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SSLC Question Papers June 2014 English Version : MATHEMATICS

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Serial No. of Q. C. A. B. Roll No. Jl o V MS : 58 ] [ Total No. of Questions : 58 ] [ Total No. of Printed Pages : 40 MO } MS : 81-E Code No. Jl o } lV MS : 40 : V {} : 81-E Subject : MATHEMATICS ( BMW M} / English Version ) MO : 16. 06. 2014] : V X 9-30 M 12-45 V ] @MO V : 100 ] [ Date : 16. 06. 2014 [ Time : 9-30 A.M. to 12-45 P.M. [ Max. Marks : 100 FOR OFFICE USE ONLY Q. No. Marks Q. No. Marks Q. No. Marks Q. No. Q. No. Marks 1. 14. 27. 40. 53. 2. 15. 28. 41. 54. 3. 16. 29. 42. 55. 4. 17. 30. 43. 56. 5. 18. 31. 44. 57. 6. 19. 32. 45. 58. 7. 20. 33. 46. 8. 21. 34. 47. 9. 22. 35. 48. 10. 23. 36. 49. 11. 24. 37. 50. 12. 25. 38. 51. 13. 26. 39. 52. Marks Total Marks Total Marks in words 1. 9 2. Grand Total 9 Signature of Evaluators 122595 9 Registration No. 9 Signature of the Deputy Chief Signature of the Room Invigilator [ Turn over 81-E 2 General Instructions : i) The Question-cum-Answer Booklet consists of objective and subjective types of questions having 58 questions. ii) Space has been provided against each objective type question. You have to choose the correct choice and write the complete answer along with its alphabet in the space provided. iii) For subjective type questions enough space for each question has been provided. You have to answer the questions in the space. iv) Follow the instructions given against both the objective and subjective types of questions. v) Candidate should not write the answer with pencil. Answers written in pencil will not be evaluated. ( Except Graphs, Diagrams & Maps ) vi) In case of Multiple Choice, Fill in the blanks and Matching questions, scratching / rewriting / marking is not permitted, thereby rendering to disqualification for evaluation. vii) Candidates have extra 15 minutes for reading the question paper. viii) Space for Rough Work has been printed and provided at the bottom of each page. I. Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most appropriate. Choose the correct alternative and write the complete answer along with its alphabet in the space 20 1 = 20 provided against each question. 1. If matrix A = [1 (A) 3 4 3 (C) [2 2 3 ] and B = [ 3 2 1 ] then the matrix AB l is (B) 4 3] [3 4 (D) [1 0 ]. Ans. : ( SPACE FOR ROUGH WORK ) 122595 3] 3 2. 81-E The value of 5 P1 is (A) 5 (B) 6 (C) 0 (D) 5! Ans. : 3. The meaningful among the following is (A) 2 (C) 5 (B) P2 5 P2 (D) P5 5 P 2 Ans. : 4. If 11P r = 990 , then the value of r is (A) 3 (B) 9 (C) 4 (D) 2. Ans. : 5. The standard deviation and coefficient of variation of the scores of a player are 1 5 and 15 respectively. Then the mean score of the player is (A) 1 5 (B) 10 (C) 15 (D) 1000. Ans. : 6. The L.C.M. of 2ab and 6ac 2 is 6abc 2 . Then their HCF is (A) 2a (B) 6 ab (C) 6a (D) 2 ab. Ans. : ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 81-E 4 7. The HCF of ( p q ) and ( ) p q is (A) p3 q 3 (C) ( (D) ( (B) p + q ) p q ) ( p q ). Ans. : 8. The simplified form of ( p + q r ) + ( p q r ) is pqr pqr (A) 2p + 2 q + 2 r (B) p q r (C) 0 (D) 2 p 2 q 2 r. Ans. : 9. If ab + bc + ca = 1 then ( a + b ) ( c + a ) = (A) ac (B) 1 + bc (C) bc (D) 1 + a2. Ans. : 10. If a 3 3 abc = 0 then the value of a 2 = abc (A) abc a (B) a 2 a (D) abc (C) abc 2 ab abc ab . abc Ans. : ( SPACE FOR ROUGH WORK ) 122595 81-E 5 11. The sum of 4 2, 2 and 32 is (A) 2 (B) 9 2 (C) 