B.Sc Corporate Mathematics Question Paper 2012

Loyola College B.Sc. Mathematics Nov 2012 Graphs, Diff. Equ., Matrices & Fourier Series Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – NOVEMBER 2012

MT 1501 – GRAPHS, DIFF. EQU., MATRICES & FOURIER SERIES

 

Date : 10/11/2012               Dept. No.                                          Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

Answer ALL the questions                                                                                                    (10 X 2 = 20 Marks)

  1. Let f: be defined by.  Find the  range of the function .
  2. Find the equation of the line passing through (-3,4) and (1,6).
  3. Write the normal equation of y = a+bx.
  4. Reduce y = aebx to normal form .
  5. Define Difference equation with an example.
  6. Solve yx+2 – 4yx=0.
  7. State Cayley Hamilton theorem.
  8. Find the eigen value of the matrix .
  9. Find the Fourier coefficient a0 for the function f(x) = ex in (0,2π).
  10. Define odd and even function.

PART – B

Answer any FIVE questions                                                                                                                 (5 X 8 = 40 Marks)

  1. A company has a total cost function represented by the equation y = 2x3-3x2+12x, where y

represents cost and x represent quantity.  (i) what is the equation for the Marginal cost function?

(ii) What is the equation for average cost function? What point average cost is at its minimum?

  1. The total cost in Rs.of output x is given by . Find  Cost when output is 4 units.

(i)   Average cost of output of 10 units.

(ii)  Marginal cost when output is 3 units.

  1. Fit a straight line to the following data. Estimate the sale for 1977.
Year: 1969 1970 1971 1972 1973 1974 1975 1976
Sales(lakhs) 38 40 65 72 69 60 87 95
  1. Solve yx+2 – 4yx = 9x2.
  2. Find the eigen vectors of the matrix .
  3. Verify Cayley Hamilton theorem for the matrix A =
  4. Expand f(x) = x (-π <x< π) as a Fourier series with period 2 π.
  5. Obtain a Fourier series expansion for f(x) = – x  in the range (-π,0)

=      x   in the range [0, π).

PART – C

Answer any TWO  questions                                                                                                            (2 X 20=40 Marks)

  1. (a) Fit a curve of the form y = a + bx +c x2 for the following table:
                X: 0 1 2 3 4
Y: 1 1.8 1.3 2.5 6.3

 

(b)  The total profit y in rupees of a drug company from the manufacture and sale of x drug

bottles is given by  .

(i) How many drug bottles must the company sell to achieve the maximum  profit?

(ii) What is the profit per drug bottle when this maximum is achieved ?                                                     (10+10)

  1. (a) Solve yx+2 – 7yx+1 – 8yx = x(x-1) 2x.

(b) So lve u(x+1) – au(x) = cosnx.                                                                                                                                 (10+10)

  1. (a) Find the Fourier series of period 2 π for  f(x) = x2 in (o,2 π) . Deduce

(b)  Find the Fourier (i) Cosine series (ii) Sine series for the function f(x) =  π-x  in (0, π).                        (10+10)

 

 

  1. (a) Determine the Characteristic roots and corresponding vectors for the matrix

.Hence diagonalise A.

 

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Loyola College B.Sc. Mathematics Nov 2012 Fluid Dynamics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIFTH SEMESTER – NOVEMBER 2012

MT 5405 – FLUID DYNAMICS

 

 

Date : 10/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

Section A

Answer ALL questions:                                                                                                                         10 ´ 2 = 20

 

  1. Define stream tube.
  2. Show that is a possible motion.
  3. The velocity vector q is given by determine the equation of stream line.
  4. Write down the boundary condition for the flow when it is moving.
  5. What is the complex potential of a source with strength m situated at the points z=z1
  6. Find the stream function y, if j = A(x2 – y2) represents a possible fluid motion
  7. Find the vorticity vector for the velocity
  8. Define vortex tube and vortex filament.
  9. What is lift of an aerofoil?
  10. Define camber.

Section B

Answer any FIVE questions:                                                                                        5 ´ 8 = 40

  1. Explain Material, Local and Convective derivative fluid motion.
  1. Find the equation of streamlines and path lines of a flow given by
  1. Explain the construction of a Venturi tube.
  2. Prove that for the complex potential the streamlines and equipotentials are circles.
  3. For an incompressible fluid. Find the vorticity vector and equations of stream line.
  4. Derive the equation of continuity.
  5. Find the stream function y(x, y, t) for a given velocity field u = 2Axy, v = A(a2 + x2 – y2).
  6. State and prove the theorem of Kutta-Joukowski.

