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Sample Paper – 2009

Class – X

Subject – Mathematics

 

Time : 3 hrs                             Marks :80

 

General Instructions

 

1. All questions are compulsory

2. The question paper consists of 25 questions divided in to 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 of 6 Questions of 5 marks each

3. There is no overall choice .However ,internal choice has been provided in two questions of two

   marks each, two questions of three marks each, two questions of five marks each

4. In question on construction ,drawing should be neat exactly as per the given measurements.

5. Use of calculators is not permitted.

SECTION - A

 

 

Q1. If x+3 is a factor of      and   find a and b

Q2. Reduce the following rational expression into lowest terms

             

Q3. Solve for x

             

                            OR

              Solve for x :

             

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Q4. What is the difference between the 20th  terms of two AP with same common difference and                  first terms 3 and 8 ?, justify your answer .

OR

              Find the number of terms of the AP 54, 51,48,.... so that their sum is 513.

Q5.  If the diagonal BD of a quadrilateral ABCD bisects both and ,show that

Q6.  A mixi is available for Rs 5,400 cash or Rs 1,400 cash down payment followed by Rs 4,240 after 6 months .Find the rate of interest charged under this instalment scheme  

Q7. Two coins are tossed simultaneously. find the probability of getting

                            1. Two heads                                          2. at least one head

SECTION - B

 

 

 

 

 

 

Q8. Find the common root(s) of the equations

              and

Q9. The hypotenuse of a right angles triangle is  4 more than three times the shortest side .If the third side is 4 less than four times the shortest side ,find the sides of the triangle

Q10. If a, b , c are pth ,qth , rth terms of an AP then prove that

Q11. A loan of Rs 48,800 is to be paid back in 3 equal annual instalment .If the rate of  interest is 25%



              per annum compounded annually .Find the instalment

Q12. The areas of two similar triangles are 81 Cm2 and 49Cm2 respectively .If the altitude of the bigger

              triangle is 4.5Cm find the corresponding altitude of the smaller triangle

OR

              In the trapezium ABCD AB parallel to CD and

              If ar(DAOB) = 84Cm2 , ,find ar(DCOD)

 



Q13. In the given figure ABC is a triangle in which

              A circle through B touches AC at D and  intersect AB

              at P .If D is the mid point of AC , show that

 

Q14. Construct D ABC  having perimeter 14 Cm  and   Then construct the circum circle of the triangle 

Q15. The radius and height of a solid right circular Cylinder are 10 Cm and 30 Cm respectively . It is  melted and solid cones are prepared with diameter of the base 2 Cm and height 10 Cm . Find

how many such cones are prepared from the Cylinder

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Q16. Prove that

OR

              Without using trigonometric table evaluate

             

 

 

 

 

 

Q17. Marks of 40 students in examination is represented by a frequency distribution .And their

              mean marks is 40.5 find the missing frequencies.

Class

0-10

10-20

20-30

30-40

40-50

50-60

60-70

70-80

Frequency

5

3

4

F1

7

F2

6

3

 

Q18. The co-ordinates of one end of the diameter of a circle are (3,5) and the co-ordinates of its centre

              are (7,4). Find out the co-ordinates of  the other end of the  diameter

 

 

 

 

Q19. Find the third vertex of  a triangle , if two of its vertices are at (-3,1) and (0,-2) and the centroid is

              at the origin

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Q20. Anuradha’s salary is Rs 15,000 per month and she contributes Rs 2,000 per month towards PF

              and  pays  Rs 8,000  as annual LIC premium .She invests Rs4,000 in NSC and she donates

              Rs 2,000 towards PM’s National Relief Fund .Find the income tax to be played by her for

              the financial year              



Q21. a) “In a triangle a line drawn parallel to one side to intersect the other sides in distinct  points ,divides the two sides  in the same ratio”. Prove 

b) In the figure If PQ parallel to BC and PR parallel to

              CD , Prove that

 



Q22. In the given figure O is the centre of the circle and OP

              bisects angle APD  prove that

 

 

Q23. A cone of height 15 Cm and diameter  7 Cm is mounted on a hemisphere of the same diameter               .Determine the volume of the solid thus formed .(use )

OR

Find the number of bricks each measuring required to construct a wall 24m long ,6m high and 0.4m thick The mortar occupies of  the volume of the wall              

 

 

 

Q24. A person standing on the bank of a river observes that the angle of elevation of the top  a tree

              standing on the opposite bank is . When he moves 40m away from the bank ,he finds the

              angle of elevation to be . Find the height of the tree and the width of the river

OR

              From the top of a building AB, 60 m high, the angles of depression of the top and bottom of

             a vertical lamp post CD are observed to be 300 and 600 respectively  Find

              (i) the horizontal distance between AD and CD.

              (ii) the difference between the heights of the building and the lamp post.



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Q25. The pie chart (as shown in the figure) represents the

              amount spent on different sports by a sports club in

              a year .If the amount spent by the club for hockey

              is 30,000 .Find the total amount spent and amount spent

              on each sports

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