email: [email protected] Þœªô¢ªî¦ô¢Ù 9  2019 - Directions (31 – 35): Two equations I and II are given below in each question. You have to solve these equations and give answer. 1) if x < y 2) if x > y 3) if x ≤ y 4) if x ≥ y 5) if x = y or no relation can be established 31. I. x 2 − 14x + 48 = 0 II. y 2 + 6 = 5y 32. I. x 2 + 9x + 20 = 0 II. y 2 + 7y + 12 = 0 33. I. x 2 = 529 II. y = √ ⎯⎯ 529 34. I. 2x + 3y = 14 II. 4x + 2y = 16 35. I. x 2 − 1 = 0 II. y 2 + 4y + 3 = 0 36. Out of 5 men and 3 women, a committee of 3 members is to be formed, so that it has 1 woman and 2 men. In how many different ways can it be done? 1) 20 2) 10 3) 23 4) 30 5) None of these 37. Naresh purchased a TV set for Rs. 11250 after getting discount of 10% on the labelled price. He spent Rs. 150 on trans- port and Rs. 800 on installation. At what price should it be sold, so that he earned a profit of 15%? 1) Rs. 12937.50 2) Rs. 14030 3) Rs. 13450 4) Rs. 15467.50 5) None of these 38. Mr Duggal invested 20000 with rate of interest at the rate 20% per annum. The interest was compounded half yearly for first one year and in the next year it was compounded yearly. What will be the total interest earned at the end of two years? 1) Rs. 8800 2) Rs. 9040 3) Rs. 8040 4) Rs. 9800 5) None of these 39. If the positions of the digits of a two digit number are interchanged, the number obtained is smaller than the original number by 27. If the digits of the number are in the ratio of 1 : 2, what is the original number? 1) 36 2) 63 3) 48 4) Can't be determined 5) None of these 40. If the numerator of a fraction is increased by 20% and the denominator is increased 3 by 25%, the fraction obtained is ⎯. What 5 was the original fraction? 5 4 3 1) ⎯ 2) ⎯ 3) ⎯ 7 7 8 4) Can't be determined 5) None of these Directions (41 – 45): Study the following pie chart carefully to answer the questions that follow. A farmer harvests six types of crops and vegetables in his rectangular field with dimensions 120 m × 90 m. The pie chart shows the area covered by each in terms of degree measurement. 41. What is the average area of field covered by the vegetation except mustard? 1) 1876 m 2 2) 1866 m 2 3) 1686 m 2 4) 1870 m 2 5) None of these 42. The area covered by Sugarcane is by what percent less than that of by Rice? (approx.) 1) 39% 2) 42% 3) 40% 4) 34% 5) 38% 43. Find the difference in area covered by Melons and Maize together and that of by Corns and Mustard together? 1) 1210 m 2 2) 1120 m 2 3) 1250 m 2 4) 1200 m 2 5) None of these 44. What is the ratio of area covered by Melons and that of Mustard? 1) 8 : 5 2) 7 : 8 3) 7 : 5 4) 8 : 3 5) None of these 45. The total production of rice was 125 quin 2 tals after 66 ⎯% of area covered by rice 3 was wasted away due to fire. What would be the actual production of rice (in quin- tals) if no wastage was there & production was in same rate throughout the rice field? 1) 178.8 2) 187 3) 178.5 4) 187.5 5) None of these Directions (46 – 50): Read the following graph carefully and answer the questions given below: Profit earned by three companies in different years (in crore Rs.) 46. In which of the following years was the dif- ference between the profit earned by com- pany B and company A maximum? 1) 2006 2) 2004 3) 2008 4) 2005 5) None of these 47. What was the percent increase in the prof- it earned by company C from 2006 to 2007? 1) 40% 2) 45% 3) 56% 4) 50% 5) None of these 48. In which of the following years was the total profit earned by all the three compa- nies minimum? 1) 2004 2) 2003 3) 2006 4) 2005 5) None of these 49. The profit earned by company B in 2004 is approximately what percent of that by company A in 2007 ? 1) 62% 2) 58% 3) 53% 4) 67% 5) 71% 50. What was the difference between the prof- it earned by company A in 2005 and com- pany A in 2008? 1) Rs. 50 crore 2) Rs. 100 crore 3) Rs. 150 crore 4) Rs. 1 crore 5) None of these Directions (51 – 55): What should come in place of the question mark (?) in the following number series? 51. 948, 474, ?, 118.5, 59.25, 29.625 1) 221 2) 190 3) 237 4) 189.06 5) None of these 52. 374, 355, 317, ?, 184, 89 1) 260 2) 298 3) 279 4) 241 5) None of these 53. 96, 94, 373, 3353, ?, 1341069 1) 83819 2) 53483 3) 63813 4) 53643 5) None of these 54. 1, 16, 81, 256, ?, 1296 1) 400 2) 625 3) 875 4) 1125 5) None of these 55. 281, 141, 71, 36, 18.5, ? 1) 9.5 2) 9.25 3) 10.75 4) 10 5) None fo these 56. Three Science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is 1) 80 2) 80.5 3) 81 4) 81.5 5) None of these 57. There are 50 students in a class. Their average weight is 45 kg. When one stu- dent leaves the class the average weight reduces by 100g. What is the weight of the student who left the class? 1) 45 kg 2) 47.9 kg 3) 49.9 kg 4) 50.1 kg 5) None of these 58. The simple interest on a sum of money at 4% per annum for 2 years is Rs. 80. The compound interest in the same for the same period is? 1) Rs. 82.60 2) Rs. 82.20 3) Rs. 81.80 4) Rs. 81.60 5) None of these 59. 