CBSE Board Class 10 Math Previous Year Question Papers 2011

CBSE X
Previous Paper
MATHEMATICS PAPER 2011

General Instructions:
1) All questions are compulsory.
2) The question paper consists of 25 questions divided into three sections- A, B and C. Section A contains 7 questions of 2 marks each, Section B is of 12 questions of 3 marks each and Section C is of 6 questions of 5 marks each.
3) There is no overall choice. However, an internal choice has been provided in two questions of two marks each, two questions of three marks each and two questions of five marks each.
4) In question on construction, the drawing should be neat and exactly as per the given measurements.
5) Use of calculators is not permitted. However, you may ask for Mathematical tables.
  
SECTION A

1. If  is the G.C.D of  and  find the value of 

2.  Solve for  and :

3. Find the sum of first  terms of an A.P. whose  term is

4.   P and Q are points on sides CA and CB respectively of ∆ABC, right angled at C. Prove that

5. The mean of the following frequency distribution is 62.8. Find the 
     missing frequency x
Class           frequency
0-20               5

20-40             8

40-60            10

60-80            12

80-100           7

100-120         8

6. Cards marked with numbers  are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is
     (i) divisible by 7.
    (ii) a number which is a perfect square.

7. A washing machine is available for Rs. 13,500 cash or Rs. 6,500 as cash down payment followed by three monthly installments of Rs. 2,500 each. Find the rate of interest charged under installment plan.

8. Solve the following system of equations graphically:

9. Which term of the A.P.  will be 132 more than its  term?

10. In fig. 2, TA is a tangent to the circle from a point T and TBC is a secant to  the circle. If AD is the bisector of   prove that ∆ADT  is isosceles.

11. Draw a ∆PQR with base  vertical angle  and median through P to the base is of length 4.5 cm.

12. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

13. The enrolment of a secondary school in different classes is given below.
Class       Enrolment

VI              600

VII            500

VIII           400

IX             700

X              200

14. A bag contains 5 red balls and some blue balls. If the probability of  drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.

15. Show that the points  are the vertices of an  isosceles right triangle.

16. In what ratio does the line  divides the line segment joining.

17. A man borrows money from a finance company and has to pay it back in two equal half-yearly installments of Rs. 7,396 each. If the interest is charged by the finance company at the rate of 15% per annum, compounded semi-annually, find the principal and the total interest paid.