4 2 (D) 2. Ans. : 12. If F = mV 2 then V = r (A) F m r (B) m F r (C) F m r (D) F r . m Ans. : 13. The roots of the quadratic equation x 2 5x 6 = 0 are (A) 3 and 2 (B) 3 and 2 (C) 6 and 1 (D) 6 and 1. Ans. : 14. The value of p for the equation x 2 px + 9 = 0 to have equal roots is (A) +6 (B) 6 (C) 6 (D) 13. Ans. : 15. The sum of the roots of the quadratic equation ax 2 + bx + c = 0 is (A) c a (C) (B) b a b a (D) a . c Ans. : ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 6 81-E 16. In the given figure, EF || CA and FG || AB then (A) (C) DG GB AF DF (B) (D) DE = EC GB DG AB . AD Ans. : 17. In PQR, PQR = 90 . The correct relation with respect to PQR is (A) PR 2 = PQ 2 QR 2 (B) PQ 2 = QR 2 PR 2 (C) PR 2 = PQ 2 + QR 2 (D) QR 2 = PQ 2 PR 2 . Ans. : 18. The distance between the centres of two circles of radii 3 4 cm and 1 8 cm is 3 7 cm. Then the circles are (A) externally touching circles (B) internally touching circles (C) intersecting circles (D) concentric circles. Ans. : ( SPACE FOR ROUGH WORK ) 122595 7 81-E 19. Three circles with centres A, B and C touch each other as shown in figure. If the radii of these circles are 8 cm, 3 cm and 2 cm respectively, then the perimeter of ABC is (A) 26 cm (B) 16 cm (C) 18 cm (D) 14 cm. Ans. : 20. In the figure O is the centre of the circle. AT and BT are the tangents at points A and B respectively. If OAB = 30 , then the measure of ATB is (A) 30 (B) 15 (C) 60 (D) 90 . Ans. : ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 8 81-E II. Fill in the blanks with suitable answers : 10 1 = 10 21. If A and B are disjoint sets then n ( A I B ) = . Ans. : 22. The formula to find the n th term of Harmonic progression is . Ans. : 23. P is a matrix of order 2 3. Then the order of the transposed matrix of P is . Ans. : 24. The HCF of prime expressions is . Ans. : 25. The notation form of x 2 + y 2 + z 2 is . Ans. : 26. The standard form of an adfected quadratic equation is . Ans. : 27. The angle between the radius and tangent to a circle at the point of contact is equal to . Ans. : 28. A straight line drawn parallel to one side of a triangle divides the other two sides . Ans. : 29. The curved surface area of a cone of radius r and slant height l is .. . Ans. : 30. The Euler s formula for polyhedral solid is . . Ans. : ( SPACE FOR ROUGH WORK ) 122595 9 III. 81-E 31. If the universal set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 } , P = { 2, 3, 5, 7 } and Q = { 1, 3, 5, 7, 9 } then prove that ( P U Q ) l = P l l I Q . 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 10 81-E 32. A florist has certain number of garlands. 110 of them have champak flowers, 50 have jasmine flowers and 30 garlands have both the flowers. Find the total number of garlands with him. ( SPACE FOR ROUGH WORK ) 122595 2 11 33. In a geometric progression if S = 81-E 2 and a = 1 then find the geometric 3 progression. 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 12 81-E 34. In a geometric progression the 3rd term is 8 times the 6th term, and 4th term is 4 times the 6th term. Find the common ratio of the geometric progression. ( SPACE FOR ROUGH WORK ) 122595 2 13 35. Find the value of x if 12, 1 , 20 are in Harmonic progression. x 1 81-E 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 14 81-E 3 36. If A = 5 4 1 and B = 6 7 2 then find A + 2B. 8 ( SPACE FOR ROUGH WORK ) 122595 2 15 37. If a + b + c = abc then prove that 1 + a 2 = ( 1 ab ) ( 1 ac ). 