200 litres of a mixture contains 15% water and the rest is milk. The amount of milk that must be added so that the resulting mixture contains 87.5% milk is? 1) 30 litres 2) 35 litres 3) 40 litres 4) 45 litres 5) None of these 60. In an examination, 60% of the candidates passed in English and 70% of the candi- dates passed in Mathematics, but 20% failed in both of these subjects. If 2500 candidates passed in both the subjects the number of candidates who appeared at the examination was? 1) 3000 2) 3500 3) 4000 4) 5000 5) None of these Directions (61 – 65): What will come in place of question mark (?) in the following questions ? 61. 542 − 369 + 171 − 289 = ? 1) 135 2) 55 3) 255 4) 245 5) 265 62. 25 × 26 + 35 × 34 + 39 × 41 = ? 1) 3440 2) 3330 3) 3439 4) 3339 5) None of these 1 63. 6 ⎯ × 0.25 + 0.75 − 0.3125 = ? 4 1) 5.9375 2) 4.2968 3) 2.1250 4) 2.0000 5) None of these 64. 165% of 140 + 12.5 % of 192 = ? 1) 155 2) 250 3) 255 4) 275 5) None of these 65. 15 × 18 + 16 × 17 + 12 × 11 = ? 1) 674 2) 574 3) 664 4) 764 5) None of these Directions (66 – 70): Each question consists of three statements followed by two conclu- sions I and II. Consider the statements to be true even if they are in variance with the com- monly known facts. Read all the conclusions and then decide which of the given conclu- sions logically follow from the given state- ments using all the three statements together. Mark your answer as: 1) If only conclusion I follows. 2) If only conclusion II follows. 3) If either conclusion I or conclusion II follows. 4) If neither conclusion I nor conclusion II follows. 5) If both conclusion I and conclusion II follows. 66. Statements: All artists are players. All musicians are artists. All players are singers. Conclusions: I. All singers are musicians is a possibility. II. Some singers which are artists are also a part of musicians. 67. Statements: All bricks are stones. Some stones are rocks. All rocks are mountains. Conclusions: I. Some mountains which are stones are also a part of bricks. II. No rock is brick is a possibility. 68. Statements: All sixes are scores. All boundaries are fours. No boundary is score. Conclusions: I. All sixes are fours is a possibility. II. All scores which are fours are also a part of boundaries. 69. Statements: Some cars are mobiles. All mobiles are phones. All cars are trucks. Conclusions: I. Some cars are not phones. II. All trucks are phones is a possibility. 70. Statements: Some husbands are fathers. All fathers are parents. Some husbands are not mothers. Conclusions: I. All mothers are father is a possibility. II. All husbands are parents is a possibility. Directions (71 – 75): Read the following infor- mation and answer the questions. Four people of different religions live on the same side of a sector in four houses each of different color i.e Red, Blue, Pink and Yellow. Each person has a different favorite drink i.e Tea, Coffee, Banana Shake and Milk. The Christian lives in the red house. The following additional information is: The Hindu drinks tea. The Muslim lives in the first house on the left. The Muslim lives in adjacent to the blue house. In the second house from the right they drink coffee. The Sikh drinks Banana shake. Tea is drunk in the blue house. The Pink house is to the right of red house. 71. Which of the following drink coffee? 1) Muslim 2) Hindu 3) Christian 4) Muslim and Hindu 5) None of these 72. The color of Sikh house is: 1) Yellow 2) Blue 3) Red 4) Pink 5) None of these 73. The Muslim drinks which of the following drink: 1) Tea 2) Coffee 3) Banana shake 4) Tea, Coffee 5) Milk 74. Who sits adjacent to Muslim? 1) Hindu 2) Christian 3) Sikh 4) both Hindu and Sikh 5) None of these 75. Which of the following statement is not true? 1) Hindu lives in the blue house. 2) Sikh drinks Banana shake and the colour of his house is pink. 3) Muslim drinks coffee. 4) Yellow house is occupied by Muslim. 5) None of these SBI PO's MODEL PAPER No. of Questions: 100 Max. Marks: 100 Time: 1 Hrs. Quantitative Aptitude Preliminary Exam Reasoning Ability sNªÞœê¦ ví£øŒoõª ¸ôí£æ¨ ›í@ö˺xz
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
email: [email protected]Þœªô¢ªî¦ô¢Ù 9  2019 -
Directions (31 – 35): Two equations I and IIare given below in each question. You have tosolve these equations and give answer.
1) if x < y 2) if x > y 3) if x ≤ y 4) if x ≥ y5) if x = y or no relation can be established
31. I. x2 − 14x + 48 = 0 II. y2 + 6 = 5y32. I. x2 + 9x + 20 = 0 II. y2 + 7y + 12 = 033. I. x2 = 529 II. y = √⎯⎯
529 34. I. 2x + 3y = 14 II. 4x + 2y = 1635. I. x2 − 1 = 0 II. y2 + 4y + 3 = 0 36. Out of 5 men and 3 women, a committee
of 3 members is to be formed, so that ithas 1 woman and 2 men. In how many different ways can it be done?
1) 20 2) 10 3) 23 4) 30 5) None of these37. Naresh purchased a TV set for Rs. 11250
after getting discount of 10% on thelabelled price. He spent Rs. 150 on trans-port and Rs. 800 on installation. At whatprice should it be sold, so that he earned aprofit of 15%?