 

Section C

Answer any TWO questions:                                                                                                      2 ´ 20 = 40

  1. (a) For a two-dimensional flow the velocities at a point in a fluid may be expressed in the Eulerian coordinates by u = x + y + t and v = 2x+2y + t. Determine the Lagrange coordinates as functions of the initial positions, and the time t.

(b) If the velocity of an incompressible fluid at the point (x, y, z) is given by  where . Prove that the fluid motion is possible and the velocity potential is .                                                                       (10 + 10)

 

  1. Derive the Euler’s equation of motion and deduce the Bernoulli’s equation of motion.

 

  1. (a)What arrangement of sources and sinks will give rise to the function?

(b)Obtain the complex potential due to the image of a source with respect to a circle.    (12+8)

 

  1. (a)Discuss the structure of an aerofoil.

(b)Derive Joukowski transformation.                                                                   (8+12 )

 

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Loyola College B.Sc. Mathematics Nov 2012 Business Mathematics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FOURTH SEMESTER – NOVEMBER 2012

MT 4205 – BUSINESS MATHEMATICS

 

 

Date : 05/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART A

Answer ALL the questions:                                                                                                   ( 10 X 2 = 20)

 

  1. Find the equilibrium price and quantity for the functions  and
  2. If the demand law is find the elasticity of demand in terms of x.
  3. Find if .
  4. Find the first order partial derivatives of .
  5. Evaluate
  6. Prove that .
  7. If and , find .
  8. If , find .
  9. If  then find A and B
  10. Define Linear Programming Problem.

PART B

Answer any FIVE of the following:                                                                               (5x 8=40)

  1. The total cost C for output x is given by . Find (i) Cost when output is 4 units (ii) Average cost of output of 10 units (iii) Marginal cost when output is 3 units.
  2. If then prove that .
  3. Find the first and second order partial derivatives of .
  4. Integrate with respect to x.
  5. Prove that (i) , if f(x) is an even function.

(ii) , if f(x) is an odd function.

  1. If  then show that .
  2. Compute the inverse of the matrix .
  3. Integrate with respect to x.

PART C

Answer any TWO questions:                                                              ( 2 X 20 = 40)

  1. (a) If AR and MR denote the average and marginal revenue at any output, show that elasticity of demand is equal to . Verify this for the linear demand law .

(b) If the marginal revenue function for output x is given by , find the total revenue by integration. Also deduce the demand function.

  1. (a) Let the cost function of a firm be given by the following equation: where C stands for cost and x for output. Calculate (i) output, at which marginal cost is minimum (ii) output, at which average cost is minimum (iii) output, at which average cost is equal to marginal cost .

(b) Evaluate .

  1. (a) Find the maximum and minimum values of the function .

(b) Solve the equations  by Crammer’s rule.

  1. (a) The demand and supply function under perfect competition are and Find the market price, consumer’s surplus and producer’s surplus.

(b) Food X contains 6 units of vitamin A per gram and 7 units of vitamin B per gram and costs 12  paise  per gram. Food Y contains 8 units of vitamin A per gram and 12 units of vitamin B per gram and costs 20 paise per gram. The daily minimum requirements of vitamin A and vitamin B are 100 units and 120 units respectively. Find the minimum cost of the product mix using graphical method.

 

 

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Loyola College B.Sc. Mathematics Nov 2012 Bioinformatics – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS & PHYSICS

THIRD SEMESTER – NOVEMBER 2012

PB 3208 – BIOINFORMATICS – I

 

 

Date : 09/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

                Part –A                                                               (20 marks)

 

Answer the following, each answer within 50 words:                                                    (10×2=20 marks)

 

  1. Mention the central dogma of molecular biology.
  2. Give the types of Mrna.
  3. What is DDBJ?
  4. Expand MIPS and mention its function.
  5. What is a domain?
  6. Give any two objectives of learning bioinformatics.
  7. What is BLAST?
  8. Name any two secondary structures of proteins.
  9. Which database can be accessed to retrieve protein sequences?
  10. Name any two protein structure models.

