# 2017 scheme vtu

Description
Description:
Categories
Published

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
Page 1  of 3   Model Question Paper with effect from 2018-19 17MAT31 USN Third Semester B.E.Degree Examination Engineering Mathematics-III (Common to all Branches) Time: 3 Hrs Max.Marks: 100 Note: Answer any FIVE full questions, choosing at least ONE question from each module. Module-1 1.   (a) Find the Fourier series expansion of   ,  x f    if    .0,sin 0,0     xin x xin x f    Hence deduce that   42...7.515.313.11        (08 Marks)   (b) Obtain the Fourier series of    x x f      valid in the interval   ., l l     (06 Marks)   (c)  Find the half-range cosine series of     2 1   x x f    the interval .10    x   (06 Marks)   OR 2.   (a) A periodic function    x f     of period ‘6’ specified by the following table over the interval   6,0 :  x  0 1 2 3 4 5 6    x f    9 18 24 28 26 20 9 Obtain the Fourier series up to second harmonics.  (08 Marks) (b) Obtain the Fourier series of      x x x f        2  valid in the interval   .2,0      (06 Marks) (c)  Find the half-range sine series of    24,cos 40sin      x for  x x for  x x f    ( 06 Marks) Module-2 3.   (a) If    101,1  2  x for  x for  x x f   , find the infinite Fourier transform of  f(x)  and hence evaluate dx x x x x x 2cossincos 03      (08 Marks) (b) Find the Fourier sine transform of 2 11  x   ( 06 Marks) (c) Solve 1012  0,296  uuuuu  nnnn     , by using z-transforms. ( 06 Marks) www.android.previousquestionpapers.com | www.previousquestionpapers.com | www.ios.previousquestionpapers.comwww.android.universityupdates.in | www.universityupdates.in | www.ios.universityupdates.in  Page 2  of 3   OR 17MAT31  4.   (a) Find the Fourier sine transform of .  x e  Hence show that .0., 21sin 02      medx xmx x  m     (08 Marks) (b) Find the  z  -transform of   42cos       n  ( 06 Marks) (c) Find the inverse  z  -transform of      141218  2   z  z  z   ( 06 Marks)   Module-3 5.   (a) Define Karl Pearson’s coefficient of correlation. If    is the acute angle between the lines of regression, then show that       r r   y x y x 222 1tan       . Explain the significance when .1&0    r r    (08 Marks) (b) Fit a best fitting straight line bax y   for the following data:  (06Marks)    x   1 2 3 4 5  y  10 12 13 16 19 (c) Find the real root of the equation 7log2 10    x x , lying between 0.4&5.3  correct to three decimal  places, using regula-falsi method.  (06Marks)   OR 6.   (a) Ten students got the following marks in Mathematics a   nd Electronics in a class test: Calculate the coefficient of correlation.  (08 Marks)  (b) Fit a best fitting parabola cbxax y    2 for the following data:  (06 Marks) (c) Find a real root of the equation 01cos3    x x correct to four decimal places, using  Newton-Raphson method. ( 06 Marks)   Module-4 7.   (a) Find the values  y  at (i  ) x=110 & (ii) x=390  using the following table gives the distance  y  (in nautical miles) of the visible horizon for the given heights  x   (in feet) above the earth’s surface:  ( 08 Marks) Roll No. 1 2 3 4 5 6 7 8 9 10  Marks in  Mathematics 78 36 98 25 75 82 90 62 65 39  Marks in  Electronics 84 51 91 60 68 62 86 58 53 47  x   1 2 3 4 5 6 7 8 9  y  2 6 7 8 10 11 11 10 9  x 100 150 200 250 300 350 400  y 10.63 13.03 15.04 16.81 18.42 19.90 21.27 www.android.previousquestionpapers.com | www.previousquestionpapers.com | www.ios.previousquestionpapers.comwww.android.universityupdates.in | www.universityupdates.in | www.ios.universityupdates.in  Page 3  of 3   17MAT31  (b) Using Newton’s ge neral interpolation formula, construct an interpolating polynomial for the following data: ( 06Marks)  (c) Using Weddle’s rule, evaluate       d   20 cos , by dividing   2,0     into six equal parts. ( 06 Marks)   OR 8.   (a) Use an appropriate interpolation formula to find (i) 24  y  and (ii) 54  y , given ,612 20    y  ,539 30    y  ,446 40    y  .343 50    y  ( 08 Marks)  (b) Using Lagrange’s interpolation formula to fit a polynomial for the following data:  ( 06 Marks)     0 1 3 4   -12 0 6 12 (c) Evaluate  82 10 log  xdx  , u sing Simpson’s  rd rule taking 7 equidistant ordinates. ( 06 Marks)   Module-5 9. (a) Verify Green’s theorem in the plane for      c dy xdx y xy  22  where C   is the closed curve bounded  by 2 &  x y x y    ( 08 Marks)  (b) U sing Stoke’s theorem, evaluate    dS n F   s ˆ      where k  yz  j xz i y F   2 3   and S is the surface of the paraboloid 22 2  y x z     bounded by 2   z  . ( 06 Marks)  (c) Prove that geodesics of a plane are straight lines. ( 06 Marks)   OR 10.   (a) Using Gauss divergence theorem, evaluate   dS k  xy j zxi yz   s    ˆˆˆ  where S is the surface of the sphere 2222 a z  y x    in the first octant.  (08 Marks)   (b) Derive Euler’s equation in the standard form viz., 0   y f  dxd  y f     (06 Marks)  (c) Find the extremal of the functional    dx x y y y      022 cos4 ;        y y    00  (06 Marks)   *****  x -3 0 1 3  f(x) 2 1 0 -1 www.android.previousquestionpapers.com | www.previousquestionpapers.com | www.ios.previousquestionpapers.comwww.android.universityupdates.in | www.universityupdates.in | www.ios.universityupdates.in

Sep 10, 2019

#### W221+En.pdf

Sep 10, 2019
Search
Similar documents

View more...
Tags

## Mathematical Relations

Related Search
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x