1) Rs. 12937.50 2) Rs. 140303) Rs. 13450 4) Rs. 15467.505) None of these
38. Mr Duggal invested 20000 with rate ofinterest at the rate 20% per annum. Theinterest was compounded half yearly forfirst one year and in the next year it wascompounded yearly. What will be the totalinterest earned at the end of two years?
1) Rs. 8800 2) Rs. 9040 3) Rs. 80404) Rs. 9800 5) None of these
39. If the positions of the digits of a two digitnumber are interchanged, the numberobtained is smaller than the original number by 27. If the digits of the numberare in the ratio of 1 : 2, what is the originalnumber?
1) 36 2) 63 3) 48 4) Can't be determined 5) None of these
40. If the numerator of a fraction is increasedby 20% and the denominator is increased
3by 25%, the fraction obtained is ⎯. What
5was the original fraction?
5 4 31) ⎯ 2) ⎯ 3) ⎯
7 7 84) Can't be determined 5) None of these
Directions (41 – 45): Study the following piechart carefully to answer the questions thatfollow. A farmer harvests six types of cropsand vegetables in his rectangular field withdimensions 120 m × 90 m. The pie chartshows the area covered by each in terms ofdegree measurement.
41. What is the average area of field coveredby the vegetation except mustard?
1) 1876 m2 2) 1866 m2 3) 1686 m2
4) 1870 m2 5) None of these42. The area covered by Sugarcane is by
what percent less than that of by Rice?(approx.)
1) 39% 2) 42% 3) 40% 4) 34% 5) 38%
43. Find the difference in area covered byMelons and Maize together and that of byCorns and Mustard together?
1) 1210 m2 2) 1120 m2 3) 1250 m2
4) 1200 m2 5) None of these44. What is the ratio of area covered by
Melons and that of Mustard? 1) 8 : 5 2) 7 : 8 3) 7 : 5 4) 8 : 3 5) None of these
45. The total production of rice was 125 quin2
tals after 66 ⎯% of area covered by rice 3
was wasted away due to fire. What wouldbe the actual production of rice (in quin-tals) if no wastage was there & productionwas in same rate throughout the ricefield?
1) 178.8 2) 187 3) 178.5 4) 187.5 5) None of these
Directions (46 – 50): Read the followinggraph carefully and answer the questionsgiven below:Profit earned by three companies in differentyears (in crore Rs.)
46. In which of the following years was the dif-ference between the profit earned by com-pany B and company A maximum?
1) 2006 2) 2004 3) 20084) 2005 5) None of these
47. What was the percent increase in the prof-it earned by company C from 2006 to2007?
1) 40% 2) 45% 3) 56%4) 50% 5) None of these
48. In which of the following years was thetotal profit earned by all the three compa-nies minimum?
1) 2004 2) 2003 3) 20064) 2005 5) None of these
49. The profit earned by company B in 2004 isapproximately what percent of that bycompany A in 2007 ?
1) 62% 2) 58% 3) 53% 4) 67% 5) 71%50. What was the difference between the prof-
it earned by company A in 2005 and com-pany A in 2008?
1) Rs. 50 crore 2) Rs. 100 crore3) Rs. 150 crore 4) Rs. 1 crore5) None of these
Directions (51 – 55): What should come inplace of the question mark (?) in the followingnumber series?51. 948, 474, ?, 118.5, 59.25, 29.625
1) 221 2) 190 3) 2374) 189.06 5) None of these
52. 374, 355, 317, ?, 184, 891) 260 2) 298 3) 2794) 241 5) None of these
53. 96, 94, 373, 3353, ?, 13410691) 83819 2) 53483 3) 638134) 53643 5) None of these
54. 1, 16, 81, 256, ?, 12961) 400 2) 625 3) 8754) 1125 5) None of these
55. 281, 141, 71, 36, 18.5, ?1) 9.5 2) 9.25 3) 10.754) 10 5) None fo these
56. Three Science classes A, B and C take aLife Science test. The average score ofclass A is 83. The average score of classB is 76. The average score of class C is85. The average score of class A and B is79 and average score of class B and C is81. Then the average score of classes A,B and C is
1) 80 2) 80.5 3) 814) 81.5 5) None of these
57. There are 50 students in a class. Theiraverage weight is 45 kg. When one stu-dent leaves the class the average weightreduces by 100g. What is the weight of thestudent who left the class?
1) 45 kg 2) 47.9 kg 3) 49.9 kg4) 50.1 kg 5) None of these
58. The simple interest on a sum of money at4% per annum for 2 years is Rs. 80. Thecompound interest in the same for thesame period is?
1) Rs. 82.60 2) Rs. 82.20 3) Rs. 81.804) Rs. 81.60 5) None of these
59. 200 litres of a mixture contains 15% waterand the rest is milk. The amount of milkthat must be added so that the resultingmixture contains 87.5% milk is?
1) 30 litres 2) 35 litres 3) 40 litres4) 45 litres 5) None of these
60. In an examination, 60% of the candidatespassed in English and 70% of the candi-dates passed in Mathematics, but 20%failed in both of these subjects. If 2500candidates passed in both the subjects thenumber of candidates who appeared atthe examination was?
1) 3000 2) 3500 3) 40004) 5000 5) None of these
Directions (61 – 65): What will come inplace of question mark (?) in the followingquestions ?61. 542 − 369 + 171 − 289 = ?
1) 135 2) 55 3) 255 4) 245 5) 26562. 25 × 26 + 35 × 34 + 39 × 41 = ?
