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Posted By: kavi Member Level: Gold Posted Date: 15 Sep 2008
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2008 CBSE ENGLISH AANUAL EXAMINATION Question paper
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CBSE Annual Examination Question Paper 2008
Class 10
MATHEMATICS
[Time allowed : 3 hours] [Maximum marks : 100]
General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of thirty questions divided in to 4 sections – A, B, C and D. Section A comprises of ten questions of 01 marks each, Section B comprises of five questions of 02 marks each, Section C comprises of ten questions of 03 marks each and Section D comprises of five questions of 06 marks each.
(iii) All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
(iv) There is no overall choice. However , internal choice has been provided in one question of 02 marks each, three questions of 03 marks each and two questions of 06 marks each. Yu have to attempt only one of the alternatives in all such questions.
(v) In question on construction, drawings should be neat and exactly as per the given measurements.
(vi) Use of calculators in not permitted.
SECTION – A
Question numbers 1 to 10 carry one mark each.
1. Find the value of k so that the following system of equations has no solution:
3x – y – 5 = 0; 6x – 2y – k = 0.
2. The nth term of an A.P. is 6n + 2. Find its common difference.
3. In fig. 1, AD = 4 cm, BD = 3 cm and CB = 12 cm, find cot .
4. Write the zeroes of the polynomial x2 – x – 6.
5. If is a rational number (q not equal to 0), what is condition on q so that the decimal representation of is termination?
6. From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.
7. Which measure of central tendency is giving by the x-coordinate of the point of intersection of the “more than o give” and “less than o give”?
8. In Fig. 2, O is the centre of a circle. The area of sector OAPB is 5/18 of the area of the circle. Find x.
9. In. Fig. 3, PQ = 24 cm, QR = 26 cm, PAR = 900, PA = 6 cm and AR = 8 cm. Find QPR.
10. In Fig. 4, P and Q are points on the sides AB and AC respectively of triangle ABC such that AP = 3.5 cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm, find BC.
SECTION – B
Question numbers 11 to 15 carry 2 marks each.
11. For what value of p, are points (2, 1), (p, -1) and (-1, 3) collinear?
12. Without using trigonometrically tables, evaluate the following:
13. Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeros and the co-efficients of the polynomial.
14. A die is thrown once. Find the probability of getting
(i) An even prime number
(ii) A multiple of 3
15. ABC is an isosceles triangle, in which AB = AC, circumscribed about a circle. Show that BC is bisected at the point of contract. OR
In Fig. 5, a circle is inscribed in a quadrilateral ABCD in which B = 900. If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius (r ) of the circle.
SECTION – C
Question numbers 16 to 25 carry 3 marks each.
16. Prove that: OR
Prove that: (1 + cot A – cosec A) (1 + tan A + sec A) = 2
17. Find the 10th term from the end of the A.P. 8, 10, 12,…………….,126.
18. Represent the following system of linear equations graphically. From the graph. Find the points where the lines intersect y-axis: 3x + y – 5 = 0; 2x – y – 5 = 0.
19. Find the roots of the following equation:
20. Show that 2 - is an irrational number.
21. In Fig. 6, find the perimeter of shaded region where ADC, AEB and BFC are semi – circles on diameters AC, AB and BC respectively.
OR Find the area of the shaded region in Fig. 7, where ABCD is square of side 14 cm.
22. If the distances of P(x, y) from the points A(3, 6) and B(-3, 4) are equal, prove that 3x +y = 5.
23. If the diagonals of a quadrilateral divided each other proportionally, prove that it is a trapezium. OR
Two triangles ABC and DBC are on the same base BC and on the same side of BC in which A = D = 900. If CA and BD meet each other at E, show that AE.EC = BE.ED
24. Construct a ABC in which AB = 6.5 cm, B = 600 cm, and BC = 5.5 cm. Also construct a triangle. AB’C’ similar to triangle ABC , whose each side is 3/2 times the corresponding side of the triangle ABC.
25. Determine the ratio in which the line 3x + 4y – 9 = 0 divides the line-segment joining the points (1, 3) and (2, 7).
SECTION – D
Question numbers 26 to 30 carry 6 marks each.
26. A state 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 600 and from the same point, the angle of elevation of the top of the pedestal is 450. Find the height of the pedestal (use root 3 = 1.73)
27. In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.
OR The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m, find the sides of the two squares.
28. 100 surnames were randomly picked up from a local telephone directory and the distribution of number of letters of the English alphabet in the surnames was obtained as follows:
No. of letters 1-4 4-7 7-10 10-13 13-16 16-19
Numbers of surnames 6 30 40 16 4 4
Determine the median and mean number of letters in the surnames. Also find the modal size of surnames.
29. Prove that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
Using the above result, prove the following:
In a triangle ABC, XY is parallel to BC and it divides triangle ABC into two parts of equal area.
Prove that .
30. A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also find the cost of the bucket it the cost of metal sheet used is Rs 20 per 100 cm2. (use pie = 3.14)
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