Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 6 views

    IAT 2 EM-II R19 Question Bank 2021-22

    Uploaded by

    Divyesha Bari
    The document is a question bank containing 17 multiple choice and descriptive questions related to engineering mathematics. The questions cover topics such as differential equations, integration using substitution and changing coordinates, and evaluating integrals over specific regions. They involve skills like solving differential equations using various methods, changing between Cartesian and polar/cylindrical coordinates when setting up integrals, and setting up and evaluating double and triple integrals.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    IAT 2 EM-II R19 Question Bank 2021-22

    Uploaded by

    Divyesha Bari
    6 views3 pages
    The document is a question bank containing 17 multiple choice and descriptive questions related to engineering mathematics. The questions cover topics such as differential equations, integration using substitution and changing coordinates, and evaluating integrals over specific regions. They involve skills like solving differential equations using various methods, changing between Cartesian and polar/cylindrical coordinates when setting up integrals, and setting up and evaluating double and triple integrals.

    Original Description:

    QB

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    The document is a question bank containing 17 multiple choice and descriptive questions related to engineering mathematics. The questions cover topics such as differential equations, integration using substitution and changing coordinates, and evaluating integrals over specific regions. They involve skills like solving differential equations using various methods, changing between Cartesian and polar/cylindrical coordinates when setting up integrals, and setting up and evaluating double and triple integrals.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    6 views3 pages

    IAT 2 EM-II R19 Question Bank 2021-22

    Uploaded by

    Divyesha Bari
    The document is a question bank containing 17 multiple choice and descriptive questions related to engineering mathematics. The questions cover topics such as differential equations, integration using substitution and changing coordinates, and evaluating integrals over specific regions. They involve skills like solving differential equations using various methods, changing between Cartesian and polar/cylindrical coordinates when setting up integrals, and setting up and evaluating double and triple integrals.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    St.

    John College of Engineering & Management, Palghar


    Department of First Year Engineering
    Academic Year 2021-22
    Question Bank
    SUBJECT: EM-II Semester: II
    Class: FE(ALL BRANCHES)
    ==================================================================================

    Q. Question
    No.

    I MCQ’s [One Mark each ]


    Particular Integral of (�3 − �2 )� = �
    1 �6 �2 �6 �2
    �) �. �. = + �) �. �. = − +
    6 2 6 2
    �6 �2 �6 �2
    �) �. �. = 6
    − 2
    �) �. �. = − 6
    − 2
    2 5 7 5
    The double integral � = −3 2−�
    � �, � ���� + 2 �−2
    � �, � ���� into a single term will be
    2
    given by
    5 2−� 5 2+�
    �) 0 2+�
    � �, � ���� �) 0 2−�
    � �, � ����
    5 2+� 5 2−�
    �) 0 0
    � �, � ���� �) 0 0
    � �, � ����

    The triple integral �


    �2������ is converted to cylindrical polar coordinates
    3
    �(�, �, �)������ over the volume bounded by the cylinder
    �
    �2 + �2 = �2 and the
    paraboloid �2 + �2 = � and the plane � = 0, then the upper limit of � is
    2
    �2
    a) 2 b) � �) 1 �)
    2

    4 Particular Integral of (�2 − 1)� = ����3� is


    1 3
    �) �. �. =− ����3� − ���3�
    10 5
    1 3
    b) �. �. = 10 ����3� − 5 ���3�
    −1 3
    �) �. �. = ����3� + ���3�
    10 5
    1 3
    d) �. �. = 10
    ����3� + ���3�
    5

    5 Centre of the sphere �2 +�2 +�2 =− � is


    a) (0,0,0) b) (0,0,1) c) (0,0,-1/2) d) (0,0,1/2)

    Which of following can be correct in spherical polar co-ordinates ?


