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    WWW - Manaresults.co - In: Code No: R19BS1203

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    M3 PREVIOUS Q.P

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    WWW - Manaresults.co - In: Code No: R19BS1203

    Uploaded by

    chinnidarling40
    9 views2 pages
    M3 PREVIOUS Q.P

    Original Title

    R19-2023

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    M3 PREVIOUS Q.P

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    9 views2 pages

    WWW - Manaresults.co - In: Code No: R19BS1203

    Uploaded by

    chinnidarling40
    M3 PREVIOUS Q.P

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Code No: R19BS1203 R19 SET - 1

    I B. Tech II Semester Supplementary Examinations, January/February - 2023


    MATHEMATICS-III
    (Common to CE, EEE, ECE, CSE, Chem. E, EIE, IT, Auto E, MIN E, PET E)
    Time: 3 hours Max. Marks: 75
    Answer any FIVE Questions ONE Question from Each Unit
    All Questions Carry Equal Marks
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    UNIT-I
    1. a) 1 −r [8M]
    Prove that ∇ = 3
    r r
    b) Verify stoke’s theorem for F = x 2 i + xy j around the square in z = 0 plane whose [7M]
    sides are along the lines x = 0,y = 0; x = 1, y = 1.

    (OR)
    2. a) Show that ( ) ( )
    curl curl f = ∇ × ∇ × f = ∇ ∇. f − ( ∇.∇ ) f if f ( x, y, z ) is vector [8M]

    point function.
    b) 2
    If = (3x − 2 z)i − 4 xy j − 5xk Evaluate , where v is volume bounded by [7M]
    the planes x = 0; y = 0; z = 0 and 3x + 2y – 3z = 6.
    UNIT-II
    3. a) [8M]
    Find the Laplace transform of

    b) [7M]
    Find inverse Laplace transform of
    (OR)
    4. a) Find 1+ 2 ! [8M]
    b) [7M]
    Apply convolution theorem to find " $
    #
    UNIT-III
    5. a) Find the Half range cosine of f ( x) = cos π x in [ 0,1] [8M]
    b) 1 if x < 1 [7M]
    Express the f ( x) defend by f ( x) = as a Fourier integral and
    0 if x > 1
    ∞ sin λ cos λ x
    Hence Evaluate dλ
    0 λ
    (OR)
    6. a) −π π [8M]
    x, <x<
    2 2
    Find the Fourier series for f ( x) =
    π 3π
    0, <x<
    2 2
    b) Find the Fourier Transform of f ( x) defined by [7M]

    eiqx if α < x < β


    f ( x) =
    0 otherwise

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    1 of 2
    Code No: R19BS1203 R19 SET - 1

    UNIT-IV
    7. a) Form the partial differential equation of the following by eliminating arbitrary [8M]
    constants from ( x − a)2 + ( y − b)2 + z 2 = r 2 where r is a constant and a, b are
    parameters.
    b) Solve the PDE p cos ec x + q cos ec y = cos ec z [7M]
    (OR)
    8. a) Solve the PDE %& − () * + (+ − ,& - = ,) − %+. [8M]
    b) Solve the PDE /* + /- = 2+ − 2). [7M]
    UNIT-V
    9. A String of length 100 cm is highly stretched between x =0 and x =100 and is [15M]
    displaced from its equilibrium position by imparting to each of its points an initial
    x 0 < x < 50
    velocity g ( x) = Determine the displacement at any
    100 − x 50 < x < 100
    subsequent time.
    (OR)
    10. a)
    ( 2

    )
    Solve the PDE D 2 + 2 DD1 + D1 z = x 2 + xy + y 2 [8M]

    b) ∂u ∂u [7M]
    Solve the PDE = 2 + u by variable separable method
    ∂x ∂t

    *****

    2 of 2

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