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www.sakshieducation.com www.sakshieducation.com Half-Yearly Examinations -Maths Paper-II Model Paper-II Part-A Time : 2 Hours Maximum Marks: 35 Section-I Group-A 1. Show that the lengths of two tangents drawn from an external point to a circle are equal. 2. In what ratio is the segment joining the points (–3,2) and (6,1) divided by y-axis. 3. Find the equation of the line passing through (4,–3) and is parallel to the line 4x–5y+3=0. 4. The observation of an ungrouped data are x 1 x 2 and 2x 1 and median of the data are each equal to 6. Find the observations of the data. Group-B 5. Evaluate the product of . 6. If then prove that A.A –1 = I. 7. What are the essential components of a computer? 8. Write any four computer languages. Section-II 9. Mention the properties of similar triangles. 10. Find the interest point of the medians of the triangle whose verticles are (–1,0) (5,2) (8,2). 7 5 A= 4 3 a h x (x, y) h b y ⎤⎡ ⎤ ⎥⎢ ⎥ ⎦⎣ ⎦

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    Half-Yearly Examinations -Maths Paper-II

    Model Paper-II

    Part-A

    Time : 2 Hours Maximum Marks: 35

    Section-I

    Group-A

    1. Show that the lengths of two tangents drawn from an external point to a circle are equal.

    2. In what ratio is the segment joining the points (3,2) and (6,1) divided by y-axis.

    3. Find the equation of the line passing through (4,3) and is parallel to the line 4x5y+3=0.

    4. The observation of an ungrouped data are x1x2 and 2x1 and median of the data are each

    equal to 6. Find the observations of the data.

    Group-B

    5. Evaluate the product of ..

    6. If then prove that A.A1= I.

    7. What are the essential components of a computer?

    8. Write any four computer languages.

    Section-II

    9. Mention the properties of similar triangles.

    10. Find the interest point of the medians of the triangle whose verticles are (1,0) (5,2) (8,2).

    7 5A =

    4 3

    a h x (x, y)

    h b y

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    12. If Show that A+A1=4I.

    13. Find the length of direct common tangent to externally touching circles. Whose radii are

    5cm and 6cm?

    14. What are the essential components of C.P.U.?

    Section-III

    Group-A

    15. State and prove Alternatge segment theorem.

    16. Find the co-ordinates of the points of trisection of a segment joining A(3,2) and B(9,5).

    17. Find the equation of the line which passes through the point (1,6) and whose product of

    the intercepts of the co-ordinate axis is one.

    18. Marks scored by 100 students is given below. Find the mode of the followibg data.

    Marks 15-24 25-34 35-44 45-54 55-64 65-74

    No.of

    students 8 20 28 30 10 4

    Group-B

    (Matrices, Computing)

    19. If Matrices show that (AB)1 = B1. A1.

    20. Solve the following equations using Cramer's method.

    3y= 42x ; .

    y +1x = 4

    1 1 2 0 A = ,B =

    2 1 5 3

    1 2A =

    1 3

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    21. Gopal purchased a radio set for Rs.500 and sold it for Rs. 600. Execute a flow chart, using

    the data to determine loss or gain?

    22. Draw a flow chart to compute the sum of the first 100 natural numbers.

    Section-IV

    23. Construct a triangle ABC in which BC= 4 cm, A = 50 and the perpendicular distance

    from A to BC is 3 cm?

    24. Construct a cycle quadrilateral ABCD, where AC= 4 cm, ABC= 57 , AB= 1.5cm and

    AD= 2 cm.

    PART-B

    Marks : 30=5

    1. In a triangle XYZ, if the internal bisector of X meets YZ in P then = . ( )

    A) B) C) D)

    2. If ABCD is a cyclic quadrilateral with C = 120, then A= . ( )

    A) 40 B) 50 C) 60 D) 70

    3. Find the mid point of the line segment (2,3) and (6,5) is . ( )

    A) (1,2) B) (4,2) C) (2,1) D) (1/2, 1/2)

    4. The slope of the line parallel to 3x2y+1 =0 is . ( )

    A) B) C) 3 D)

    5. The class interval of the frequency distribution having the classes 1-8, 9-16,17-24, .......

    -23

    23

    32

    xz yp xy yz

    =

    xy pz xz xp

    =

    xy xz pz yp

    =xy yp xz pz

    =

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    A) 8 B) 9 C) 7 D) 3

    6. If mean = x, median =y, then mode = . ( )

    A) 3y2x B) 3x2y C) 2x3y D) 2y3x

    7. If and A. B = .( )

    A) B) C) D)

    8. If ; then AB = . ( )

    A) (5x2y) B) [5x+2y] C) D)

    9. All parts of a computer are under the control of . ( )

    A) Mouse B) C.P.U. C) Memory unit D) Output

    10. These are used in IV generation computers . ( )

    A) Transisters B) Transforms

    C) Vaccum Tubes D) Very large scale integrated circuits

    Answers : 1. A 2. C 3. C 4. A 5. A

    6. A 7. B 8. B 9. B 10. D

    II. Fill in the blanks with suitable words Marks : 10=5

    11. The number of circles drawn through three non collinear points is .

    12. In ABC, 90, ADBC then AD2 = .

    [ ]5 + x 2 y+5x2y

    xA =

    y [ ]A = 5 2

    1 23 4

    1 32 4

    1 23 4

    1 00 1

    1 0 1 2 A = , B =

    0 1 3 4

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    13. The angle between the lines x2=0, y+3=0 is .

    14. The slope of a line perpendicular to 2x+3y=4 is = .

    15. The term cummulative frequency is used in finding .

    16. In finding Mode 2 = .

    17. If and ad= bc then A is called matrix.

    18. If A= AT then matrix A is called .

    19. A design or a plan to obtain solution to a problem is called = .

    20. The rhombus shaped box is used in a flow chart for .

    Answers

    11. One 12. BD.DC

    13. 90 14. 3/2

    15. Median 16. (ff2)

    17. Singular 18. symmetric matrix

    19. Algorithm 20. Decision

    III. Match the following Marks : 10=5

    Group-A Group-B

    21. Angle in a semicircle ( ) A) 1

    22. If two circles touch

    internally, then the number ( ) B) x=0

    a bA

    c d

    =

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    23. The equation of y-axis is ( ) C) 3/2

    24. The slope of ( ) D) 90 (or) right angle

    25. The ( ) E) 2/3

    F) y=0

    G)

    H) 2

    Answers : 21. D 22. A 23. B 24. C 25. G

    Group-A Group-B

    26. ( ) A) PASCAL

    27. Inverse of the matrix ( ) B) 21

    28., then the order ( ) C) 1

    of matrix A is

    29. Second generation computers ( ) D) does not exist

    1 1A (1,2)

    0 2

    =

    1 1A

    0 2

    =

    9 75 4

    n 12+

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    F) 12

    G) ENGLISH

    H) 0

    Answers : 26.C 27. D 28. B 29. E 30. A

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