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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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