
Player A Player B
B1 B2
A1 −6 7
A2 4 −5
A3 −1 −2
A4 −2 5
A5 7 -6
iii) Explain the principle of Dominance in Game Theory and solve the following
game :
Player A Player B
B1 B2 B3
A1 17 2
A2 62 7
A3 52 6
3. Attempt any two of the following : 10
i) Determine the optimal sequence of jobs that minimise the total elapsed time
based on the following information. Processing time on machines is given in
hours. Also compute the minimum time and ideal time for each machine.
(Processing order is AB).
Job I II III IV V VI VII
Machine A 3 12 15 6 10 11 9
Machine B 8 10 10 6 12 1 3
ii) Construct a network of project whose activities and their precedence
relationships are as given below :
Activity ABCDEFG H I J
Predecessor - A B B B C C F, G D, E, H I
iii) Find the optimum solution of the following constrained multivariable problem :
Minimize ( )( )2
3
2
2
2
1 −+++= 1x1xxZ
Subject to the constraint
x1 + 5x2 – 3x3 = 6.
4. Attempt any one of the following : 10
i) A small project consists of seven activities, the details of which are as given
below :
 -3- [4317] – 408
Activity
Duration (days)
Immediate
Most Predecessor
likely Optimistic Pessimistic
A3 1 7 -
B 6 2 14 A
C3 3 3 A
D 10 4 22 B, C
E 7 3 15 B
F 5 2 14 D, E
G4 4 4 D
a) Draw network diagram for this project.
b) Compute the expected project completion time.
ii) A project schedule has the following characteristics :
Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10
Duration
(days) 411165481257
a) Draw the network and find the critical path.
b) Find project completion time.
c) Determine the total float and free float of each non-critical activity.
————————
B/I/13/1,180
[4317] – 408 -4- 
P.T.O.
 [4317] – 409
T.Y.B.Sc. (Semester – IV) Examination, 2013
MATHEMATICS (Paper – VII) (Ele. – II)
MT-347 : Improper Integrals and Laplace Transforms
(New) (2008 Pattern)
Time : 2 Hours Max. Marks : 40
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
1. Attempt any five of the following : 10
a) Prove that ∫
∞
−
0
x e dx is convergent.
b) Find Cauchy’s Principal Value of dx
x
1 ∫ 3
∞
∞−
.
c) Prove that dx
x
Sinx
1
∫ 2
∞
is absolutely convergent.
d) By using the integral test prove that ∑
∞
=1n
2 n
1
is convergent.
e) Classify the following integrals according to the types of improper integrals :
dx
x
Sinx )( 1
0∫ α ∫ − β 3
1 2 )4x(
dx )(
f) Evaluate ⎭
⎬
⎫
⎩
⎨
⎧
+
−
)1s(s
1 L 1 .
g) If C1 and C2 are any two constants and L {F1(t)} = f1(s), L{F2(t)} = f2(s); then
prove that L{C1F1(t) + C2F2(t)} = C1f
1(s)+C2f
2(s).
Seat
No.
[4317] – 409 
B/I/13/1,320
2. Attempt any two of the following : 10
i) Show that the improper integral dx
x
1
a
∫ p
∞
converges if p > 1 and diverges if
p < 1.
ii) Prove that e dx
1
2x
∫
∞ − is convergent.
iii) Prove that ∫ −
1
0 )x1(x
dx
is convergent.
3. Attempt any two of the following : 10
i) Evaluate ⎭
⎬
⎫
⎩
⎨
⎧
+
−
)1S(S
1 L 23
1 .
ii) If L–1{f(s)} = F(t), then prove that L–1 {e–asf(s)}=G(t), where
⎩
⎨
⎧
<
>− = at,0
at(F ), at )t(G
iii) Discuss the convergence of ∫ − 1
0
1n x logx dx .
4. Attempt any one of the following : 10
i) State and prove the convolution theorem .
ii) Solve :
a) ( ) 1 2 ′′ Y9Y =+ Cos = Y,1)0(Y:t2 π −= .
b) Evaluate ∫
π
θ
2 θ
0 tan
d .
—————————
P.T.O.
 [4317] – 410
T.Y.B.Sc. (Semester – IV) Examination, 2013
MATHEMATICS (New Course) (Paper – VII) (Ele. – II)
MT-347 : C PROGRAMMING – II
(2008 Pattern)
Time : 2 Hours Max. Marks : 40
N.B. : i) All questions are compulsory.
ii) Figures to the right indicate full marks.
1. Attempt any five of the following : 10
i) What does the statement : int s = sizeof (struct point) ; do ?
ii) Write C statement that defines a pointer to another pointer that points to an
integer value.
iii) State True/False.