 

Part B                                                            

 

Answer the following each within 500 words. Draw diagrams wherever necessary:

(5×7=35 marks)

  1. a) Explain the structure of chromosome.

 

(OR)

 

  1. b) Explain the secondary structure of Proteins.

 

  1. a) Define PIR database and explain its types.

 

(OR)

 

  1. b) Define Genomic database and explain the subfields in Genomics.

 

  1. a) Mention the uses of FASTA and BLAST in sequence alignment.

 

(OR)

 

  1. b) Write about Local alignment and Multiple Sequence alignment.

 

 

  1. a) How to study the physical properties of proteins using internet?

 

(OR)

 

  1. b) What are repetitive sequences and how are they masked?

 

  1. a) Compare the usage of WEBTHERMODYN and DNAlive in predicting the physical properties of

DNA.

 

(OR)

 

  1. b) Write about any one protein visualization tool.

 

 

 

                                         Part C                                                                  

 

Answer any three of the following each within 1200 words. Draw diagrams wherever necessary:                                                                                                                                (3×15=45 marks)

 

  1. Explain the structure and function of DNA.
  2. Describe the projects carried out by HGP and mention their applications.
  3. What is OMIM? Mention its significance and the procedure.
  4. Explain Needleman- Wunsch and Smith-Waterman Algorithms.
  5. Describe the steps involved in Gene Finding.

 

 

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Loyola College B.Sc. Mathematics Nov 2012 Astronomy Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

THIRD SEMESTER – NOVEMBER 2012

MT 3502/5503 – ASTRONOMY

 

 

 

Date : 05/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer all questions:                                                                                           (10 x 2 = 20)

  1. What are cardinal points?
  2. Define Zenith and Nadir.
  3. Define Aberration of a celestial body.
  4. What is the use of a Gnomon?
  5. Define sidereal year.
  6. Define dynamical mean sun.
  7. Define an umbra.
  8. What is Harvest Moon?
  9. What are the chief elements present in sun?
  10. Define chromosphere.

PART – B

 

Answer any five questions:                                                                                 (5 X 8 = 40)

 

  1. Write a note on the equatorial system of coordinates.
  2. Trace the variations in the duration of day and night in a place of latitude 5N.
  3. Derive the tangent formula for refraction.
  4. Find an analytical expression for the equation of time.
  5. What are Astronomical seasons? Find their duration.
  6. Give a brief description of the surface structure of moon.
  7. Explain how solar and lunar eclipses are caused?
  8. Write a note on comets.

PART – C

Answer any two questions:                                                                                (2 X 20 = 40)

  1. (i) What is Twilight? Find the number of days that twilight may last throughout night

in a given place.

(ii) Write a note on Morning stars, Evening stars and Circumpolar stars.

  1. (i) Explain any one astronomical instrument with a neat diagram.

(ii) Write a note on the different types of Calendar.

  1. (i) Describe the successive phases of moon with a neat diagram.

(ii) Find the maximum number of eclipses possible in a year.

  1. (i) Describe any two planets of the solar system.

(ii) Write a note on any four constellations visible over Chennai.

 

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Loyola College B.Sc. Mathematics Nov 2012 Analytical Geometry Of 2D,Trig. & Matrices Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – NOVEMBER 2012

MT 1503 – ANALYTICAL GEOMETRY OF 2D,TRIG. & MATRICES

 

 

Date : 10/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

Answer all questions:                                                                                           (10 x 2 = 20)

  1. Write down the expression of cos 4θ in terms of cosθ and sinθ.
  2. Give the expansion of sinθin ascending powers of θ.
  3. Express sin ix and cosix in terms of sin hx and coshx.
  4. Find the value of log(1 + i).
  5. Find the characteristic equation of A = .
  6. If the characteristic equation of a matrix is , what are its eigen values?
  7. Find pole of lx + my + n = 0 with respect to the ellipse
  8. Give the focus, vertex and axis of the parabola
  9. Find the equation of the hyperbola with centre (6, 2), focus (4, 2) and e = 2.
  10. What is the polar equation of a straight line?

