VIEWS: 57 PAGES: 31 CATEGORY: Geometry POSTED ON: 4/10/2012
81-E 2 General Instructions : i) The question-cum-answer booklet contains two Parts, Part – A & Part – B. ii) Part – A consists of 60 questions and Part – B consists of 16 questions. iii) Space has been provided in the question-cum-answer booklet itself to answer the questions. iv) Follow the instructions given in Part – A and write the correct choice in full in the space provided below each question. v) For Part – B enough space for each question is provided. You have to answer the questions in the space provided. vi) Space for Rough Work has been printed and provided at the bottom of each page. PART – A Four alternatives are suggested to each of the following questions / incomplete statements. Choose the most appropriate alternative and write the answer in the space provided below each question. 60 × 1 = 60 1. A = { 1, 2, 4 } and B = { 1, 4, 5 } . The set denoted by A I B is (A) { 4, 5 } (B) { 1, 5 } (C) { 1, 4 } (D) { 2, 5 } Ans. : 2. If U = { 1, 2, 3, 4, 5, 6 } A = { 1, 2, 3 } B = { 2, 4 } , then the diagram that denotes A I B is (A) (B) (C) (D) Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 3 81-E 3. With respect to the Venn diagram given below n ( A ) is A B 8 5 7 (A) 8 (B) 5 (C) 7 (D) 13. Ans. : 4. Among the formulae given below, De Morgan’s law is denoted by (A) n(A)+n(B)=n(A U B)+n(A I B) (B) n ( A ) l = n ( U )–n(A) (C) A U (B I C)=(A U B) I (A U C) (D) ( A I B ) l = A l U B l . Ans. : 5. A and B are two sets. If n ( A ) = 11, n ( B ) = 7 and n ( A I B ) = 3, then n ( A U B ) is (A) 21 (B) 15 (C) 8 (D) 10. Ans. : 6. In a sequence T n = 2n 2 – 1 the pair of first two terms is (A) 3, 7 (B) 1, 3 (C) 1, 7 (D) 1, 15. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 4 7. Among the following, arithmetic progression is (A) 1, 4, 6, …… (B) 12, 10, 14, …… (C) 35, 30, 25, …… (D) 8, 13, 19, …… . Ans. : 8. Which one of the following formulae is related to geometric progression ? n (A) S n = (a +l) (B) T n = a + ( n – 1 ) d 2 2ab (C) H = (D) T n = ar n – 1 . a + b Ans. : 9. The harmonic mean between 1 and 4 is 7 8 (A) (B) 5 5 6 7 (C) (D) . 5 4 Ans. : 1 2 10. If A = then A + A l is 3 4 2 5 2 4 (A) (B) 5 8 6 8 0 – 1 2 5 . (C) (D) – 1 0 8 5 Ans. : 0 3a 11. If A = is a skew symmetric matrix, then the value of a is a – 8 0 (A) – 4 (B) 4 (C) – 2 (D) 2. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 5 81-E 8 12. The value of P 2 is (A) 16 (B) 28 (C) 56 (D) 15. Ans. : 13. A boy has 4 shirts, 3 pants and 2 caps. The different ways of wearing these items is (A) 9 (B) 24 (C) 6 (D) 5. Ans. : 14. The value of |3 + |2 – |0 is — — — (A) 7 (B) 8 (C) 5 (D) 4. Ans. : 15. Number of straight lines that can be drawn by using 6 non-collinear points is (A) 30 (B) 15 (C) 9 (D) 6. Ans. : 16. There are 4 men and 3 women in a group. Number of ways to form a committee of 2 men and 1 woman is given by (A) 4P 2 × 3P 1 (B) 4P 2 × 3C 1 (C) 4C 2 × 3C 1 (D) 4C 2 × 3P 1 . Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 6 n n 17. If C r = 10 and P r = 20, then the value of r is (A) 200 (B) 30 (C) 10 (D) 2. Ans. : 18. In a statistical data, sum of the squares of deviations of 10 scores is 130. The variance is (A) 1300 (B) 140 (C) 13 (D) 130. Ans. : 19. The variance of a statistical data is 16. The standard deviation is (A) 4 (B) 4·5 (C) 32 (D) 250. Ans. : 20. The coefficients of variations of Anand and Shankar in 5 class tests are 7·5 and 12·3 respectively. The true statement of comparison among the following is (A) Shankar has higher consistency (B) Shankar has lower consistency (C) both have equal consistency (D) Anand has lower consistency. Ans. : 21. The L.C.M. of 18x 3 y 4 z 9 and 15x 4 y 7 z 5 is (A) 90x 4 y 7 z 5 (B) 90x 3 y 4 z 5 (C) 90x 4 y 7 z 9 (D) 90x 4 y 4 z 9 . Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 7 81-E 22. If a, b, c are variables, then ∑ a 2 + b is a‚ b‚ c (A) a 2 + b + b 2 + c + c 2 + a (B) a 2 – b + b 2 – c + c 2 – a (C) a 2 + b – c + b 2 + c – a (D) a 2 + b 2 + c 2 . Ans. : 23. ∑ x ( y – z ) is expanded and simplified to obtain x‚ y‚ z (A) xy – xz (B) 0 (C) xz – xy (D) y(z–x) Ans. : 24. If a + b + c = 0, then the value of ( a + b ) ( b + c ) ( c + a ) is (A) abc (B) 0 (C) ± abc (D) – abc. Ans. : 25. The factors of a 2 – b 2 are (A) (a–b)(a–b) (B) (a+b)(a+b) (C) ( a – b ) 2 (D) ( a + b ) ( a – b ). Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 8 26. The sum of 9a and 25a is (A) 34a (B) 8a (C) 8 a (D) 2 a . Ans. : 8 27. If the denominator of is rationalised and simplified, its form is 2 (A) 4 2 (B) 4 (C) 8 2 (D) 8. Ans. : 28. When 10 – 2 is multiplied by its rationalised factor we get (A) 6 (B) 8 (C) 96 (D) 98. Ans. : 29. The set of like radicals among the following is 3 3 (A) 10 , 4 7 (B) 6 2 , 10 2 (C) 54 8 , 5 4 3 (D) 4 3 ,4 2 . Ans. : 30. The quadratic equation among the following is (A) a 3 + 3 = 2a (B) x + 5 = 10 2 (C) x+4(x +1)=0 (D) y = . y Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 9 81-E 31. The discriminant of the quadratic equation ax 2 + bx + c = 0 is b (A) – (B) b 2 – 4ac a c – b ± b 2 – 4ac (C) (D) . a 2a Ans. : 32. If the roots of the quadratic equation x 2 + 4x + c = 0 are equal, then the value of c is (A) 3 (B) 4 (C) 5 (D) 12. Ans. : 33. The sum and product of the roots of the quadratic equation 4x 2 + 1 = 0 are respectively (A) 1 and 4 (B) 0 and 1 1 1 (C) 0 and – (D) 0 and . 4 4 Ans. : 34. The hypotenuse of a right-angled triangle is 13 cm. If one side of the remaining is 5 cm greater than the other, they can be related with each other as (A) x + ( x + 5 ) = 13 (B) x 2 + ( x 2 + 5 ) = 13 2 (C) x 2 + ( x + 5 ) 2 = 13 2 (D) x 2 + ( 5 – x ) 2 = 13 2 . Ans. : 1 35. If the roots of a quadratic equation are 0 and – , the equation is 2 1 (A) 2x 2 + x = 0 (B) x 2 + =0 2 (C) 2x 2 + 1 = 0 (D) 2x 2 – x = 0. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 10 36. If the roots of the quadratic equation mx 2 + 6x + 1 = 0 have to be equal, then the value of m is (A) 6 (B) 1 (C) 9 (D) 5 Ans. : 37. If a 2 = b 2 + c 2 , then c is given by (A) ± b 2 + a 2 (B) ± a 2 + b 2 (C) ± a – b (D) ± a 2 – b 2 . Ans. : 38. If A = 4πr 2 , r is given by A A (A) ± (B) 4π 4π Aπ (C) 4Aπ (D) . 4 Ans. : 39. Twice the square of a number added to three times the number is equal to 65. This statement in the form of equation is (A) 3x 2 + 2x = 65 (B) 2x 2 + 3x = 65 (C) 2x 2 + 3x 2 = 65 (D) 3x 2 + 2x 2 = 65. Ans. : 40. In a quadratic equation if the value of b 2 – 4ac = – 7, the nature of the roots of the quadratic equation is (A) real and equal (B) real and distinct (C) imaginary (D) negative numbers. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 11 81-E 41. Parabola is the name of the graph of (A) linear equation (B) simultaneous equation (C) quadratic polynomial equation (D) polynomial equation. Ans. : 42. The correct statement among the following is (A) 8 ≡ – 7 ( mod 3 ) (B) 7 ≡ – 2 ( mod 4 ) (C) 10 ≡ 6 ( mod 3 ) (D) 18 ≡ 10 ( mod 5 ). Ans. : 43. If 3x ≡ 2 ( mod 4 ), then value of x is (A) 1 (B) 2 (C) 3 (D) 4. Ans. : 44. In the given figure, the line segment which subtends right angle in the semicircle is (A) AB (B) CO (C) DE (D) FG. Ans. : 45. For two concentric circles, (A) direct common tangents can be drawn (B) transverse common tangents can be drawn (C) common tangents cannot be drawn (D) both direct and transverse common tangents can be drawn. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 12 46. In the figure, DE BC, AD : AB = 1 : 2, BC = 6 cm, then DE is (A) 1 cm (B) 2 cm (C) 3 cm (D) 4 cm. Ans. : AB BC AC 47. In ∆ ABC and ∆ DEF if = = , then the correct pair of DE EF DF corresponding equal angles is (A) ∠ A and ∠ E (B) ∠ C and ∠ F (C) ∠ B and ∠ D (D) ∠ A and ∠ F. Ans. : 48. The two corresponding sides of similar triangles are 3 cm and 4 cm. The area of larger triangle is 48 sq.cm. The area of smaller triangle is (A) 80 sq.cm (B) 64 sq.cm (C) 36 sq.cm (D) 27 sq.cm. Ans. : 49. A straight pole of height 2 ft casts a shadow of 6 ft long at a definite time. The height of another pole which casts a shadow of 12 ft at the same time is (A) 3 ft (B) 4 ft (C) 8 ft (D) 20 ft. Ans. : 50. Two circles of radii 4 cm and 2 cm have their centres 7 cm apart. These circles (A) touch each other externally (B) touch each other internally (C) do not touch each other (D) intersect each other. