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Sample Paper – 2009

Class – X

Subject – Mathematics

 

  1. Fins the value of 2 cos6700/ sin230 - tan400/cot500
  2. If the radius of a sphere is made thrice what will be its new S.A.
  3. Two dice are thrown once find  the probability of doublets.
  4. Find the missing value in the A.P.   ?  13,  ?  3
  5. Find the number of spheres of radius 2cm can be arranged in a cuboid of size
    12cm x 6cm x 8cm.
  6. If tanA= 4/3 ,find secA
  7. Determine k so that 4k+8 , 2k2+3k+6 , 3k2+4k+4 are the three consecutive terms of an A.P.
  8. A sphere of radius r is divided into four identical parts. Find the total surface area of one part.
  9. If x-2 is a factor of x2+ax+b and a+b=1,find a and b.
  10. In a tr ABC ÐB = 2ÐC and the bisector of ÐB bisects AC at D . Prove that
    BD/ DA= BC/BA

 

  1. It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. What is the probability that it is non defective bulb?
  2. For what value of p the equation has coincident roots :
    (1+p)x2 +2(1+2p)x + (1+p) =0

 

  1. A roll of paper is 60cm in diameter and paper is wound on  a wooden cylinder of diameter 4cm. If the paper is 0.008cm thick , what length of paper will be rolled.
  2. Solve for a and b:

            2a+3b = 17 , 2a+2 – 3 b+1=5        

  1. Metallic spheres, each of radius 2 cm, are packed into a rectangular box of internal dimension 16 cm ´ 8 cm ´ 8 cm. Find the number of  spheres  packed and the volume of liquid filled as preservative.
  2. If tana= ntanb and sina= msinb
    then prove that cos2a =(m2-1)/(n2-1)
  3. Two concentric spheres having radii r and 2r .A cone is inscribed in the bigger sphere which is also circumscribing the smaller sphere. Show that the volume of the cone is 3pr3 and its CSA is 6pr2
  4. A balloon moving in a straight line passes vertically above points A and B on a horizontal plane 1000 m apart. When above A it has an altitude of 600 as seen from B and when at B it has an altitude of 450 as seen from A. Find the distance from A of the point where the balloon will touch the ground.
  5. A wireless pole 20 m high is fixed on the top of the verandah of a house which is 5 m high. At a point A on the ground directly opposite, the wireless pole and the verandah subtends equal angles. Find the distance of A from the verandah.
  6. ABCD is a trapezium in which L amd M are the mid points of the diagonal AC and BD respectively. Prove that AB2+BC2+CD2+DA2 = AC2+BD2+4LM2.
  7. A cylindrical vessel open at one end, is made of thin copper sheet. The area of the inner surface is 148.5sqdm and the area of the base is 38.5sqdm. How many cubic dm of milk can be hold by the vessel.
  8. An employee finds that if he increases the wages of each worker by Rs50 and the employs one worker less he reduces his weekly wages bill by Rs230 from Rs6800 to Rs6570. taking the original weekly wages be x obtain eq in x and find the weekly wages of each worker.     
  9. Find the value of sin25° + sin210°  + sin215°              + ……….. + sin2 85°  + sin290°
  10. Traveler starts from A towards B at 7am and another starts at the same time
    from B towards A. They meet at 9am. At 36 km from A. When one arrives at A ,the other is 30km from B. What is the distance between A and B.
     
  11. A conical vessel of radius 6cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides , it is just immersed. What fraction of water is over flowed.
  12. The radius of a sphere is 10cm. If the radius is increased by 5% by how much percent the volume is increased.
  13. If the ratio of sums of n terms of two A.Ps. is (3n+2) : (5n+6) ,find the ratio of their 11th terms.
  14. Mohan purchased a car for Rs22000 he paid Rs4000 cash and promised to pay the balance in 18 annual instalment of Rs1000 along with interest due on unpaid amount. If the rate of interest is 10% p.a. , what will the car cost to Mohan.
  15. A man is standing ‘a’ meters behind and opposite the middle of football goal observe that the angle of elevation of the nearer cross bar is a and that of the farther cross-bar is b. Show that the length of the field is
    a{ (tana - tanb)/ tanb} .

 

  1. Find the value of p in case

xi               5               8               11               p               17

fi                            2              4              8              4              2

Given than the Arithmetic mean of this distribution is 11.

 

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