PART – B

Answer any five questions.                                                                                 (5 X 8 = 40)

  1. Expandcos6θ in terms of sinθ .
  2. If sinθ = 0.5033 show thatθ is approximately .
  3. Prove that .
  4. If tany = tanα tanhβ ,tanz = cotα tanhβ, prove that tan (y+z) = sinh2βcosec2α.
  5. Verify Cayley Hamilton theorem for A =
  6. Prove that the eccentric angles of the extremities of a pair of semi-conjugate diameters of an ellipse differ by a right angle.
  7. Find the locus of poles of all tangents to the parabola with respect to

 

  1. Prove that any two conjugate diameters of a rectangular hyperbola are equally inclined to the asymptotes.

 

PART – C

Answer any two questions:                                                                                (2 X 20 = 40)

  1. (i) Prove that .

 

(ii) Prove that .

  1. (i) Prove that if

(ii) Separate into real and imaginary parts tanh(x + iy).

  1. Diagonalise A =
  2. (i) Show that the locus of the point of intersection of the tangent at the extremities of a pair of

conjugate diameters of the ellipse is the ellipse

(ii) Show that the locus of the perpendicular drawn from the pole to the tangent to the circle r = 2a

     cosθ  isr = a(1+cosθ).

 

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Loyola College B.Sc. Mathematics Nov 2012 Algebra, Calculus And Vector Analysis Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – NOVEMBER 2012

MT 1503 – ANALYTICAL GEOMETRY OF 2D,TRIG. & MATRICES

 

 

Date : 10/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

Answer all questions:                                                                                           (10 x 2 = 20)

  1. Write down the expression of cos 4θ in terms of cosθ and sinθ.
  2. Give the expansion of sinθin ascending powers of θ.
  3. Express sin ix and cosix in terms of sin hx and coshx.
  4. Find the value of log(1 + i).
  5. Find the characteristic equation of A = .
  6. If the characteristic equation of a matrix is , what are its eigen values?
  7. Find pole of lx + my + n = 0 with respect to the ellipse
  8. Give the focus, vertex and axis of the parabola
  9. Find the equation of the hyperbola with centre (6, 2), focus (4, 2) and e = 2.
  10. What is the polar equation of a straight line?

PART – B

Answer any five questions.                                                                                 (5 X 8 = 40)

  1. Expandcos6θ in terms of sinθ .
  2. If sinθ = 0.5033 show thatθ is approximately .
  3. Prove that .
  4. If tany = tanα tanhβ ,tanz = cotα tanhβ, prove that tan (y+z) = sinh2βcosec2α.
  5. Verify Cayley Hamilton theorem for A =
  6. Prove that the eccentric angles of the extremities of a pair of semi-conjugate diameters of an ellipse differ by a right angle.
  7. Find the locus of poles of all tangents to the parabola with respect to

 

  1. Prove that any two conjugate diameters of a rectangular hyperbola are equally inclined to the asymptotes.

 

PART – C

Answer any two questions:                                                                                (2 X 20 = 40)

  1. (i) Prove that .

 

(ii) Prove that .

  1. (i) Prove that if

(ii) Separate into real and imaginary parts tanh(x + iy).

  1. Diagonalise A =
  2. (i) Show that the locus of the point of intersection of the tangent at the extremities of a pair of

conjugate diameters of the ellipse is the ellipse

(ii) Show that the locus of the perpendicular drawn from the pole to the tangent to the circle r = 2a

     cosθ  isr = a(1+cosθ).

 

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Loyola College B.Sc. Mathematics Nov 2012 Algebra, Analy. Geo., Calculus & Trigonometry Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc., DEGREE EXAMINATION – MATHEMATICS

THIRD SEMESTER – NOVEMBER 2012

MT 3501/3500 – ALGEBRA, CALCULUS AND VECTOR ANALYSIS

 

 

 

Date : 02-11-2012              Dept. No.                                        Max. : 100 Marks

Time : 9.00 – 12.00

 

PART – A

 

ANSWER ALL THE QUESTIONS:                                                                                                (10 x 2 =  20)

 

  1. Evaluate .
  2. Evaluate .
  3. Eliminate the arbitrary constants from .
  4. Find the complete solution for
  5. Find , if .
  6. Prove that div , where is the position vector.
  7. Find L(Sin2t).
  8. Find .
  9. Find the number and sum of all the divisors of 360.
  10. State Fermat’s theorem.

 

PART – B

ANSWER ANY FIVE QUESTIONS:                                                                                  (5 x 8 = 40)

  1. Change the order of integration and evaluate the integral  .
  2. Express  in terms of Gamma functions and evaluate the integral .
  3. Solve
  4. Solve
  5. Find .
  6. Find .
  7. Show that
  8. Show that is divisible by 22.

