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					                              Model Question Paper - Xth
                                     Mathematics
Time : 2½ hrs.                                                  Max.marks 100

I. Choose the best answer

1. In a G.P. r<1 then the s is ____
a. a
  1-r
b. a
  r-1
c. 
d. None

2. The sum of 2+3+4+...................+10 is ____
a. 50        b. 54          c. 55             d. 10

3. The volume of the two spheres is in the ratio 64 : 125, then their radius ratio is
____
a. 4 : 5            b. 8 : 25    c. 4 : 25              d. 8 : 5

4. If A = {3, 8, 9}, then A∩A is = ____
a. {3} b. 3             c. {9}      d. {3, 8, 9}

5. f(x)=x2, g(x)=3x then fog (2) is ____
a. 36          b. 9          c. 18           d. 2

6. The quadratic equation with roots (2+3), (2-3) is ____
a. x2 + 4x - 1 = 0  b. x2 - 4x - 1 = 0   c. x2 - 4x + 1 = 0     d. x2 + 4x + 1 = 0

7. x2-25 is ____
    x-5
a. (x-5) b. (x+5) c. 0 d. 1

8. A point 4x + 4y < 5 is
a. (1,1) b. (2,0) c. (0,7) d. None

9. In a rt. angled LB = 90; AB=8 cm, BC=15 cm then AC is
a. 13 cm b. 10 cm c. 17 cm d. 20 cm

10. Angle is the major segment is ____
a. Acute angle b. Obtuse angle c. Right angle d. Reflexive angle

11. Two similar triangles have corresponding sides proportional to 3 : 4 then their
areas are proportional to ____
a. 3 : 4 b. 4 : 3 c. 9 : 16 d. 16 : 9
12. The centroid G of the triangle whole vertices are (1, 10), (-7, 2), (-3, -9) is
a. (3, 7) b. (-3, -7) c. (3, 7) d. (-3, 7)

13. The given st. lines 3x + 5y = 10, 6x + 8y = 15 are
a. Parallel b. Not Parallel c. Perpendicular d. None

14. The x intercept of the line 3x + 5y = 15 is
a. 5 b. 3 c. 15 d. None

15. 3tanθ = 4 then cosθ is ____
a. 3/4 b. 3 c. 4

d.
4
3

II. Answer any TEN questions only                                        10 x 2 = 20

16. Find the 10th term of the A.P. 10, 10.5, 11, .....

17. Find the sum 17+19+21+.........+30 upto 30 terms.

18. Find the volume of a cylinder of diameter 8 cm and height 10 cm.

19. If A = {1,2,3,4}, B = {3,4,5,6} find A-B

20. Find the quotient and remainder : x3 - 3x2 - 6x - 5  x - 2

21. Factorise : x3 + 2x2 + 2x + 1

22. Determine the nature of the roots of the equation 4x2 - 28x + 49 = 0

23. If θ = 45 Evaluate 2tan2 θ - sin2 θ - 1

24.            A

           6       3               In triangle ABC DE II BC
          D            E           Find the value of
                                   AD = 6
     10                    X       DB = 10
                                   AE = 3
B                              C   EC = x

25. Find the point p which divides the line joining the points (3, 4) and (-6, 2)
internally in the ratio 1 : 3
26. An integer is chosen from 1 to 50. Find the probability that it is a multiple of 9.

27. Find the equation of st. line whose slope is 3/4 and 'y' intercept is - 4.
              C

28.                                     In the figure O is the centre
                                        mOAC = 35
      35O     45         mOBC = 45 then find mAOB
        A                  B

29. A chord of 12 cm from the centre of the circle of radius 10 cm. Find the
distance between the centre and the chord.

30. Draw the graph of 2x + 4 ≥ 4

III. Answer any nine questions only, choosing either of the alternatives.

                                                                           9 x 5 = 45

31. In a G.P. the sixth term is 63 and tenth term is 5103 find the G.P.

                                           (OR)

Find the sum of all the integers divisible by 9 lying between 400 and 600.

32. The total volume of a cone and a sphere is equal to the volume of a cylinder
whose radius is 4 cm and height is 8 cm. The radius of the cone is 4 cm and
height is 22 cm. Find the radius of the sphere.

                                           (OR)

The noon meal is kept in 3 cylindrical vessels. The diameter of the vessels is 1.4
mts and the height is 54 cm. The meal is served twice in a hemispherical bowl of
radius 14 cm. Find the number of students who got the meal.

33. Among the girls studying in a class, 28 speak tamil, 24 speak telugu, 18
speak malayalam, 10 speak both tamil and telugu, 6 speak tamil and malayalam
whole 7 speak telugu and malayalam. If 3 can speak all the three languages find
the number of girls.

                                         (OR)
            2
f(x) = 4x - 1, g(x) = 1 + x Prove that fog ≠ go f

34. Solve          2x - 2y + 4z = -12
                   3x + 2y + 2z = 19
                -x + y - z = 3

                                        (OR)

(x-7), (x-4) are the factors of px3 + qx2 - 5x + 84 find the values of P, Q

35. Find the square root of 16x4 - 24x3 - 31x2 + 30x + 25

                                        (OR)

The perimeter of the rectangle is 36 cm. Its area is 80 cm2. Then find its length
and breadth.

36. Solve the L.P.P. Minimize z = 5x + 4y subject to 4x + 4 ≥ 40; 2x + 3y ≥ 90. (x
≥ 0) (y ≥ 0)

                                        (OR)

The following table gives the activities in a construction project and relevant
information

Activity         1-2    1-3      2-3      3-4       3-5      4-6      5-6      6-7
Duration days    5      10       3        4         6        6        5        5

Draw the network for the project and find the critical path. Compute the project
duration.

37. Prove : The sum of the opposite angles of a cyclic quadrilateral is 180
                                     (OR)

In the given diagram prove that PQ+RS=PS+QR.

                                  P        D       S


                                 A        O         C



                                 Q        B        R


38. Find the area of the Triangle whose vertices are (5, 6), (2,4), (1,-3)

                                        (OR)
Find the equation of the straight line joining the point (4,5) and the point of
intersection of the st. lines 5x - 3y = 8 and 2x - 3y = 5.

39. Find the area of an isosceles triangle with base 20cm and vertical angle 48
40'.
                                       (OR)

Two men are on the opposite side of a tower. They measure the angles of
elevation of the top of the tower as 30 and 45 respectively if the height of the
tower is 150 m. find the distance between the men.

40. When two dice are thrown at a time. Find the probability of getting the sum of
numbers that appear on the two dice (i) to be 9 (ii) to be less than 9.
                                     (OR)
The following are the marks scored out of 50 in five tests by two students.

Arun          : 45   35      17     40      23
Ramesh        : 30   47      32     41      28 find who is more consistent is scoring
marks.

IV. Answer both the questions choosing either of the alternatives
                                                               2 x 10 = 20

41. Draw a circle of radius 3 cm. Mark a point which is at a distance of 8 cm from
its centre. Draw two tangents through the point and measure its length.

                                         (OR)

Draw a triangle ABC such that AB = 4.5 cm, MC = 70 the altitude drawn from C
to AB is 3.5 cm.

42. Solve Graphically y = x2 + 2x - 8 = 0

                                         (OR)

A man takes 10 days to complete a work by working 8 hrs a day. Draw the graph
showing the relation and from the graph find our how many days he will take if he
works 5 hrs a day.

				
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