Y

P

X Z

B A

O 3002

Model Examination -2011- 2012X A MATHEMATICS Marks 50

Time : 1½

1. Find the number of negative numbers in the sequence -90, -83, -76. (2)2. PQ is the diameter of a circle and R is a point on the circle. What is ∠ PRQ ? If R is

outside circle what about ∠ PRQ ? What about ∠ PRQ if P is inside ? (3)3. On which side of (-1, 4) is (-5, 4) ; Find two points at right of (-1, 4) on the line joining

them. (2)4. The first and seventh terms at an AP are 6 and 22. What is the 4th term. Find common

difference what is its algebra ? (3)5. P is the centre of the circle.

Prove that ∠XPZ = 2(∠ XZY + ∠ YXZ) (3)

6. One solution of quadratic equation 2x2 + Kx-6= 0 is 2. Find the value of K and the solution. (3)

7. The longest side of a right angled triangle is 18m. The angle made by this side with another side is 240. Find the area of triangle. (3)

8. A sector of central angle 2160 is cut out from a circle of radius 25 cm and it is rolled up into a cone. What is the base radius and height of that cone? What is its volume?(3)

9. What are the co-ordinates of points A and B in the fig. (3)

10. A point was marked in the picture below without looking. What is the probability that it is within the circle ? What is the probability that it is outside the circle ? (3)

11. Find the values of K for which 4x2-5x + K= O gives two equal roots. (3)12. The radius of the circle whose centre (-3, -2) is 4 units check whether the point (-2, 1)

lies inside the circle or not. (3)13. The table below classifies according to weight, the infants born during a week in a

hospital.

Wt. in Kg No. of infants2.500 42.600 62.750 82.800 103.000 123.150 103.250 83.300 73.500 5 Find median weight. (4)

. O

Q

R

P400 (5cm

30 cm 25 cm

14. The sum of 1st is terms of an AP is 2n2-n. Find the algebra form of the sequence. (4)15. Draw a triangle within a circle having circum radius 3 cm. Two angles of this triangle

should be 300 and 500. (3)16. The circle in the fig below touches all the three lines.

Prove that the termeter of right angled triangle is equal to diameter of circle. (4)

17. Construct the following fig using the given measurements. (4)

18. a) Write x2-9x+20 as the product of two first degree polynomialsb) Using remainder theorem find the remainder when 2x2+x2-2x-4 is divided by x-1.

By adding a suitable number, convert this to a polynomial so that (x-1) is a factor of it. (4)

19. The table below classifies the members of a committee according to their ages. Calculate the mean age of members of this committee. (3)

Age No. of members25-30 630-35 1435-40 1640-45 2245-50 550-55 455-60 3

20. 200 rupees is invested in a scheme giving interest compounded annually. After two years the amount became 2205 rupees. What is the rate of interest. (5)

21. The length of two sides of a triangle are 6 cm and 4cm and angle between them is 500. What is the area of this triangle. (5)

22. The opened shape of a solid is given. What is the most suitable name for it? Which measures are given to be 30cm and 25cm. What is its volume and surface area? (5)

23. What is the slope of the line 4x+2y-9=0. What is the equation of the line with the same slope passing through (4,7) ? (5)

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