1) 3440 2) 3330 3) 34394) 3339 5) None of these
163. 6 ⎯ × 0.25 + 0.75 − 0.3125 = ?
41) 5.9375 2) 4.2968 3) 2.12504) 2.0000 5) None of these
64. 165% of 140 + 12.5 % of 192 = ?1) 155 2) 250 3) 2554) 275 5) None of these
65. 15 × 18 + 16 × 17 + 12 × 11 = ?1) 674 2) 574 3) 6644) 764 5) None of these
Directions (66 – 70): Each question consistsof three statements followed by two conclu-sions I and II. Consider the statements to betrue even if they are in variance with the com-monly known facts. Read all the conclusionsand then decide which of the given conclu-sions logically follow from the given state-ments using all the three statements together.Mark your answer as:
1) If only conclusion I follows.2) If only conclusion II follows.
3) If either conclusion I or conclusion II follows.
4) If neither conclusion I nor conclusion IIfollows.
5) If both conclusion I and conclusion II follows.
66. Statements: All artists are players.All musicians are artists.All players are singers.
Conclusions: I. All singers are musiciansis a possibility.
II. Some singers which are artists are also apart of musicians.
67. Statements: All bricks are stones.Some stones are rocks.All rocks are mountains.
Conclusions: I. Some mountains which arestones are also a part of bricks.II. No rock is brick is a possibility.
68. Statements: All sixes are scores.All boundaries are fours.No boundary is score.
Conclusions: I. All sixes are fours is a possibility.II. All scores which are fours are also a part
of boundaries.69. Statements: Some cars are mobiles.
All mobiles are phones.All cars are trucks.
Conclusions: I. Some cars are not phones.II. All trucks are phones is a possibility.
70. Statements: Some husbands are fathers.All fathers are parents.Some husbands are not mothers.
Conclusions: I. All mothers are father is apossibility.II. All husbands are parents is a possibility.
Directions (71 – 75): Read the following infor-mation and answer the questions.
Four people of different religions live on thesame side of a sector in four houses each ofdifferent color i.e Red, Blue, Pink and Yellow.Each person has a different favorite drink i.eTea, Coffee, Banana Shake and Milk. TheChristian lives in the red house. The followingadditional information is:
