CBSE Board Class 10 Math Previous Year Question Papers 2007

PREVIOUS YEAR PAPER-2007
CLASS 10

MATHEMATICS

SECTION   A
Questions number 1 to 7 carry 2 marks each.

1. Find the GCD of the following polynomials :
12x 4 + 324x ;    36x 3 + 90x 2 — 54x

2. Solve for  x  and  y : 31x + 29y = 33,     29x + 31y = 27

3. Find the sum of all three digit whole numbers which are multiples of  7.

4. In Figure 1,   PQ | | AB   and   PR | | AC.   Prove that   QR | | BC. ABC  touches  its   sides  AB,   BC   and  CA  at  D,   E   and  F respectively. If AB = AC, prove that BE = EC.

5. If the mean of the following frequency distribution is 49, find the missing frequency p :
Class Frequency
0 -   20     2
20 - 40     6
40 - 60     p
60 - 80     5
80 - 100   2

6. A wrist-watch is available for Rs. 1,000 cash or Rs. 500 as cash down payment followed by three equal monthly instalments of Rs. 180. Calculate the rate of interest charged under the instalment plan.

7. An unbiased die is tossed once. Find the probability of getting
(i) a multiple of  2 or 3.
(ii) a  prime number greater than 2.

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

8. Solve the following system of equations graphically :
2x + y = 8;    x + 1 = 2y

9. Simplify the following rational expression in the lowest terms :

10. If the sum to first n terms of an A.P. is given by S n = n (n + 1), find the 20 th term of the A.P.

11. In a cyclic quadrilateral ABCD, diagonal AC bisects C. Prove that the tangent to the circle at A is parallel to the diagonal BD.

12. Construct a ABC in which base BC = 6 cm, B = 45°  and C =  60°.  Draw a circumcircle of ABC.

13. The diameter of a solid copper sphere is 18 cm. It is melted and drawn into a wire of uniform cross-section. If the length of the wire is 108 m, find its diameter.

14. The expenditure (in rupees) of a family for a month is as follows : Item Rent Food Education Electricity and Water Others
Expenditure 800 3000 1200 400 1800 Represent the above data by a pie-chart.

15. From a pack of 52 cards, red face cards are removed. After that a card is drawn at random from the pack. Find the probability that the card drawn is
(i) a queen.
(ii) a  red card.
(iii) a  spade card.

16. Prove that :
If A, B and C are the interior angles of a triangle ABC,   show that

17. The coordinates of the mid-points of the sides of a triangle are (4, 3), (6, 0) and (7, —2). Find the coordinates of the centroid of the triangle.

18. If the distance of P (x, y) from two points with coordinates (5, 1) and (—1, 5) is equal, prove that   3x = 2y.

19. A loan of Rs. 24,600 is to be paid back in two equal semi-annual instalments. If the interest is charged at 10% per annum, compounded semi-annually, find the instalment.

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

20. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Using the above, prove the following : O is the centre of the circle. If BAO = 30° and BCO = 40°,   find the value of AOC.

21. State and prove Pythagoras theorem. Use the above to prove the following : ABC is an isosceles right triangle, right angled at C.   Prove that   AB 2 = 2AC 2

22. The side of a square exceeds the side of another square by 4 cm and the sum of areas of two squares is 400 sq. cm. Find the dimension of the squares. A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hour less than that of the fast train, find the speeds of the
two trains.

23. A hollow copper sphere of external and internal diameter 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone. If the radii of the circular ends of a bucket 45 cm high, are 28 cm and 7 cm, find the
capacity and surface area of the bucket. 

24. An observer in a lighthouse observes two ships on the same side of the lighthouse, and in the same straight line with the base of the lighthouse. The angles of depression of the ships approaching it are 30° and 60°. If the height of the lighthouse is 150 m, find the distance between the ships.

25. Satish (aged 67 years) has monthly income of Rs. 30,000 (excluding HRA). He donates Rs. 80,000 to a charitable orphanage (50% exemption). He contributes Rs. 30,000 towards Public Provident Fund and purchases NSCs worth Rs. 20,000. He pays Rs. 1,500 as income tax per month for 11 months. Calculate the income tax to be paid by him in the
 12 th 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 for Senior Citizens (over 65 years)NSlab Income tax
(i) Upto Rs. 1,85,000 No tax
(ii) From Rs. 1,85,001 to Rs. 2,50,000 20%  of the  taxable  income  exceeding Rs. 1,85,000
(iii) From Rs. 2,50,001 and above Rs. 13,000 +  30%  of  the taxamble exceeding Rs. 2,50,000
(c) Education Cess 2% of Income tax payable30/2/1 11 P.T.O.