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 13 81-E 51. Two circles touch each other internally. The distance between their centres is 1·5 cm. If the radius of one circle is 3·5 cm, then the radius of the other circle is (A) 5 cm (B) 4 cm (C) 3 cm (D) 2 cm. Ans. : 52. In the given figure, O is the centre of the circle. AC and BC are the tangents. If ∠ BOC = 65° then ∠ ACO is (A) 25° (B) 35° (C) 65° (D) 115°. Ans. : 53. In the given figure, O is the centre of the circle. XY is a tangent. If ∠ PQY = 55°, ∠ OPQ is P O 55° X Y Q (A) 125° (B) 120° (C) 110° (D) 35°. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 14 54. A = 2πr ( r + h ). This formula can be used to find (A) lateral surface area of a cylinder (B) total surface area of a cylinder (C) volume of a cylinder (D) surface area of a sphere. Ans. : 55. Volume of a hemisphere can be calculated by using the formula 1 4 (A) V = πr 2 h (B) V = πr 3 3 3 2 3 (C) V = πr 3 (D) V = πr 3 . 3 4 Ans. : 56. The solid described by revolution of a semicircle about a fixed diameter is (A) cone (B) cylinder (C) hemisphere (D) sphere. Ans. : 57. The volume of a cone is 90 cm 3 . The volume of a cylinder whose height and radius is same as that of the cone is (A) 30 cm 3 (B) 45 cm 3 (C) 90 cm 3 (D) 270 cm 3 . Ans. : 58. The volume of a cylinder is 1540 cm 3 . Its height is 10 cm. The area of its base is (A) 15400 sq.cm (B) 154 sq.cm (C) 1540 sq.cm (D) 1550 sq.cm. Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 15 81-E 59. A polyhedral graph is given in the figure. The polyhedral solid obtained by this is (A) Icosahedron (B) Dodecahedron (C) Hexahedron (D) Tetrahedron. Ans. : 60. Which of the following is a traversable network ? (A) (B) (C) (D) Ans. : ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 16 PART – B 61. There are 10 boxes on a table. Ramu places 4 marbles in first box, 7 marbles in the second box, 10 marbles in the third box and so on. Find the total number of marbles placed in all the boxes. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 17 81-E 0 1 62. If A = , find A 2 . 2 2 3 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 18 63. The marks scored by Rani in 5 class tests are 56, 60, 59, 68, 57. Find the standard deviation for these scores. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 19 81-E 64. If a + b + c = 0, prove that a 3 + b 3 + c 3 ≡ 3 abc. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 20 65. Rationalise the denominator and simplify : 5 – 3 2 5 + 3 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 21 81-E 66. In the given figure, O is the centre of the circle. AB = 2 cm, AC = 3 cm, CE = 6 cm. Find DE. 2 E A C . .O B D ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 22 67. Three circles of radii 3·5 cm, 4·5 cm and 5 cm touch each other externally as shown in the figure. Find the sides of ∆ ABC and perimeter of ∆ ABC given that A, B and C are the centres of the circles. 2 3·5 cm 4·5 cm A . .B 5 cm . C ( SPACE FOR ROUGH WORK ) VIII I-E-912130 23 81-E 68. Construct the matrix for the given network. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 24 69. Solve 4x 2 – 3x – 2 = 0 using formula. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 25 81-E 70. Draw a circle of radius 3 cm. Draw a chord AB of length 5 cm in it. Construct a tangent to the circle at A. 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 26 71. Draw the plan of a level ground using the information given below. ( Scale : 1 cm = 10 m ) 2 Metres To C 100 D 30 70 E 30 50 20 B 30 From A ( SPACE FOR ROUGH WORK ) VIII I-E-912130 27 81-E 72. Find the LCM of x 3 + 2x 2 + 2x + 1 and x 3 – x 2 – x – 2. 4 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 28 73. State and prove Pythagoras theorem. 4 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 29 81-E 2 1 74. In an H.P., the 10th term is and third term is . Find the eleventh term. 4 13 3 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 30 75. Draw two direct common tangents to the circles of radii 4 cm and 2 cm having their centres 8 cm apart. 4 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 31 81-E 76. Draw the graph of y = 2x 2 . 2 ( SPACE FOR ROUGH WORK ) VIII I-E-912130 [ Turn over 81-E 32 ( SPACE FOR ROUGH WORK ) VIII I-E-912130