81-E 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 16 81-E 38. Find the product of and . ( SPACE FOR ROUGH WORK ) 122595 2 17 39. Rationalise the denominator and simplify : 5 + 3 5 3 81-E 2 . ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 18 81-E 40. What is a pure quadratic equation ? Give one example. ( SPACE FOR ROUGH WORK ) 122595 2 19 81-E 41. If m and n are the roots of the quadratic equation x 2 3x + 1 = 0 , then find the m n + value of . 2 n m ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 20 81-E 42. Construct Cayley s table on A = { 2, 4, 6, 8 } under mod 10. ( SPACE FOR ROUGH WORK ) 122595 2 21 81-E 43. In a circle of radius 3 cm draw two radii such that the angle between them is 60 . Construct tangents at the ends of the radii. 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 22 81-E 44. A mansion has 12 cylindrical pillars, each having the circumference 50 cm and height 3 5 m. Find the cost of painting the lateral surface of all pillars at Rs. 150 per sq. m. 2 ( SPACE FOR ROUGH WORK ) 122595 23 81-E 45. 21 spheres of equal radii are melted to form a cylinder of radius 14 cm and height 49 cm. Find the radius of sphere. 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 24 81-E 46. Draw the plan of the field for the following data : 2 [ Scale : 25 m = 1 cm ] 50 to E To D ( in metres ) 100 75 50 25 From A ( SPACE FOR ROUGH WORK ) 122595 75 to C 50 to B 25 81-E 47. In the given network, write the number of regions and number of arcs. 2 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 26 81-E 48. Draw the graph for the given matrix : 2 1 0 1 4 1 0 1 2 ( SPACE FOR ROUGH WORK ) 122595 2 27 IV. 81-E 49. A basket contains 3 white and 5 red flowers. 4 flowers are removed from the basket at random. a) In how many ways can 4 flowers be removed ? b) Out of 4 flowers, how many of them may contain 2 white flowers ? 3 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 28 81-E 50. Find the standard deviation for the following data : 3 Scores ( x ) 32 37 42 47 52 Frequency ( f ) 2 5 6 5 2 ( SPACE FOR ROUGH WORK ) 122595 29 51. Find the L.C.M. of 81-E a 3 3a 2 10a + 24 and a 3 2a 2 9a + 18 by division method. 3 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 81-E 30 ( SPACE FOR ROUGH WORK ) 122595 31 81-E 52. The perimeter of a right angled triangle is 30 cm and its hypotenuse is 13 cm. Find the length of other two sides of the triangle. 3 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 32 81-E 53. ABCD is a trapezium in which AB || CD and BC AB. If AB = 7 5 cm, AD = 13 cm and CD = 12 5 cm, find the length of BC. ( SPACE FOR ROUGH WORK ) 122595 3 33 81-E 54. Prove that the tangents drawn from an external point to a circle are equal. 3 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 34 81-E V. 55. Three numbers are in arithmetic progression and their sum is 18 and the sum of their squares is 140. Find the numbers. ( SPACE FOR ROUGH WORK ) 122595 4 35 81-E 56. Construct two direct common tangents to two circles of radii 4 cm and 2 cm such that the distance between their centres is 10 cm. Measure the length of the tangents and write. 4 ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 36 81-E 57. Prove that the areas of similar triangles are proportional to the squares of their corresponding sides. 4 ( SPACE FOR ROUGH WORK ) 122595 37 81-E ( SPACE FOR ROUGH WORK ) 122595 [ Turn over 38 81-E 58. Solve graphically : x 2 x 2 = 0. 4 ( SPACE FOR ROUGH WORK ) 122595

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