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    Board of Intermediate Education, A.P. Mathematics - IIB Model Question Paper (W.e.f. 2013-14)

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    Sasi
    1. The document is a model question paper for mathematics with 3 sections - A, B and C. Section A contains 10 very short answer questions carrying 2 marks each. Section B contains 5 short answer questions carrying 4 marks each. Section C contains 5 long answer questions carrying 7 marks each. 2. The questions cover a range of mathematics topics including circles, ellipses, hyperbolas, integration, differential equations, and coordinate geometry. Sample questions include finding equations of circles and conic sections given conditions, evaluating definite integrals using reduction formulas, solving differential equations, and proving geometric properties. 3. Students are required to show their working clearly for partial or full marks. Questions test a variety of skills from computation

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    Board of Intermediate Education, A.P. Mathematics - IIB Model Question Paper (W.e.f. 2013-14)

    Uploaded by

    Sasi
    44 views2 pages
    1. The document is a model question paper for mathematics with 3 sections - A, B and C. Section A contains 10 very short answer questions carrying 2 marks each. Section B contains 5 short answer questions carrying 4 marks each. Section C contains 5 long answer questions carrying 7 marks each. 2. The questions cover a range of mathematics topics including circles, ellipses, hyperbolas, integration, differential equations, and coordinate geometry. Sample questions include finding equations of circles and conic sections given conditions, evaluating definite integrals using reduction formulas, solving differential equations, and proving geometric properties. 3. Students are required to show their working clearly for partial or full marks. Questions test a variety of skills from computation

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    Sasi

    Original Title

    maths2-bN

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    1. The document is a model question paper for mathematics with 3 sections - A, B and C. Section A contains 10 very short answer questions carrying 2 marks each. Section B contains 5 short answer questions carrying 4 marks each. Section C contains 5 long answer questions carrying 7 marks each. 2. The questions cover a range of mathematics topics including circles, ellipses, hyperbolas, integration, differential equations, and coordinate geometry. Sample questions include finding equations of circles and conic sections given conditions, evaluating definite integrals using reduction formulas, solving differential equations, and proving geometric properties. 3. Students are required to show their working clearly for partial or full marks. Questions test a variety of skills from computation

    Copyright:

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

    Board of Intermediate Education, A.P. Mathematics - IIB Model Question Paper (W.e.f. 2013-14)

    Uploaded by

    Sasi
    1. The document is a model question paper for mathematics with 3 sections - A, B and C. Section A contains 10 very short answer questions carrying 2 marks each. Section B contains 5 short answer questions carrying 4 marks each. Section C contains 5 long answer questions carrying 7 marks each. 2. The questions cover a range of mathematics topics including circles, ellipses, hyperbolas, integration, differential equations, and coordinate geometry. Sample questions include finding equations of circles and conic sections given conditions, evaluating definite integrals using reduction formulas, solving differential equations, and proving geometric properties. 3. Students are required to show their working clearly for partial or full marks. Questions test a variety of skills from computation

    Copyright:

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

    BOARD OF INTERMEDIATE EDUCATION, A.P.

    Mathematics - IIB
    Model Question Paper (w.e.f. 2013-14)

    Note: This Question paper consists of three sections A. B and C.

    Time: 3 Hrs Max. Marks: 75

    SECTION – A

    I. Very Short Answer type Questions


    (i) Answer all Questions
    (ii) Each Question carries 2 marks 10 x 2 = 20

    2 2
    1. If ax + bxy + 3y – 5x + 2y – 3 = 0 represents a circle, find the values of a and
    b. Also find its radius and centre.
    2. State the necessary and sufficient condition for lx + my + n= 0 to be a, normal
    to the circle x2 + y2 + 2gx + 2fy + c = 0
    3. Find the angle between the circles x 2 + y 2 − 12x − 6y + 41 = 0 and

    x 2 + y 2 + 4 x + 6 y − 59 = 0
    4. Find the equation of the parabola whose focus is S(1, -7) and vertex is A(1, -2).
    x 2 y2
    5. Find the angle between the asymptotes of the hyperbola − = 1.
    a 2 b2
    1
    6. Evaluate ∫ ( x + 3) x+2
    dx

    sin 4 x
    7. Evaluate ∫ cos 6 x
    dx

    1
    x2
    8. Evaluate ∫
    0
    x2 +1
    dx

    π
    sin 2 x − cos 2 x
    9. Evaluate ∫
    0
    sin3 x + cos3 x
    dx

    6/5
     d 2y  dy  3 
    10. Find the order and degree of the differential equation  2 −   = 6y .
     dx  
     dx 
    SECTION – B

    II. Short Answer type Questions


    (i) Answer any five Questions
    (ii) Each Question carries 4 marks 5 x 4 = 20

    2 2
    11. Show that the tangent at (–1, 2) of circle x + y – 4x – 8y + 7 = 0 touches the
    2 2
    circle x + y + 4x + 6y = 0. Also find its point of contact.
    12. Find the equation of the circle passing through the points of intersection of
    2 2 2 2
    the circles x + y – 8x – 6y + 21 = 0, x + y – 2x – 15 = 0 and (1, 2).
    13. Find the length of major axis, minor axis, latus rectum, eccentricity of the
    2 2
    ellipse 9x + 16y = 144.
    14. Show that the point of intersection of the perpendicular tangents to an ellipse
    x 2 y2
    + = 1 , (a > b) lies on a circle.
    a 2 b2
    2 2
    15. Find the equation of the tangents to the hyperbola 3x – 4y = 12 which are
    (i) Parallel to (ii) Perpendicular to the line y = x – 7.
    π
    2

    ∫ sin
    n
    16. Find the reduction formula for x dx
    0
    2 -1
    17. Solve: (1 + y ) dx -= (Tan y – x)dy

    SECTION – C
    III. Long Answer type Questions
    (i) Answer any five Questions
    (ii) Each Question carries 7 marks 5 x 7 = 35

    18. Show that the points (1, 1), (–6, 0), (–2, 2) and (–2, –8), are concyclic.
    19. Find the direct common tangents to the circles
    2 2 2 2
    x + y + 22x – 4y – 100 = 0, x + y – 22x + 4y + 100 = 0.
    20. If y1, y2 , y3 are the y-coordinates of the vertices of the triangle in the parabola

    y 2 = 4ax then show that the area of the triangle is


    1
    (y1 − y2 )(y2 − y3 )(y3 − y1 ) square units.
    8a
    9 cos x − sin x
    21. Evaluate ∫4 sin x + 5 cos x
    dx
    22. Evaluate ∫
    (1 + x ) 3 + 2x − x 2
    1 log (1 + x)
    23. Evaluate ∫
    0 1+ x2
    dx

    dy 2x + y + 3
    24. Solve: =
    dx 2y + x + 1
    ******

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