The Hindu drinks tea. The Muslim lives inthe first house on the left. The Muslim lives inadjacent to the blue house. In the secondhouse from the right they drink coffee. TheSikh drinks Banana shake. Tea is drunk in theblue house. The Pink house is to the right ofred house.71. Which of the following drink coffee?
1) Muslim 2) Hindu 3) Christian4) Muslim and Hindu 5) None of these
72. The color of Sikh house is:1) Yellow 2) Blue 3) Red4) Pink 5) None of these
73. The Muslim drinks which of the followingdrink:
1) Tea 2) Coffee 3) Banana shake4) Tea, Coffee 5) Milk
74. Who sits adjacent to Muslim?1) Hindu 2) Christian 3) Sikh4) both Hindu and Sikh 5) None of these
75. Which of the following statement is nottrue?
1) Hindu lives in the blue house.2) Sikh drinks Banana shake and the colour
of his house is pink.3) Muslim drinks coffee.4) Yellow house is occupied by Muslim.5) None of these
SBI PO's MODEL PAPERNo. of Questions: 100 Max. Marks: 100 Time: 1 Hrs.
Quantitative Aptitude
Preliminary Exam
Reasoning Ability
sNªÞœê¦ ví£øŒoõª ¸ôí£æ̈ ›í@ö˺xz
email: [email protected]Þœªô¢ªî¦ô¢Ù 9  2019 -
Ó꟪hõª n- ë]«ô¦õª (vAÚÁ-é-NªA)
ë]”ù‡d-¸ôÜ (Line of Sight): ÖÚÛ ÷ú£ªh-÷±šíj ÑìoGÙë]ª÷± ìªÙ# í£J-Q-õ-ÚÛªè… ÚÛÙæ¨E ÚÛL›í ¸ôÜìªë]”ù‡d-¸ôÜ ÍÙ-æ°ô¢ª.-Ò-ô¢–y-ÚÁéÙ (Angle of elevation): ë]”-ù‡d-¸ôܤ¨Aá ú£÷«Ù-êŸô¢ ¸ôÜÚÛª šíjì Ñìo-í£±pè[ª î¦æ¨÷ªëÅ]u Ôô¢pè˶ ÚÁé°Eo Òô¢–y-ÚÁéÙ ÍÙæ°ô¢ª.-E-÷ªo-ÚÁéÙ (Angle of depression): ë]”-ù‡d-¸ôܤ¨Aá ú£÷«Ù-êŸô¢ ¸ôÜÚÛª Ú¨Ùë] Ñìo-í£±pè[ª î¦æ¨÷ªëÅ]u Ôô¢pè˶ ÚÁé°Eo E÷ªo-ÚÁéÙ ÍÙæ°ô¢ª.-H ÖÚÛ ÷ú£ªh÷± ð»è[÷± öË¶ë¯ Ó꟪hìª ÚÛìª-ÚÁ\-÷-
è¯-EÚ¨; ·ôÙè[ª ÷ú£ªh-÷±õ ÷ªëÅ]u ë]«ô¦EoöËμÚ¨\Ù-àŸ-è¯-EÚ¨ vAÚÁ-é-Nª-BóŸª Eù£p-꟪h-õìªÑí£-óμ«-T-þ§hô¢ª.-
÷«-CJ ú£÷ª-ú£uõª1. -- òÅ¡«Nªšíj ÖÚÛ å÷ô Eæ°-ô¢ªÞ¥ ÑÙC.- ë¯E
Íè[ª-Þœª-òÅ°-Þ¥-EÚ¨ 15 Oªåô¢x ë]«ô¢Ùö˺ ÑìoËÖÚÛ GÙë]ª÷± ìªÙ# Î å÷ô šíjÚ•-ììª 45°Òô¢–¬y-ÚÁ-éÙö˺ í£J-Q-L›úh å÷ô Ó꟪h ÓÙêŸ?(Oªå-ô¢xö˺)1) 15 2) 30 3) 25 4) 50
ú£÷«-ëůìÙ:- (1)
í£åÙö˺AB = å-÷ô Ó꟪h h
BC = å-÷ô Íè[ª-Þœª-òŰޜ٠ìªÙ# í£J-Q-õìGÙë]ª-÷±ÚÛª Þœõ ë]«ô¢Ù 15 Oª.-
∠ACB = 45°, ∠ABC = 90°
ABí£-åÙö˺ tan 45° = ⎯BCh
tan 45° = ⎯15
h1 = ⎯ (... tan 45° = 1) -15
h = 15 Oª.ví£:-- ôÁè[ª“ í£ÚÛ\ì Eæ°-ô¢ªÞ¥ Ñìo ÖÚÛ æ©O
å÷ô šíjÚ•-ììª ôÁè[ª“ÚÛª Í÷-êŸL î�μjí£±ìªÙ# í£J-Q-L›úh 60° Òô¢–¬y-ÚÁéÙ à¶ú£ªhÙC.-å÷ô ð§ë]Ù ìªÙ# Ð þ§–û¦Eo ÚÛL›í ú£ô¢-üŒ-¸ô-Üšíj 10 Oªåô¢x ë]«ô¢Ù áJ-Tê¶ å÷ôšíjÚ•ì 30° Òô¢–¬y-ÚÁéÙ à¶ú£ªhÙC.- Íô³ê¶Î ôÁè[ª“ î�μè[õªp ÓÙêŸ? (Oªå-ô¢xö˺)
1) 3 2) 4 3) 5 4) 6
ú£÷«-ëůìÙ:- (3)
AB = æ©O å-÷ô Ó꟪h h
AC = ôÁè[ª“ î�μè[õªp x
CD = 10 Oª.-, ∠ACB = 60°, ∠ADB = 30°ABΔABC ö˺ tan 60° = ⎯AC
