# Sample Papers

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CBSE (CLASS – IX) MATH FINAL EXAM MOCK TEST

FULL MARKS : 90 MAX. TIME : 3 hrs

Section: A

1. Any point on the line x + y = 0 is of form a. ( , ) b. (0, ) c. ( , 0)

(1 * 8 = 8)

d. ( , − )

2. The coefficient of y in the equation 3(2x – y) + x + 2y = 5 is a. 7 b. -5 c. -1 d. 1

3. If in a sphere, volume and surface area are numerically equal, then radius will be: a. 1 b. 3 c. 2 d. 4

4. The length of longest pole that can be put in a room of dimensions (10m x 10m x 5m) is a. 15m b. 16m c. 10m d. 12m

5. If in a quadrilateral, diagonals are equal, then it cannot be a : a. Square b. Rhombus c. Parallelogram d. Rectangle

6. The median of a triangle divide it into two a. Triangles of equal area b. Right triangles c. Equilateral triangles d. Isosceles triangles.

7. A fair die is thrown. The probability that a prime number will occur is a. 2 3

b.

1 2

c.

3 5

d.

1 6

8. If the mean of x, x +2, x+4, x+ 6, x+ 8 is 24, then x = a. 22 b. 21 c. 20 d. 24

Section: B

(2 * 6 = 12)

9. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the 22 base of the cylinder. Assume π = . 7 10. In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. 11. The blood groups of 30 students of Class VIII are recoded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table.

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Biswa Ranjan Pradhan (+91 9474756470)

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12. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 13. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. 14. In the given figure, ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.

Section: C

15. Give the geometric representation of y = 3 as an equation i) In one variable ii) in two variables

(3 * 10 = 30)

16. Give the equations of two lines passing through (2, 14). How many more such lines are there, and why? 17. A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find 22 i) Inner curved surface area ii) Outer curved surface area iii) Total surface area (Assume π = ) 7 18. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained. 19. 1500 families with 2 children were selected randomly, and the following data were recorded: Number of girls in a family Number of families 2 475 1 814 0 211 (i) 2 girls (ii) 1 girl (iii) No girl

Compute the probability of a family, chosen at random, having

20. The following number of goals was scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median and mode of these scores. 21. Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm. OR Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. 22. If the diagonals of a parallelogram are equal, then show that it is a rectangle. 23. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that, ar∆ ( APB ) = ar∆ ( BQC ) . 24. In a triangle ABC, E is the mid-point of median AD. Show that, ar∆ ( BED ) = 1 ar∆ ( ABC ) 4

Biswa Ranjan Pradhan (+91 9474756470)

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Section: D

(4 * 10 = 40)

25. If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord. 26. Prove that parallelograms on the same base and between same parallels have the same area. 27. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively....

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