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Ae-Ac-At 51_engg Maths 1

Oct 11, 2015

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SubhroBarua

Some Solved Engineering Mathematics Problem
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  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 1

    Q.2 a. If Z is a homogeneous function of degree n in x and y, show that

    ( )z 1nny

    zyyxzxy2

    xzx 2

    22

    2

    2

    22 =

    +

    +

    Answer: Page Number 221 of Text Book 1 b. Use method of differentiation under integral sign to show that

    ( ) 0a,a1log2

    dx)x1(x

    axtan

    02

    1+

    =

    +

    Answer:

    Q.3 a. Change the order of integration and then evaluate dy dxay2

    a4y

    a4

    0 2

    Answer: Page Number 298-299 of Text Book 1 b. Find the volume bounded by the xy-plane, the cylinder 1yx 22 =+ and

    the plane x+y+z = 3. Answer:

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 2

    Q.4 a. Find the eigen values and eigen vectors of the matrix

    312132

    226

    Answer:

    b. Determine the rank of the following matrices:

    (i)

    562241321

    (ii)

    0211201311011310

    Answer: Page Number 40 of Text Book 1

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 3

    Q.5 a. Use Regula-Falsi method to compute real root of 2xex = correct to three decimal places.

    Answer:

    b. Find by Runge-Kutta method of order four, an approximate value of y at

    x = 0.2 for the equation ( ) 10y,xyxy

    dxdy

    =+

    = . Take h = 0.2.

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 4

    Answer:

    Q.6a. Solve the differential equation ( ) ye21dxdy1x =++

    Answer:

    b. Find the orthogonal trajectories of family of curves 32 xay = Answer:

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 5

    Q.7 a. Solve the differential equation Sinxxey25dxdy6

    dxyd x22

    2++=+

    b. Solve the equation 222

    xxlog12

    dxdy

    x1

    dxyd

    =+

    Answer:

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 6

    Q.8 a. Obtain the series solution of ( ) 0y2dxdyx2

    dxydx1 2

    22 =+

    Answer:

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 7

    b. Show that ( )nm

    n mn,m

    +=

    Answer: Page Number 854 of Text Book 1 Q.9 a. State and prove Rodrigues formula. Answer:

  • AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013

    IETE 8

    b. Prove that ( ) ( ) ( )nJxn2nJnJ n1n1n =+ +

    Answer:

    TEXT BOOKS

    1. Higher Engineering Mathematics, Dr. B.S.Grewal, 40th edition 2007, Khanna publishers, Delhi. 2. Text book of Engineering Mathematics, N.P. Bali and Manish Goyal, 7th Edition 2007, Laxmi Publication (P) Ltd.