h⇒ √⎯3 = ⎯ (..
. tan 60° = √⎯3 )x
⇒ h = √⎯3 x
ABΔADB ö˺ tan 30° = ⎯AD
1 h 1⎯ = ⎯⎯ (... tan 30° = ⎯ )√⎯3 x + 10 √
⎯3
x + 10 x + 10⇒ h = ⎯⎯ ⇒ √⎯3 x = ⎯⎯
√⎯3 √
⎯3
⇒ 3x = x + 10 ⇒ 2x = 10
10⇒ x = ⎯ = 5 Oª.2
∴ ôÁè[ª“ î�μè[õªp (x) = 5 Oª.-ví£:-- 9 Oª.- Ó꟪h-Þœõ ÖÚÛ Në]ªuê ú£hÙòÅ°-EÚ¨
÷ªô¢-÷ªt꟪ à¶óŸ«L.- ë¯EÚ¨ Î ú£hÙòÅ¡ÙšíjìªÙ# 2 Oª.- êŸÚÛª\÷ Ó꟪hÚÛª à¶ô¦L.-ÖÚÛ Eàμa-ììª òÅ¡«Nªšíj 60° ÚÁéÙêÁÑÙ#ê¶ Eàμaì Íè[ªÞœª òŰޜ٠ìªÙ#ú£hÙòÅ¡Ù Íè[ª-Þœª-òÅ°-Þ¥-EÚ¨ ÷ªëÅ]u Þœõ ë]«ô¢-îμªÙêŸ? (Oªå-ô¢xö˺)
7 141) 7√⎯3 2) ⎯ 3) 14√
⎯3- 4) ⎯
√⎯3 √
⎯3
ú£÷«-ëůìÙ:- (2)
í£åÙö˺ AB = N-ë]ªuê ú£hÙòÅ¡Ù Ó꟪h =- 9 Oª.-BC = 2 Oª.-AC = 9 −- 2 =- 7 Oª.∠ADC = 60°
AD =- Eàμaì Íè[ªÞœª òŰޜ٠ìªÙ# ú£hÙòÅ¡ÙÍè[ªÞœª òÅ°Þ¥-EÚ¨ Þœõ ë]«ô¢Ù x Í-ìª-ÚÛªÙë¯Ù
ACΔ ADCö˺ tan 60° = ⎯AD
7 7√⎯3 =- ⎯ x = ⎯ Oª. -x √
⎯3
úˆšï°àÂ. ô¦ëůÚÛ”ù£g Nù£óŸªEí£±éªõª
ô¢àŸô³êŸ
ÎôÂÎôÂHí£K¤Ûõ ví£ê¶uÚÛÙ
Þœé̈êŸÙ
1. -- ÖÚÛ ÷uÚ¨h ÖÚÛ òÅ¡÷ìÙ ìªÙ# Ú•ÙêŸ ë]«ô¢Ùö˺Eö˹aE Î òÅ¡÷ìÙ ÍvÞœ-òÅ°-Þ¥Eo 30° Òô¢–y-ÚÁ-éÙêÁ àŸ«ø‹è[ª.- Î þ§–ìÙ ìªÙ# 40Oª.- òÅ¡÷ìÙ î�μjí£±Þ¥ ìè…# ÷ªô¢ö° ë¯EÍvÞœ-òÅ°-Þ¥Eo 60° Òô¢–¬y-ÚÁ-éÙêÁ àŸ«ø‹è[ª.-Íô³ê¶ Î òÅ¡÷ìÙ Ó꟪h ÓÙêŸ? (Oªå-ô¢xö˺)1) 10-√⎯
3 2) 20√⎯3
3) 25√⎯3 4) 30√
⎯3
2. -- ÖÚÛ ò°õªè[ª ÖÚÛ Në]ªuê ú£hÙòÅ¡Ù Íè[ª-Þœª-òÅ°-Þ¥-EÚ¨ 15 Oªåô¢x ë]«ô¢Ùö˺ ÑìoGÙë]ª÷± ìªÙ# ú£hÙòÅ¡Ù šíjòÅ°-Þ¥Eo 60°Òô¢–y-ÚÁ-éÙêÁ í£J-Q-LÙ-à¦è[ª.- Íô³ê¶ Îú£hÙòÅ¡Ù Ó꟪h ÓÙêŸ?(Oªå-ô¢xö˺)1) 15-√⎯
3 2) 18-√⎯3
3) 17.-5√⎯3 4) 7.-5√
⎯3
3. -- ÖÚÛ Ú¥Ùvæ°-ÚÛdô ð§ôÂ\ö˺ í‡õxõª Îè[ª-ÚÁ-÷-è -̄EÚ¨â°ô¢ªè[ª ñõxìª Ôô¦påª à¶óŸ«-õ-ìª-ÚÛª-û¦oè[ª.-
ë¯Eo 1.-5 Oª. Ó꟪h, òÅ¡«NªêÁ 30° ÚÁéÙඛúö° Ôô¢p-ô¢-à¦-õ-ìª-ÚÛªÙç˶ Î â°ô¢ªè[ª ñõxð»è[÷± ÓÙêŸ ÑÙè¯L? (Oªå-ô¢xö˺)1) 1.-5√
⎯3 2) 3√
⎯3 3) 3 4) 6
4. -- šï°L-Ú¥-í£d-ôÂö˺ Ñìo ÖÚÛ ÷uÚ¨h òÅ¡«NªšíjÑìo êŸì ›úo-꟪-è…E 45° E÷ªo-ÚÁ-éÙêÁí£J-Q-LÙ-à¦è[ª.- šï°L-Ú¥-í£dô òÅ¡«Nªšíj ìªÙ# 175⎯ Oª.- Ó꟪hö˺ ÓÞœª-ô¢ª-꟪Ùç˶ î¦J-ë]ÌJ √
⎯2
÷ªëÅ]u Þœõ ë]«ô¢Ù ÓÙêŸ?1751) ⎯ Oª.- 2) 175-√⎯
3 Oª.- √
⎯2
3) 175-√⎯2 Oª.- 4) 175 Oª.-
5. -- Ñë]óŸªÙ Ôè[ª ÞœÙå-õÚÛª 18 Oª.- Ó꟪h ÞœõÖÚÛ ú£hÙòÅ¡Ù Fè[ ð»è[÷± 6√
⎯3 Oª.- Íô³ê¶
Î ú£÷ª-óŸªÙö˺ ú£«ô¢u-Ú¨-ô¢-é°õª òÅ¡«NªêÁඛú ÚÁéÙ? 1) 30° 2) 45° 3) 60° 4) 90°
áî¦ñªõª: 1n-2; 2n-1; 3n-3; 4n-4; 5n-3.
ÍòÅ°uú£ ví£øŒoõª
l
ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?ú£«ô¢uÚ̈ô¢é°õª òÅ¡«NªêÁ ඛú ÚÁéÙ?
ë]”ù‡d¸ôÜë]”ù
‡d¸ôÜ
÷ú£ªh÷±
÷ú£ªh÷±ÚÛìªo
ÚÛìªo
O
O
θθ = Òô¢–¬yÚÁéÙ
θ = E÷ªoÚÁéÙ¤¨Aá ú£÷«ÙêŸô¢ ¸ôÜ
¤¨Aá ú£÷«ÙêŸô¢ ¸ôÜ B
h
A x C D10 Oª.30°60°
þ§ëÅ]ì:-
C
B
A x D
9 Oª.7 Oª.
2 Oª.
60°
þ§ëÅ]ì:-
C 15 Oª.