 

PART – C

 

ANSWER ANY TWO QUESTIONS                                                                                               (2x 20 = 40)

 

  1. (a) Evaluate taken over the positive quadrant of the circle .

(b)  Prove that

  1. (a) Solve

 

(b) Solve (y+z)p + (z+x)q = x+y.

 

21.(a)  Verify Stoke’s theorem for  taken over the upper half surface of

the  sphere  x2+y2 +z2 = 1, z 0 and the boundary curve C, the x2+y2  = 1, z=0.

 

(b)  State and prove Wilson’s Theorem.

  1. Using Laplace transform solve the equation given y(0) = 0 , y1(0)= -1.

 

 

 

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Loyola College B.Sc. Mathematics Nov 2012 Algebra, Anal.Geo & Calculus – II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – NOVEMBER 2012

MT 1500 – ALGEBRA, ANALY. GEO., CALCULUS & TRIGONOMETRY

 

 

 

Date : 08/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

 

Answer ALL the questions:                                                                                     (10 x 2 = 20 marks)

 

  1. Write the nth derivative of
  2. If y = a show that
  3. Define the evolute of a curve.
  4. Find the p-r equation of the curve r = a sin q.
  5. Determine the quadratic equation having 3 – 2 i as a root.
  6. Diminish the roots of by 2.
  7. Show that
  8. Express in locus of logarithmic function.
  9. Define a rectangular hyporbola.
  10. Write down the angle between the asymptotes of the hyperbola

PART – B

Answer any FIVE questions:                                                                                   (5 x 8 = 40 marks)

 

  1. Show that in the parabola the subtangent at any point is double the abscissa and the subnormal is a constant.
  2. Find the radius of curvature at the point ‘O’ on
  3. Show that if the roots of
  4. Find the p-r equation of the curve with respect to the focus as the pole.
  5. Separate into real and uniaguinary parts.
  6. Find the sum of the series
  7. Find the locus of poles of ale Laugets to with respect to
  8. Derive the polar equation of a comic.

 

PART – C

Answer any TWO questions:                                                                             ( 2 x 20 = 40 marks)

 

  1. a) If prove that
  2. b) Show that r = a sec2 and r = b cosec2 intersect at right angles.
  3. a) Find the minimum value of
  4.        b) Find the radius of  curvature of .
  5. a) Solve: given that the roots are in geometric progression.

 

  1. b) Solve: .

 

  1. a) Express cos8q in locus of power of sinq.

 

  1. b) If e1 and e2 are the eccentricities of a hyperbola and its conjugate show that .

 

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Loyola College B.Sc. Mathematics Nov 2012 Algebra And Calculus – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

SECOND SEMESTER – NOVEMBER 2012

MT 2501/2500 – ALGEBRA, ANAL.GEO & CALCULUS – II

 

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART-A

Answer ALL the questions:                                                                                                 (10 x 2=20)

  1. Evaluate
  2. Evaluate
  3. Verify whether is exact?
  4. Solve
  5. Prove that the series is convergent.
  6. Find the values of k for which the series
  7. Prove that
  8. Using binomial expansion, find the value of correct to two decimal places.
  9. Find the direction cosines of the line
  10. Find the centre and radius of the sphere

PART-B

 

Answer any FIVE questions:                                                                                               (5 x 8=40)

  1. Evaluate
  2. Prove that the area and the perimeter of the cardioids are and
  3. Solve
  4. Solve
  5. Using D’Alembert’s ratio test, examine the convergence of the series
  6. Prove that
  7. When is small , prove that
  8. Find the equation of the plane passing through and and perpendicular to the plane

PART-C

Answer any TWO questions:                                                                                               (2 x 20=40)

 

  1. a) Evaluate
  2. b) Define the length of the curve and find the length of one loop of the curve
  3. a) Solve when
  4. b) Apply the method of variation of parameters to solve
  5. a) Using Rabee’s test, Examine the convergence and divergence for the series
  6. b) Prove that
  7. a) Prove that the lines and are coplanar. Find the point of intersection .Also find the equation of the plane determined by the lines.
  8. b) Find the equation of the sphere passing through the points,and having the centre of the sphere on the line

 

 

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