    6 a) ������ = �����������
    b) ������ = �2 ����������
    c) ������ = ����2�������
    d) ������ = �2 ������
    Complementary Function of the Differential Equation : (�2 − 4� + 4)2 � = �−� is
    a) �1 �2�
    b) (�1 + �2 �)�2�
    c) (�1 + �2 � + �3 �2 )�2�
    7
    d) (�1 + �2 � + �3 �2 + �4 �3 )�2�

    8 Particular Integral of the Differential Equation : (�2 − 4� + 4)� = �2� is


    1
    a) 2 �2�
    �
    b) 2 �2�
    �2 2�
    c) 2
    �
    3
    � 2�
    d) 2
    �

    Particular Integral of the Differential Equation (�2 − 2� + 1)� = ��� is


    9 �
    a) ��
    2
    �3
    b) 6 ��
    5
    � �
    �) �
    12
    �7
    d) ��24
    10 Particular Integral of the Differential Equation: (�2 + � + 1)� = ���2 � is
    1
    a) 2 1 − 2���2�
    1
    b) 2 1 + 2���2�
    1
    c) 2 � − 2���2�
    1
    d) 2 � + 2���2�

    11 The area bounded by � = �2 and � = �2 is given by


    1 1 1
    �) �) �) 1 �)
    2 6 3
    12 Which of the following is equation of Paraboloid
    �) �2 + �2 = 4 �) �2 − �2 = 4
    �) �2 + �2 = � �) �2 − �2 = �
    13 Vertex of the parabola � = �2 + 2� is
    �) 1, − 1 �) −1,1 �) 1,1 �) ( − 1, − 1)
    14 After changing from cartesian to spherical polar coordinates the integral
    �
    � �2 +�2 +�2
    ������ reduces to �
    �(�, �, �)������, then � �, �, � is
    �) ����� �) ����� �) �������� �) ���������
    � �
    15 The value of 0 � � �� ��, if evaluating in polar coordinate is
    �3 �3 �2 �2
    �) �) �) �)
    3 6 3 2
    II Descriptive [5 Marks each ]
    1 Solve the following differential equation: �3 − 2�2 + � + 4 � = ����� + �� �2
    2 Solve the following differential equation:
    1
    �2 − 1 � =
    1 + ��
    3 Solve �4 − 1 � = �� + ���� ���3�
    4 Using method of variation of parameters solve
    �2 + 1 � = ���� ����
    5 Using method of variation of parameters solve
    �
    �2 + 3� + 2 � = ��
    6 Solve (� − 2)2 � = 8(�2� + ���2� + �2 )
    7 Evaluate � =
    1 � 2 2
    � � ( �2 + �2)����
    0 0
    8 Evaluate � = 2
    � � ���� where R is the region bounded by �� = 16, � = �, � = 0 ��� � = 8.
    9 1 1−�2 � ����
    Change the order of integration and evaluate: 0 0 (1+�2 ) 1−�2−�2

    10 Change the order of integration and evaluate:


    � ��
    �
    �= ����
    0 � �2 + �2
    11 Evaluate � = � 3� + 4�2 ���� where R is the region in the upper half of the area bounded by
    the circles �2 + �2 = 1, �2 + �2 = 4.
    12 �������� (�2 + �2 )dx dy over the area of the triangle whose vertices are (0,0), (1,0),
    (1,2).
    13 Evaluate � = 0 0
    1 1−� 1−�−�
    �2 �� ������
    0
    14 Evaluate � = �2 �� �� ��, over the volume common to the sphere �2 + �2 + �2 = 1 and the
    2 2
    cylinder � + � = �.
    15 Evaluate the following integration by changing to the polar coordinates.
    1 1−�2
    �= (�2 + �2 )dx dy
    0 0
    16 Express the following integral in polar coordinates and evaluate
    � �2 −�2
    ����
    �=
    0 �2 − �2 − �2
    ��−�2
    17 2
    Find the area between the parabola � = � − 6� + 3 and the line � = 2� − 9

    You might also like