Class X- 2009
Time allowed: 3 hours; Maximum Marks: 80
|1)||All questions are compulsory.|
|2)||The question paper consists of thirty questions divided into 4 sections A, B, C and D. Section A comprises of ten questions of 01 mark each, Section B comprises of five questions of 02 marks each, Section C comprises ten questions of 03 marks each and Section D comprises of five questions of 06 marks each.|
|3)||All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.|
|4)||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. You have to attempt only one of the alternatives in all such questions.|
|5)||In question on construction, drawing should be near and exactly as per the given measurements.|
|6)||Use of calculators is not permitted.|
Question number 1 to 10 carry 1 mark each.
1. Find the [HCF X LCM] for the numbers 100 and 190.
2. If 1 is a zero of the polynomial p(x) = ax2 – 3(a – 1)x – 1, then find the value of a.
3. In ΔLMN, ∠L = 50° and ∠N = 60°. If Δ LMN ~ ΔPQR, then find ∠Q.
4. If sec2θ (1 + sin θ)(1 – sin θ) = k, then find the value of k.
5. If the diameter of a semicircular protractor is 14 cm, then find its perimeter.
6. Find the number of solutions of the following pair of linear equations:
x + 2y – 8 = 0
2x + 4y = 16
8.If 4/5a, 2 are three consecutive terms of an A.P., then fine the value of a.
9.In figure below, ΔABC is circumscribing a circle. Find the length of BC
10. Two coins are tossed simultaneously. Find the probability of getting exactly one head.
Questions number 11 to 15 carry 2 marks each.
11.Find all the zeroes of the polynomial x³ + 3x² – 2x – 6, if two of its zeroes are -√2 and √2 .
12. Which term of the A.P. 3, 15, 27, 39, … will be 120 more than its 21st term?
13.In the figure below, ΔABD is a right triangle, right-angled at
A and AC ^ BD. Prove that AB² = BC . BD.
14.If cot =15/8 then evaluate (2+2sinθ ) (1-sinθ )/1+cosθ ) (2+ cosθ)
15.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.
Question number 16 to 25 carry 3 marks each.
16. Prove that (3+√2) is an irrational number.
17. Solve for x and y:
ax – by = 2ab
18. 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.
19. Evaluate: 2/3 cosec 58° – 2/3 cot 58° tan 32°- 5/3 tan 13 °tan 37°tan 45° tan 53° tan 77°
20. 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 ¾ times the corresponding sides of the first triangle.
21. In the figure below, AD is perpendicular to BC and BD = 1/3 CD. Prove that 2 CA² = 2 AB² + BC².
22. Find the ratio in which the point (2, y) divides the line segment joining the points (-2, 2) and (3, 7). Also find the value of y.
23. Find the area of the quadrilateral ABCD whose vertices are A(-4, -2), B(-3, -5), C(3, -2) and D(2, 3)
24. The area of an equilateral triangle is 49√3 cm2. Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle.
Find the area of triangle not included in the circles. [Take √3 = 1.73
25. 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?
26. Solve the following equation for x.
9×2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0
27. Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Using the above theorem, prove that:
If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC
28.An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.
29. A juice seller serves his customers using a glass as shown in figure. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use p = 3.14)
30. During the medical checkup of 35 students of a class, their weights were recorded as follows:
Weight (in kg) Number of students
38 – 40 3
40 – 42 2
42 – 44 4
44 – 46 5
46 – 48 14
48 – 50 4
50 – 52 3
Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph.