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    XII-Maths Science CHAPTER 1 To 9 (05-11-17)

    Uploaded by

    Rupesh Kumar Singh
    1. The document contains a math exam with 3 sections - Section A has 6 multiple choice questions, Section B has 13 theoretical questions, and Section C has 6 numerical questions. The exam is worth a total of 152 marks and was administered over 3 hours. 2. Some example questions include solving equations involving matrices, derivatives, integrals, and geometry concepts like finding the area of regions bounded by curves. 3. The document provides details of the exam paper such as the subject, class, duration, and breakdown of marks for each section, followed by the list of 25 questions across the 3 sections.

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

    XII-Maths Science CHAPTER 1 To 9 (05-11-17)

    Uploaded by

    Rupesh Kumar Singh
    38 views3 pages
    1. The document contains a math exam with 3 sections - Section A has 6 multiple choice questions, Section B has 13 theoretical questions, and Section C has 6 numerical questions. The exam is worth a total of 152 marks and was administered over 3 hours. 2. Some example questions include solving equations involving matrices, derivatives, integrals, and geometry concepts like finding the area of regions bounded by curves. 3. The document provides details of the exam paper such as the subject, class, duration, and breakdown of marks for each section, followed by the list of 25 questions across the 3 sections.

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    Original Title

    XII-Maths Science CHAPTER 1 to 9 (05-11-17)

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    1. The document contains a math exam with 3 sections - Section A has 6 multiple choice questions, Section B has 13 theoretical questions, and Section C has 6 numerical questions. The exam is worth a total of 152 marks and was administered over 3 hours. 2. Some example questions include solving equations involving matrices, derivatives, integrals, and geometry concepts like finding the area of regions bounded by curves. 3. The document provides details of the exam paper such as the subject, class, duration, and breakdown of marks for each section, followed by the list of 25 questions across the 3 sections.

    Copyright:

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

    XII-Maths Science CHAPTER 1 To 9 (05-11-17)

    Uploaded by

    Rupesh Kumar Singh
    1. The document contains a math exam with 3 sections - Section A has 6 multiple choice questions, Section B has 13 theoretical questions, and Section C has 6 numerical questions. The exam is worth a total of 152 marks and was administered over 3 hours. 2. Some example questions include solving equations involving matrices, derivatives, integrals, and geometry concepts like finding the area of regions bounded by curves. 3. The document provides details of the exam paper such as the subject, class, duration, and breakdown of marks for each section, followed by the list of 25 questions across the 3 sections.

    Copyright:

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

    Marks – 94 Chapter – 1 to 9 Time – 3 hours

    Sub – Maths Std – XII

    Section – A ( 1 × 6 = 6)
    1. Write the principle value of : tan−1 ( √ 3 )−cot−1 (−√ 3 ).

    2. Write the value of : tan 2 sin [(


    −1 √ 3
    2
    . )]
    3. For what value of x, is the matrix

    [ ]
    0 1 −2
    A = −1 0 3 a skew – symmetrics matrix?
    x −3 0

    4. If matrix A = [−11 −11 ] and A = KA, I then write the value of k.


    2

    5. The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its
    total revenue (marginal revenue). If the total revenue (in ruppes) reciveved from the sale of x units of a
    product is given by

    R (x) = 3 x 2+ 36 x+5 , find the marginal revenue, when x = 5, and write which value does the question
    indicate.
    4
    x
    6. Evaluate: ∫ 2 dx
    2 x +1

    Section – B ( 4 × 13 = 52)
    7. Consider f: R+¿→ ¿¿ ) given by f (x) = x 2 + 4. Show that f is invertible with the inverse f −1 of f given f −1 (y)
    = √ y−4 where R+¿ ¿ is the set of all non – negative real numbers.

    8. Show that: tan ( 12 sin 34 )= 4−3√7 .


    −1

    OR

    Solve the following equation: cos ( tan x ) =sin cot


    −1
    ( −1 3
    4).

    GYAN VRIDDHI INSTITUTE U 10-13 City light complex OppDevdarshan Appt. City Light Surat. M:-9925199909
    1
    9. Using properties of determinants, prove the following:

    | |
    x x+ y x+2 y
    2
    x +2 y x x + y =9 y ( x+ y).
    x + y x+ 2 y x
    2
    dy ( 1+ log y )
    10. If y x =e y−x , prove that = .
    dx log y

    ( )
    x +1 x
    −1 2 .3
    11. Diffrentiate the following with respect to x: sin x
    1+ ( 36 )

    {
    √ 1+kx− √1−kx
    x
    12. Find the value of k, for which f(x) , if – 1 ≤ x< 0 Is continuous at x = 0.
    2 x +1
    if 0≤ x <1
    x −1

    cos 2 x−cos 2 ∝
    13. Evaluate: ∫ dx
    cos x−cos ∝

    x +2
    14. Evaluate: ∫ dx
    √ x +2 x+ 3
    2

    dx
    15. Evluate: ∫ dx
    x ( x 5+3)
    2π

    16. Evluate: ∫ 1+1e sinx dx


    0

    17. Find the values of x for which y = [x(x-2)]2 is an increasing function.


    2 2
    x y
    18. Find the equations of the tangent and normal to the curve − = 1 at the point (√ 2 a, b).
    a2 b 2

    dy −1
    19. Solve the differential equation (1 + x 2) + y = e tan x
    dx

    Section – C ( 6 × 6 = 36)
    20. Find the area of the greatest rectangle that can be inscribed in an ellipse
    2 2
    x y
    + =1.
    a2 b 2

    21. Find the area of the region bounded by the parabola y = x 2 and y = |x|.

    GYAN VRIDDHI INSTITUTE U 10-13 City light complex OppDevdarshan Appt. City Light Surat. M:-9925199909
    2
    22. Find the particular solution of the differntial equation ( tan−1 y −x ¿ dy =( 1+ y 2 ) dx , given that when x
    = 0, y = 0.

    23. The management committee of a residential colony decided to award some of its members (say x) for
    honesty, some (say y) for helping other (say z) for supervising the workers to keep the colony neat and
    clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and
    supervision added to two times the number of awardeed for honesty is 33. If the sum of the number of
    awardees for honesty and suprvision is twice the number of awardees for helping others, using matrix
    method, find the number to awardees of each category. Apart from these values, namely, honesty,
    cooperation and suprvision, suggest one more value which the management of the colony must include for
    awards.

    24. Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of
    4r 8
    radius r is . Also show that the maximum volume of the cone of the volume of the sphere.
    3 27

    1
    25. Evaluate: ∫ cos 4 x+sin 4 x dx.
    26. Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2), (1, 5) and
    (3, 4).

    GYAN VRIDDHI INSTITUTE U 10-13 City light complex OppDevdarshan Appt. City Light Surat. M:-9925199909
    3

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