CBSE Exam Results 2013

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CBSE question Paper 2009 for Class X - Mathematics

by saumil shrivastava

General Instruction for CBSE question Paper

(i) All questions are compulsory.

(ii) The question paper consists of 30 questions divided into four sections A, B, C and D. Section A comprises of ten questions of 1 mark each. Section B comprises of five questions of 2 marks each. Section C comprises of ten questions of 3 marks each and Section D comprises of five questions of 6 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, an internal choice has been provided in one questions of 2 marks each, three questions of 3 marks each and two questions of 6 marks each. You have to attempt only one of the alternative in all such questions.

(v) In question on construction, the drawings should be neat and exactly as per the given measurements.

(vi) Use of calculators is not permitted.


1. The decimal expansion of the rational number  \cfrac{43}{2^4 . 5^3}, will terminate after how many places of decimals ?

2. For what value of k,(-4) is zero of the polynomial  x^2 - x - (2k + 2) \ ?

3. For what value of  \rho , are  2 \rho - 1, 7\ and\ 3 \rho three consecutive terms of an A.P ?

4. In fig. 1, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm, and BC = 7 cm, then find the length of BR.

5. In Fig. 2,  \angle M = \angle N = 46^{^{\circ}}. Express x in terms of a, b and c where a, b and c are length of LM, MN and NK respectively.

6. If  \sin \theta = \cfrac{1}{3}, then the value of  (2 \cot^2 \theta + 2).

7. Find the value of a so that the point (3, a) lies on the lines represented by  2x - 3y = 5

8. A cylinder and a cone are the same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.

9. Find the distance between the points  \Bigg(\cfrac{-8}{5},2\Bigg)\ and \ \Bigg(\cfrac{2}{5},2\Bigg).

10. Write the median class of the following distribution :

Classes Frequency
0-10 4
10-20 4
20-30 8
30-40 10
40-50 12
50-60 8
60-70 4

Section B

11. If the polynomial  6x^4 + 8x^3 + 17x^2 + 21x + 7 is divided by another polynomial  3x^2 + 4x + 1, the remainder comes out be (ax + b), find a and b.

12. find the value(s) of k for which the pair of linear equation kx - 3y = k - 2 and 12x + ky = k has no solution.

13. If  S_n, the sum of first n terms of an A.P. is given by  S_n = 3n^2 - 4n, then find its nth term.

14. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that  \angle APB = 2 \angle OAB.


Prove that the parallelogram circumscribing a circle is a rhombus.

15. Simplify :  \cfrac{\sin^3 \theta + \cos^3 \theta}{\sin \theta + \cos \theta} + \sin \theta \cos \theta

Section C

16. Prove that  \sqrt{5} is an irrational number.

17. Solve the following pair of equations :

 \cfrac{5}{x-1} + \cfrac{1}{y-2} = 2

 \cfrac{6}{x-1} - \cfrac{3}{y-2} = 1

18. The sum of 4th and 8th terms of an A.P. is 24 and sum of 6th and 10th terms. is 44. Find A.P.

19. Construct a  \triangle ABC in which BC = 6.5 cm, AB = 4.5 cm and  \angle ABC = 60^{^{\circ}}. Construct a triangle similar to this triangle whose sides are  \cfrac{3}{4} of the corresponding sides of the triangle ABC.

20. In Fig. 4,  \triangle ABC is right angled at C and DE  \perp AB. Prove that  \triangle ABC \sim \triangle ADE and hence find the lengths of AE and DE.


In Fig. 5, DEFG is a square and  \angle BAC = 90^{^{\circ}}. Show that  DE^2 = BD \times EC.

21. Find the value of  \sin 30^{^{\circ}} geometrically.


Without using trigonometrical table, evaluate :

22. Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2).


The line segment joining the points A (2,1) and B (5, -8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by  2x - y + k = 0, Find the value of k.

23. If P(x,y) is any point on the line joining the points A (a, 0) and B (0, b), then show that  \cfrac{x}{a} + \cfrac{y}{b} = 1.

24. In Fig. 6, PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Find the area of shaded region (take  \pi = 3.14 )

25. The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs.

Section D

26. The sum of the squares of two consecutive odd numbers is 394. Find the numbers.


Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other. they meet in 1 hour. What are the speeds of the two cars ?

27. Prove that, If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Using the above result, do the following :
In Fig 7, DE||BC and BD = CE. Prove that  \triangle ABC is an isosceles triangle.

28. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of  30^{^{\circ}}, Which is approaching the foot of the tower with a uniform speed. Six seconds later the angle of depression of the car is found to be  60^{^{\circ}}. Find the time taken by the car to reach the foot of the tower from this point.

29. From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm, is hollowed out. Find the volume of the remaining solid correct to two places of decimals. Also find the total surface area of the remaining solid. ( taken  \pi = 3.1416 )


In Fig 8, ABC is a right triangle right angled at A. Find the area of shaded region if AB = 6 cm, BC = 10 cm and O is the centre of the incircle of  \triangle ABC (taken  \pi = 3.14)

30. The following table gives the daily income of 50 workers of a factory :

Daily income (in Rs.) 100-120 120-140 140-160 160-180 180-200
Number of workers 12 14 8 6 10

Find the Mean. Mode and Median of the above data.

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    ShanicFri, 24 Jan 2014 14:33:15 -0000

    Its gd but i want questions from construction

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    smrithySun, 28 Aug 2011 16:13:50 -0000

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    smvkhanSat, 18 Dec 2010 03:56:34 -0000

    sir i want weightage of marks for subject chapter wise for ssc and icse 10th class please

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Last Updated At Dec 07, 2012


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