Bitwise operators only work on limited types : int and char (and variations of int)
iv) Explain the use of #undef.
v) Justify True/False
A variable of register storage type is always stored in the computers Random
Access Memory (RAM).
vi) Explain the use of feof() function.
vii) What does the following C statement define ?
char *name [10];
2. Attempt any two following : 10
i) Define a structure called point having two members of type int indicating the
pair (x, y). Write a C program that translates this point by a value ‘v’ to
obtain a new point. Display the x and y values of the translated point.
ii) Explain the concept of passing parameters to a function by reference. Write
C function void swap (int *x, int *y) that swaps the values of variables x and y.
iii) What are bitwise operators ? Explain any four bitwise operators.
Seat
No.
[4317] – 410 
B/I/13/380
3. Attempt any two of the following : 10
i) Write a C program to display the sum of diagonal elements of a square
matrix. Accept the matrix form the user.
ii) Explain the fprint () and fscanf() functions with the help of examples.
iii) Explain the auto and extern storage class with the help of examples.
4. Attempt any one of the following : 10
i) a) Trace the output of the following piece of C code
#include<stdio.h>
#define A 4 – 2
#define B 3 – 1
int main () {
int ratio=A/B;
printf (“%d”, ratio);
return 0;
}
b) Write a short note on pointer arithmetic.
ii) a) Trace the output of the following piece of C code
void main ()
{
int i = 4, j = 3;
xyz (&i, &j);
printf (“%d, %d”, i, j);
}
void xyz (int *i, int*j)
{
*i = *i * *i;
*j = *j * *j;
b) What is a union ? Differentiate between a union and a structure data type.
———————
P.T.O.
 [4317] – 411
T.Y. B.Sc. (Semester – IV) Examination, 2013
MATHEMATICS (Paper – VII)
MT 347 : Dynamics (Ele. – II)
Time : 2 Hours Max. Marks : 40
Instructions : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
1. Attempt any five of the following : 10
a) A particle moves along the curve r = b cos pti – c sin ptj where b, c, p are
positive constants. Show that the acceleration is directed towards the origin.
b) A body having mass 0.25 kg starts from rest with uniform acceleration and
travels 8 meters in 2 seconds. Find the force acting on it.
c) If the maximum horizontal range of a particles is R, show that the greatest
height attained is R
4
1 .
d) If a particle is projected up an inclined plane with inclination α with initial
velocity u. Determine the time when the particle will come to instantaneous
rest.
e) The pedal equation of an ellipse referred to focus as pole is
1
r
a2
p
b
2
2
−=
Find the law of force if the particle is moving along this ellipse.
f) A body whose true weight is 13 kg appeared to weigh 12 kg by means of a
spring balance in a moving lift. What was the acceleration of the lift at the
time of weighing ?
g) If the angular velocity of a moving particle about a fixed origin be constant,
show that its transverse acceleration varies as its radial velocity.
Seat
No.
[4317] – 411 
2. Attempt any two of the following : 10
a) Obtain tangential and normal components of velocity and acceleration.
b) The sum of two weights of an Atwood’s machine is 16 kg. The heavier weight
descends 24.5 meters in 4 seconds. What is each weight ?
c) A particle is projected vertically upwards with a velocity u m/sec and after t
seconds, another particle is projected upwards from the same point and with
the same velocity. Prove that the particles will meet at a height g8
tgu4
222 −
meters after a time ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ +
g
u
2
t seconds from the start.
3. Attempt any two of the following : 10
a) A particle of mass m is projected from a fixed point with velocity u in the
horizontal plane, in a direction making an angle α with the horizontal. Obtain
the equation of the trajectory.
b) Prove that the work done in stretching an elastic string AB, of natural length l
and modulus of elasticity λ , from tension T1
to tension T2 is ( ) 2
1
2
2 − TT
λ
l .
c) Show that for a given velocity of projection, the maximum range down a plane of
inclination α is greater than that up the plane in the ratio (1 + sin α ) : (1 – sin α ).
4. Attempt any one of the following : 10
a) i) For a particle describing a central orbit, derive the equation
⎥
⎦
⎤ ⎢
⎣
⎡
θ = + 2
2
22
d
ud uuhF
ii) To a man walking at the rate of 4 km/hr, rain appears to fall vertically. If
actual velocity of rain is 8 km/hr, find its actual direction.
b) i) State Kepler’s Laws of planetary motion. Also, state Newton’s law of
Gravitation.
ii) A particle is projected with a velocity of 60 m/sec at an angle 60° with the
horizontal, from the foot of an inclined plane of inclination 30° with the
horizontal. Find the time of flight and the range of the particle on the inclined
plane.
————————
B/I/13/215
 [4317] – 416
T.Y. B.Sc. (Semester – IV) Examination, 2013
PHYSICS (Paper – IV)
PH-344 : Nuclear Physics
(2008 Pattern)
Time : 2 Hours Max. Marks : 40
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
3) Use of log table and calculator is allowed.
1. Attempt all of the following (1 mark each) : 10
a) Define the term – Packing fraction.
b) State any two properties of β rays.
c) Find the amount of energy released, when a milligram of mass is converted
into energy.
d) Define Half life of a radioactive substance.
e) State any two limitations of shell model of nuclear structure.
f) Which type of material is used for ionization in solid state counters ?
g) Define threshold energy of the projectile in nuclear reaction.
h) Define effective multiplication factor for chain reaction in the nuclear reactor.
i) What is meant by heterogeneous reactor ?
j) What is dead time in the GM counter ?
2. Attempt any two of the following :
a) What are mesons ? Explain in brief Meson theory of nuclear forces. 5
b) What is nuclear reactor ? Explain swimming pool type reactor. 5
c) Show that the Q value is given by 5
− θ ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −− ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ += cos
m
EEmm2
E
m
m 1E
m
m 1Q
3
4141
1
3
1
4
3
4
Seat
No.
P.T.O.
[4317] – 416 -2- 
3. Attempt any two of the following :
a) Calculate the binding energy and binding energy per nucleon in the case of
29Cu64 whose mass is 63.9297 amu
Give mp = 1.007825 a.m.u.
mn = 1.008665 a.m.u. 5
b) What thickness of cadmium sheet would absorb 99 percent of the thermal
neutrons incident on it ? The thermal neutron cross section of Cd112 is 2537
barn, density of Cd is 8.6 g/cm3. 5
c) A cyclotron has a magnetic field of 1.5 Wb/m2. The extraction radius is 0.5 m.
Calculate (i) the frequency of oscillator for accelerating the deuterons
(ii) the energy of the extracted beam. 5
4. A) Attempt any one of the following :
a) Describe the shell model of nuclear structure with reference to assumptions
and evidences. 8
b) Give theory of successive disintegration of radioactive substance. Explain
what is radioactive equilibrium ? 8
B) Attempt any one of the following :
a) Compute the mass of 1 curie of C14. The half life of C14 is 5700 yrs. 2
b) Define the terms : Mass defect and Binding Energy. 2
–––––––––––––––––
B/I/13/2,220
 [4317] – 418
T.Y. B.Sc. (Semester – IV) Examination, 2013
PHYSICS (Paper – VI) (Elective – II)
PH-346 (1) : Electro Acoustics and Entertainment Electronics
(2008 Pattern)
Time : 2 Hours Max. Marks : 40
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
3) Use of log table and calculator is allowed.
1. Attempt all of the following (one mark each) : 10
a) Give frequency theory of hearing.
b) Draw a diagram showing construction of condenser microphone. Give its
equivalent circuit.
c) What is articulation test ?
d) What is meant by dynamic range ?
e) What is volume expander ?
f) Define directivity factor for a microphone.
g) Give two advantages of folded horns.
Seat
No.
P.T.O.
[4317] – 418 -2- 
h) What is an equalizer ?
i) What do you mean by articulation score ?
j) Give place theory of hearing.
2. Attempt any two :
a) Explain how is the required output power of an amplifier, to be installed in an
auditorium, calculated ? 5
b) Give strengths of medical ultrasonography. 5
c) Distinguish between monophonic and stereophonic sound reproducing systems. 5
3. Attempt any two :
a) Determine the cut-off frequency of an exponential horn having a flare constant
of 4.9 on being used outdoors at a temperature of 40°C. 5
b) On a level detector type reverberation time measuring instrument, the upper
and lower levels are 2.1 volts and 1.1 volts respectively. If the time elapsed
between the two levels is 0.11 sec, determine the reverberation time. 5
c) A condenser microphone diaphragm of radius 0.01 m is stretched to a tension
of 2 × 104 N/m. If the spacing between the diaphragm and the backing plate is
4 × 10–5 m, determine the open circuit voltage response for a polarizing
voltage of 250 V. 5
4. A) Attempt any one :
a) Discuss acoustics of hearing mechanism in humans. 8
b) Compare variable area and variable density motion picture sound recording
systems. 8
B) Attempt any one :
a) Distinguish between voiced and unvoiced sounds. 2
b) Sketch the super cardioid and hyper cardioid polar response of microphones. 2



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