h
B
45°
Aþ§ëÅ]ì:-
EöËÀ ú£Kû ڕêŸhJÚ¥ô¢ª“
òÅ°ô¢êŸ àμúà vÚ©è¯Ú¥ô¢ªè[ªEöËÀ ú£Kû 2600 Óö˺¸ôæ¨ÙÞ ð»ÙCì ÷´èÁ ÍAí‡ìo ÷óŸªú£ª\è…Þ¥ JÚ¥ô¢ª“ú£”ù‡dÙà¦è[ª. ¸Úô¢üŒÚÛª àμÙCì Ð 14 ÔüŒx ò°õªè[ª úˆyè[ûÂö˺E ÷«ö˺tö˺áô¢ªÞœªêŸªìo êμší ú‡·Þ÷ªû àμúà æ˺Koö˺ Ð ÷«ôÂ\ìª à¶ô¢ªÚÛªû¦oè[ª.ÞœêŸÙö˺ â°û ñª·ô\ sÍîμªJÚ¥, 13 ÔüŒ‰xz, O Ð sàμjû¦, 14 ÔüŒx 4ûμõõ 30 ôÁVõªz #ìo ÷óŸªú£ªö˺ 2600 ¸ôæ¨ÙÞ ÍÙë]ªÚÛªû¦oô¢ª.ú£Kû 14 ÔüŒx 10 ûμõö˺x Ð íÆ£ªìêŸ þ§CÅÙà¦è[ª. í£J÷«Jbû û¶T s15ÔüŒx 11 ûμõõªz ›íJå Ñìo JÚ¥ô¢ª“ìª ÍCÅÞœNªÙ# #ìo ÷óŸªú£ªö˺2600 Óö˺ ¸ôæ¨ÙÞ þ§CÅÙ#ì ê•L òÅ°ô¢êŸ ÎåÞ¥è…Þ¥ ú£Kû JÚ¥ô¢ª“þ»ÙêŸÙ à¶ú£ªÚÛªû¦oè[ª
Ôíˆ ú£÷«à¦ô¢ ÚÛNªù£ìôÂÞ¥ ô¦â°ÎÙvëÅ]ví£ë¶øË ô¦ù£Z ú£÷«à¦ô¢ ÚÛNªù£ìôÂÞ¥ Õö°í£±ô¢Ù ô¦â°EóŸªNªêŸªöËóŸ«uô¢ª. ÎóŸªì EóŸ«÷ªÚ¥EÚ¨ ú£ÙñÙCÅÙ#ì ë]ú£YÙšíjÞœ÷ô¢oô ìô¢ú‡ÙûË  6ì Îîμ«ë]÷³vë] î˶ø‹ô¢ª. ô¦â° NáóŸªî¦è[ö˺ú‡NöËÀ ÏÙ>FJÙÞÂ, ÍîμªJÚ¥ö˺E ì«u uÙíÚùjô ڥö˶@ö˺ ÓÙHÔí£²Jh à¶ø‹ô¢ª. Õö°í£±ô¢Ù ›úî¦ú£NªA, Húˆ ÕÚÛuî˶CÚÛ ÎëÅ]yô¢uÙö˺ ›úî¦Ú¥ô¢uvÚÛ÷«õª Eô¢yÙà¦ô¢ª.
÷ªJÚ•Eo...* êμöËÙÞ¥é ô¦Nª·ôè…“Þ¥ ›íô¢ªð»ÙCì ê•LêŸô¢Ù Ñë]u÷ªÚ¥ô¢ªè[ª
ÞœªÙè¯ ô¦Nª·ôè…“ s101z Íû¦ôÁÞœuÙ Ú¥ô¢éÙÞ¥  7ìšïj°ë]ô¦ò°ëÂö˺ ÷ªô¢é¨Ùà¦ô¢ª. ìö˹_Ùè[ >ö°x WôÂìÞœôÂê¦õ«Ú¥ ÞœªÙè[xí£Lxö˺ áEtÙ#ì ô¦Nª·ôè…“ 1945ö˺ Ú•è[ÙÞœöËÀö˺ê¦õ«Ú¥ Ú¥ô•p¸ôù£ûË Îíƈú£ôÂÞ¥ ÑëÁuÞœÙö˺ à¶ô¦ô¢ª. 1958 áì÷J27ì êŸì ÑëÁuÞ¥EÚ¨ ô¦@û¦÷« à¶ú‡ êμöËÙÞ¥é ð¼ô¦æÙö˺ð§ö˹_û¦oô¢ª. Íí£påªoÙචÎóŸªìÚÛª êμöËÙÞ¥é ô¦Nª·ôè…“Þ¥ ›íô¢ª÷#aÙC.
* ñ÷³Ü ví£â°‘ø‹L, þ§ï‡°Bî˶êŸh, ÷«û¦ví£Þœè[ øË™ù£þ§ô³  7ìNáóŸªìÞœô¢Ùö˺ ÚÛìªo÷´ø‹ô¢ª. ÎóŸªì 1927 ÎÞœú£ªd 14ì í£Pa÷ªÞÁë¯÷J >ö°x Eè[÷ªvô¢ª ÷ªÙè[öËÙö˺E Þœªìí£vô¢ªö˺ áEtÙà¦ô¢ª.XàŸÙë]ìÙ, Xú£êŸuë¶÷ øŒêŸÚÛÙ, ÎÙvëÅ] þ§ï‡°êŸuÙö˺ ú£uÙ,X÷ªLxÚ¥ô¢ªbì øŒêŸÚÛÙ, ví£ú£ìo òÅ°ú£\ô¢Ù, áóŸªë¶÷ ú£ô¢ú£yA,Xšíjè…êŸöËx÷ªt î¦J ú£ªví£òÅ°ê¦öËìª ô¢#Ùà¦ô¢ª.
