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Posted Date: 31 May 2009 Posted By: CIJU Member Level: Gold
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2009 CBSE School Level Courses Maths MATHEMATICS PAPER 2009. University Question paper
SECTION A
Question number 1 to 10 carry 1 mark each.
Question 1
1. Find the [HCF X LCM] for the numbers 105 and 120.
2. Find the number of solutions of the following pair of linear equations:
x + 2y – 8 = 0
2x + 4y = 16
Question 3
3. If a, 2 are three consecutive terms of an A.P., then fine the value of a.
Question 4
4. Two coins are tossed simultaneously. Find the probability of getting exactly one head.
uestion 6
6. If the diameter of a semicircular protractor is 14 cm, then find its perimeter.
Question 7
7. If 1 is a zero of the polynomial p(x) = ax2 – 3(a – 1)x – 1, then find the value of a.
Question 8
8. In ?LMN, ?L = 50° and ?N = 60°. If ? LMN ~ ?PQR,
then find ?Q.
Question 9
9. If sec2? (1 + sin ?)(1 – sin ?) = k, then find the value of k.
11. Find all the zeroes of the polynomial 2x3 + x2 – 6x – 3,13. If the points A(4, 3) and B(x, 5) are on the circle with the centre O(2, 3), find the value of x.14. Which term of the A.P. 3, 15, 27, 39, … will be 120 more than its 21st term?
15. In figure 2, ?ABD is a right triangle, right-angled at A and AC ^ BD. Prove that AB2 = BC . BD.
SECTION C
19. Two dice are thrown simultaneously. What is the probability that
(i) 5 will not come up on either of them?
(ii) 5 will come up on at least one?
(iii) 5 will come up at both dice?
20. The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteenth terms of the A.P.
22. Find the ratio in which the point (x, 2) divides the line segment joining the points (-3, -4) and (3, 5). Also find the value of x.
23. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3).
24. Solve for x and y:ax – by = 2ab
25. Draw a right triangle in which sides (other than hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph.
30. Solve the following equation for x.
9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0
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