10 Class Maths Paper

SAMPLE PAPER – 2008 Class – X SUBJECT – MATHEMATICS Time: 3 hrs Marks: 80 General Instructions: ( I ) All questions are compulsory. ( ii ) The question paper consists of 30 questions divided into four sections –A, B, C and D. Section A contains 10 questions of 1 mark each, Section B is of 5 questions of 2 marks each, Section C is of 10 questions of 3 marks each and section D is of 5 questions of 6 marks each. ( iii ) There is no overall choice. However, an internal choice has been provided in one question of two marks each, three questions of three marks each and two questions of six marks each. ( iv ) In question on construction, the drawing should be neat and exactly as per the given measurements. ( v ) Use of calculator is not permitted. SECTION A ( Qns 1 – 10 carry 1 mark each ) 1. If HCF ( a, b ) = 12 and a x b = 1800. Find LCM ( a, b ). 2. Find the zeros of the quadratic polynomial from the graph.Y 4 3 2 1 X X’ -4 -3 -2 -1 0 1 2 3 4 -1 -2 -3 Y’ 3. If the pair of linear equations x – y = 1 and x + ky = 5 has a unique solution x = 2, y = 1, find the value of k. 4. If x = 4sin2? and y = 4 cos2? + 1. Find the value of x + y. 5. Find the value of P, if cos( 810 + ? ) = sin( P/3 – ? ). 6. A horse is tied to a peg at one corner of an equilateral triangle shaped grass field of side 15m by means of a 7m rope.Find the area of that part of the field in which the horse can graze. 7. Two tangents PQ and PR are drawn from an external point P to a circle with centre O. If LQOR = 1200, then what is the value of LOPQ? Q O P R 8. An observer 1. 5m tall is 28. 5m away from a tower. The angle of elevation of the top of the tower from her eye is 450. What is the height of the tower? A B 450 C 1. 5m D 28. 5m E 9. The graph of the less than ogive and more than ogive intersect at the point ( 4, 15). What is the value of the median? 0. Suppose you drop a die on the rectangular region shown in fig. What is the probabil ity that it will land inside the circle with diameter 1m ? 2m 3m SECTION B ( Qns 11 – 15 carry 2 marks each ) 11. If 9th term of an A. P is 99 and 99th term is 9, find its 108th term. 12. A letter of English alphabet is chosen at random. What is the probability that the chosen letter is ( i ) a vowel ( ii ) a consonant. 13. If 2x + y = 35 and 3x + 4y = 65, find the value of x/y. 14.Show that the three points ( 3, 3 ), ( h, 0 ) and ( 0, k ) are collinear if 1/h + 1/k = 1/3 15. Find the zeros of the quadratic polynomial x2 + 11x + 30, and verify the relationship between the zeros and coefficients. OR Divide the polynomial p ( x ) by g ( x ) and find the quotient and remainder. p( x ) = x4 – 3Ãâ€"2 + 4x + 5 g ( x ) = x2 + 1 – x SECTION C ( Qns 16 – 25 carry 3 marks each ) 16. A shopkeeper buys a number of books for Rs80. If he had bought 4 more books for the same amount, each book would cost him Re 1 less. How many books did he buy? 7. Prove that v3 is irra tional. 18. Find the values of k for which the quadratic equation 2Ãâ€"2 – kx + x + 8 = 0 will have real and equal roots. 19. Draw a right triangle in which the sides ( other than hypotenuse ) are of length 4cm and 3cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle. 20. Prove the following identity: 1 – 1 = 1 – 1 . cosec? – cot? sin? sin? cosec? + cot? OR Without using trigonometric tables, evaluate:Sec2100 – cot2800 + sin150cos750 + cos150sin750 . Cos? sin( 900 – ? ) + sin? cos( 900 – ? ) 21. In fig. DE // OQ and DF // OR. Show that EF // QR. P D E F O Q R OR XP and XQ are two tangents to a circle with centre O from a point X out side the circle. ARB is tangent to a circle at R. Prove that XA + AR = XB + BR. P A O RX Q B 22. Show that the line segment joining the points ( -5, 8 ) and ( 10, -4 ) is trisected by the coordinate axes. 23.The line segment joining A ( 6, 3 ) to B ( -1, -4 ) is doubled in length by having half its length added to each end. Find the coordinates of the new ends. 24. In fig. LACB = 900 and CD + AB. Prove that BC2 = BD AC2 AD C A D B 25. Find the area of the shaded region if radii of the two concentric circles with centre O are 14cm and 21cm respectively and LAOC = 300. O 300 B D A C OR Calculate the area of the designed region in fig. common between two quadrants of circles of radius 8cm each. cm ***** 8cm ****** 8cm ****** * * 8cm SECTION D ( Qns 26 – 30 carry 6 marks each ) 26. Prove that in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle. Using the above do the following: In quadrilateral ABCD, LB = 900. If AD2 = AB2 + BC2 + CD2, then prove that LACD = 900. D C A B 27. From a stationary shop, Joseph bought two pencils and three chocklates for Rs11 and Sumeet bought one pencil and two chocklates for Rs7.Represent this problem in the form of a pair of linear equations. Find the price of one pencil and one chocklate graphically. 28. A man standing on the deck of a ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 600 and angle of depression of the base of the hill as 300. Calculate the distance of the hill from the ship and the height of the hill. 29. A vessel is in the form of a hemispherical bowl, surmounted by a hollow cylinder.The diameter of the hemisphere is 12cm and the total height of the vessel is 16cm. Find the capacity of the vessel. Also find the internal surface area of the vessel. OR A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line-segments into which the cone’s altitude is divided by the plane. 30. The following table gives the distribution of the life time of 400 neon lamps: Life time ( in hours ) |Number of lamps | |1500 – 2000 |14 | |2000- 2500 |56 | |2500 – 3000 |60 | |3000 – 3500 |86 | |3500 – 4000 |74 | |4000 – 4500 |62 | |4500 – 5000 |48 | Find the median life time of a lamp. OR Find the mean marks from the following data: |Marks |Number of students | |Below 10 |4 | |Below 20 |10 | |Below 30 |18 |Below 40 |28 | |Below 50 |40 | |Below 60 |70 | M . P . S U R E S H B A B U Mob: 9 4 4 7 1 4 2 9 3 4 E-mail:suresh_ [email  protected] co. in ANSWERS |1. 150 |11. 0 |21. †¦Ã¢â‚¬ ¦.. or †¦Ã¢â‚¬ ¦ | |2. 3, 1 |12. 5/26, 21/26 |22. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. | |3. k = 3 |13. 3 |23. ( 19/2, 13/2 ),(-9/2, -15/2) | |4. 5 |14. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ |24. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. | |5. p = 270 |15. -6, -5 |25. 64 1/4cm2 or 36 4/7cm2 | | |or q (x ) = x2 + x – 3, r = 8 | | |6. 25 2/3cm2 |16. 16 |26. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. | |7. 00 |17. †¦Ã¢â‚¬ ¦.. |27. Re 1, Rs 3 | |8. 30m |18. 9, -7 |28. 10 v3m, 40m | |9. 4 |19. †¦Ã¢â‚¬ ¦.. |29. 1584cm3, 602. 88cm2 | | | |or 1:2 | |10. ? /24 |20. †¦Ã¢â‚¬ ¦. Or 2 |30. 3406. 98 hours | | | |or 40. 7 |