CBSE Board Class 10 Math Previous Year Question Papers 2009

PREVIOUS PAPER 2009
CLASS 10 
MATHS

1. Find the LCM 

2. Solve for x and y :
8x —9y = 6xy
10x + 6y = 19xy
OR
Solve for x and y :

8x —9y = 6xy
10x + 6y = 19xy

3. In an A.P., the sum of its first n terms is   n2 + 2n.   Find its 18 th  term.

4. In Figure 1, two circles touch each other externally at C. Prove that the common tangent
at C bisects the other two common tangents.
OR
D is any point on the side BC of a
ABC such that
ADC =
BAC. Prove that
CA2
= BC .CD.

5. Find the mean of the following distribution :
Class Frequency
0-10 8
10-20 12
20-30 10
30-40 11
40-50 93

6. A ceiling fan is marked at Rs. 970 cash or for Rs. 210 as cash down payment followed
by three equal monthly instalments of Rs. 260. Find the rate of interest charged under
the instalment plan.

7. A box contains 5 red balls, 4 green balls and 7 white balls. A ball is drawn at random
from the box. Find the probability that the ball drawn is
(a) white.
(b) neither red nor white.

SECTION B
Questions number 8 to 19 carry 3 marks each.

8. Solve the following system of linear equations graphically :
2x + 3y = 12
2y — 1 = x

9. Simplify :

10. The first term, common difference and last term of  an  A.P. are 12, 6 and 252
respectively. Find the sum of all terms of this A.P.

11. Prove that any four vertices of a regular pentagon are cyclic.
                                         OR
BC is a chord of a circle with centre O. A is a point on arc BAC as shown in Figure 2.
Prove that  
BAG +
OBC = 90°.30/1 6

12. Draw a circle of radius 4.5 cm. At a point A on it, draw a tangent to the circle without
using the centre.

13. A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter
of the base of the conical portion is 7 cm and the total height of the toy is 14.5 cm. Find
the volume of  the toy. [Use   ]

14. The expenditure on different heads of a household (in hundreds of rupees) is as follows :
Head Education Games Entertainment Gardening Decoration
Expenditure 20 10 15 10 17
Draw a pie diagram to represent the above data.

15. All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A
card is then drawn at random from the remaining pack. Find the probability of getting
(a) a black face card, (b) a queen, (c) a black card.

16. Prove that :
OR
Evaluate without using trigonometric tables

17. Three consecutive vertices of a parallelogram are (—2, —1); (1, 0) and (4, 3). Find the
coordinates of the fourth vertex.

18. If the  point  C (—1,  2)  divides  the line  segment AB  in  the  ratio  3 : 4,  where  the
coordinates of  A  are (2, 5), find the coordinates of  B.

19. A loan of Rs. 2550 is to be paid back in two equal half-yearly instalments. How much is
each instalment if interest is compounded half-yearly at 8% per annum ?

SECTION C
Questions number 20 to 25 carry 5 marks each.

20. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the
squares of their corresponding sides.
Use the above for the following :
If the areas of  two similar triangles are equal, prove that they are congruent.

21. If a line touches a circle and from the point of contact a chord is drawn, prove that the
angles which this chord makes with the given line are equal respectively to the angles
formed in the corresponding alternate segments.
Use the above for the following :
In Figure 3, ABCD is a cyclic quadrilateral and PQ is the tangent to the circle at C.
If BD is the diameter and  DCQ = 40° and  ABD = 60°, find (i)  ADB (ii)  BCP.30/1 9 P.T.O.

22. The numerator of a fraction is one less than its denominator. If three is added to each of
the numerator and denominator, the fraction is increased by  . Find the fraction.
OR
The  difference  of squares of two natural numbers is  45.  The  square  of the smaller
number is four times the larger number. Find the numbers.

23. A hemispherical bowl of internal diameter 36 cm is full of some liquid. This liquid is to
be filled in cylindrical bottles of radius 3 cm and height 6 cm. Find the number of bottles
needed to empty the bowl.
OR
Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of
80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By
how much will the level of water rise in the tank in half an hour ?30/1 10

24. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the
pole observed from a point A on the ground is 60° and the angle of depression of point
A from the top of the tower is 45°. Find the height of the tower. (Take 
   = 1.732)

25. The salary of Hukam Singh is Rs. 42,000 per month (exclusive of HRA). He donates
Rs. 30,000 to Prime Minister’s Relief Fund (100% exemption). He contributes Rs. 6,500
per month towards Provident Fund and Rs. 5,000 quarterly towards LIC premium. He
also purchases NSC worth Rs. 10,000. He pays income tax of Rs. 5,100 per month for
11 months. Calculate the income tax he has to pay in the 12th month of the year.
Use the following to calculate income tax :
(a) Savings 100% exemption for permissible savings
upto Rs. 1,00,000
(b) Rates of Income tax
Slab Income tax
(i) Upto Rs. 1,00,000 No tax
(ii) From Rs. 1,00,001 to Rs. 1,50,000 10%  of the  taxable  income  exceeding
Rs. 1,00,000
(iii) From Rs. 1,50,001 to Rs. 2,50,000 Rs. 5,000 +  20%  of   the amount
exceeding Rs. 1,50,000
(iv) Rs. 2,50,001 and above Rs. 25,000 + 30%  of the amount
exceeding Rs. 2,50,000
(c) Education Cess 2% of Income tax