* ð§öË÷´ô¢ªnô¢ÙÞ¥·ôè…“ ÓAhð¼êŸöË í£ëÇ]Ú¥EÚ¨ í£ô¦u÷ô¢é Íìª÷ªêŸªöËÚÁú£Ù WûË 4÷ ê¶D ìªÙ# vÞ¥÷ªú£òÅ¡õª Eô¢yÙàŸìªû¦oô¢ª. Ðvð§âËμÚÛªd Îô¢ª >ö°xöË í£JCÅö˺ 12.30 öˤÛöË ÓÚÛô¦öËÚÛª þ§ÞœªFô¢ªÍÙCÙàŸìªÙC. vð§âËμÚÛªd ÷«ô¢_Ùö˺E vÞ¥÷«öËêÁ ð§åª šïj°ë]ô¦ò°ëÂìÞœô¦EÚ¨ ê¦ÞœªFô¢ª, í£JvøŒ÷ªöË Í÷ú£ô¦öËÚÛª Fæ¨E ÍÙCÙàŸìªÙC.Xø˘jöËÙ îËμìªÚÛ áö°öË Îëůô¢ÙÞ¥ EJtú£ªhìo vð§âËμÚÛªd í£JCÅö˺ 5ë]øŒöË ÓAhð¼êŸöË í£ëÇ]Ú¥õª, 5 áö°øŒóŸ«õª EJtú£ªhû¦oô¢ª.÷ªï£°ñ«òËÀìÞœôÂ, û¦ô¦óŸªé›íæ, û¦ÞœôÂÚÛô¢«oõª, NÚ¥ô¦ò°ëÂ,ô¢ÙÞ¥·ôè…“, ìö˹_Ùè[ >ö°xöË í£JCÅö˺ 72 ÷ªÙè[ö°õª Ð vð§âËμÚÛªdí£JCÅö˺ڨ ô¦ìªû¦oô³.
* NCÅ Eô¢yéö˺ vð§é°õª ê¦uޜ٠à¶ú‡ì Ïë]Ìô¢ª òÅ°ô¢BóŸ³õª ú£ï£„115 ÷ªÙC ø‹ÙA í£Jô¢¤Ûé ú‡ñ(ÙCÚ¨ ÕÚÛuô¦áu ú£NªA sÕô¦ú£zíÆ£ªìÙÞ¥ Eî¦üŒ‰öËJpÙ#ÙC. Í÷ªô¢ªö˺x Ú¥ÙÞÁö˺E Õô¦ú£ ú£ªú‡–ô¢êŸNªù£ûËÂö˺ ›ú÷öËÙCÙ#ì òÅ°ô¢êŸ ð¼Mú£ª ÍCÅÚ¥J >ê¶Ùë]ô ÚÛª÷«ôÂ;òÅ°ô¢êŸ í£ô¦u÷ô¢é, ÍæO, î¦ê¦÷ô¢é ÷«ô¢ªpöË ø‹ÜÚÛªÍìªñÙëÅ]ÙÞ¥ Õô¦ú£ ÍGÅ÷”CÌÄ Ú¥ô¢uvÚÛ÷ª sóŸ´ÓûËÂè†íˆzÚÛìqöËμdÙæËÀÞ¥ í£Eà¶ú‡ì PÝ°Þ¥ôÂ_ Ñû¦oô¢ª. NªÞœê¦ 113÷ªÙC Õô¦ú£ú‡ñ(ÙC. Oô¢Ùê¦ 2018 áì÷J n 2019 ÷«JaË ÷ªëÅ]u ø‹ÙA ›ú÷ö˺vð§é°õª ÚÁö˺póŸ«ô¢ª.
* îμªivÚÁþ§íÆÃd ú£Ùú£– ví£Aÿ§’êŸtÚÛÙÞ¥ Eô¢yÙ#ì cÏ>ûË ÚÛíà ÷ô¢öËÀ“àŦÙí‡óŸªûËÂù‡íÃeö˺ îμ³ë]æ¨ ñ÷ªAE ÍîμªJÚ¥ÚÛª àμÙCì cæ©îªÐ@Þœ«xÚÁâËËÀe ·ÞõªàŸªÚÛªÙC. òÅ°ô¢êÂÚÛª àμÙCì ÷³Þœª_ô¢ª Në¯uô¢ª–õª·ôÙèÁ þ§–ìÙö˺ síÆ£úÃd ô¢ìoô¢íÃÞ¥z ELà¦ô¢ª. Oô¢ª þ§tôÂd Îæ˺çËμèÂÚ¥õªù£u EôÁëÅ]ÚÛ, Øù£ëÅ] ñæ°yè¯ ÷«úÃ\ìª êŸóŸ«ô¢ªà¶ø‹ô¢ª.Ïö°Ùæ¨ þ§ëÅ]û¦Eo ô¢«ð»ÙCÙàŸè[Ù ví£í£ÙàŸÙö˺û¶ ÏC ê•Lþ§J.ÎÚ¥øËÂ, î¦ú£ª Ú˽PÚÂ, òÅ¡ô¢ê ú£ªÙë]öËÀ Îú£–÷«, Dô¢+Ú¥LÚÛ ø‹yú£ÚÁøŒú£÷ªú£uõªìo ôÁÞœªöËÚÛª Ñí£óμ«Þœí£è˶ c›úLe Íû¶ þ§ëÅ]û¦Eoô¢«ð»ÙCÙà¦ô¢ª. íƇvñ÷Jö˺ ú‡è†oö˺ áJTì Îú‡óŸ« vð§ÙBóŸªêŸªC ð¼æ©ö˺ c›úLe îμ³ë]æ¨ þ§–ìÙö˺ EL#ÙC.
÷ªJÙêŸ ú£÷«à¦ô¢Ù www.eenadupratibha.net ö˺
Related Documents
![TG · 2019-09-26 · TG šïj°ë]ô¦ò°ë ޜªô¢ªî¦ô¢Ù šúšídÙñô¢ª 26, 2019) e-mail: edc@eenadu.in F FFF ûÁ æ© úà ò º ô¢ª“ ví£òÅ¡ªêŸ y](https://static.cupdf.com/doc/110x72/5e9249f8f017e761867cd216/tg-2019-09-26-tg-j-d.jpg)
