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 Page 1


     
  
  
  
 
 
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
 
SAT ANSWER KEY 
 
QUE. 1 2 3 4 5 6 7 8 9 10 
ANS.  4 2 3 1 2 1 3 4 4   1 
  
          
QUE. 11 12 13 14 15 16 17 18 19 20 
ANS.  3 2  1   3 4 3 2 4 1 2 
  
          
QUE. 21 22 23 24 25 26 27 28 29 30 
ANS. 1  2 2 1 1 2  4 4 1 2 
  
          
QUE. 31 32 33 34 35 36 37 38 39 40 
ANS.  3 4 2 2 1 4 2 3 2 4 
  
          
QUE. 41 42 43 44 45 46 47 48 49 50 
ANS.  2 4 2 3 1 4 3 2  1 4  
           
QUE. 51 52 53 54 55 56 57 58 59 60 
ANS.  2 3  4 4 3 4 1 3 2 2 
  
          
QUE. 61 62 63 64 65 66 67 68 69 70 
ANS.  1 3 3 3 1 4 1 2 2 4 
  
          
QUE. 71 72 73 74 75 76 77 78 79 80 
ANS.  1 3 1 3 2 1 3 2 2 4 
  
          
QUE. 81 82 83 84 85 86 87 88 89 90 
ANS.  3 1 1 3 1 1 1 3 2 4 
  
          
QUE. 91 92 93 94 95 96 97 98 99 100 
ANS. 2  1 3 1 4 4 1 3 3 3 
 
SAT SOLUTIONS 
 
1. (4) 
 Theory :- Light bonds due to difference in R.I. of air layers. 
 
2. (2) 
General Knowledge 
 
3. (3) 
 Theory:-  Universal law of gravitation 
 
Page 2


     
  
  
  
 
 
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
 
SAT ANSWER KEY 
 
QUE. 1 2 3 4 5 6 7 8 9 10 
ANS.  4 2 3 1 2 1 3 4 4   1 
  
          
QUE. 11 12 13 14 15 16 17 18 19 20 
ANS.  3 2  1   3 4 3 2 4 1 2 
  
          
QUE. 21 22 23 24 25 26 27 28 29 30 
ANS. 1  2 2 1 1 2  4 4 1 2 
  
          
QUE. 31 32 33 34 35 36 37 38 39 40 
ANS.  3 4 2 2 1 4 2 3 2 4 
  
          
QUE. 41 42 43 44 45 46 47 48 49 50 
ANS.  2 4 2 3 1 4 3 2  1 4  
           
QUE. 51 52 53 54 55 56 57 58 59 60 
ANS.  2 3  4 4 3 4 1 3 2 2 
  
          
QUE. 61 62 63 64 65 66 67 68 69 70 
ANS.  1 3 3 3 1 4 1 2 2 4 
  
          
QUE. 71 72 73 74 75 76 77 78 79 80 
ANS.  1 3 1 3 2 1 3 2 2 4 
  
          
QUE. 81 82 83 84 85 86 87 88 89 90 
ANS.  3 1 1 3 1 1 1 3 2 4 
  
          
QUE. 91 92 93 94 95 96 97 98 99 100 
ANS. 2  1 3 1 4 4 1 3 3 3 
 
SAT SOLUTIONS 
 
1. (4) 
 Theory :- Light bonds due to difference in R.I. of air layers. 
 
2. (2) 
General Knowledge 
 
3. (3) 
 Theory:-  Universal law of gravitation 
 
    
  
 
  
4. (1) 
 P = 
F
A
= 
2 6 2
6
50
N / m 100 10 N / m
0.5 10
?
? ?
?
  
 
5. (2) 
 Theory:- Property of human eye 
 
6. (1) 
Theory 
 
7. (3) 
 Theory 
 
8. (4) 
 Theory:- Filed lines originate from north pole and end on south pole outside magnet 
 
9. (4) 
 Theory:- Phenomenon is reflection 
 
10. (1) 
 Theory:- Electromagnetic Induction 
 
11. (3) 
 Q = it = 0.4 ? 3 ? 60 = 72C 
 
12. (2) 
 Theory:- Image formation by concave mirror 
 
13. (1) 
 Theory:- Circuit diagram for Ohm’s Law 
 
14. (3) 
 Ionisation energy decreases down the group and increases across the period. Hence K 
 
15. (4) 
 K 19 1 18
?
? ? ?  
 
2
Cl 17 1 18
Ca 20 2 18
?
?
? ? ?
? ? ?
  
 Hence Only K 
 
16. (3) 
 
2 4 2 4
Na SO BaCl BaSO 2NaCl ? ? ?  
 
17. (2) 
 
4
4 2 4
Blue white anhydrous CuSO
CuSO 5H O CuSO ? ?  
 
18. (4) 
 Ant sting contains methanoic acid also called formic acid. 
 
19. (1) 
 Na 2CO 3 is formed from NaOH and H 2CO 3 i.e. strong base and weak acid. 
 Hence Na 2CO 3. 
 
20. (2) 
 HCl . Rest all are ionic 
 
21. (1) 
 Copper lies below H in reactivity series. 
 
22. (2) 
 CH 3COOH and C 2H 5COOH 
 a difference of -CH 2 
 
23. (2) 
 
3 2
CH CH CH ? ?  
 
Page 3


     
  
  
  
 
 
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
 
SAT ANSWER KEY 
 
QUE. 1 2 3 4 5 6 7 8 9 10 
ANS.  4 2 3 1 2 1 3 4 4   1 
  
          
QUE. 11 12 13 14 15 16 17 18 19 20 
ANS.  3 2  1   3 4 3 2 4 1 2 
  
          
QUE. 21 22 23 24 25 26 27 28 29 30 
ANS. 1  2 2 1 1 2  4 4 1 2 
  
          
QUE. 31 32 33 34 35 36 37 38 39 40 
ANS.  3 4 2 2 1 4 2 3 2 4 
  
          
QUE. 41 42 43 44 45 46 47 48 49 50 
ANS.  2 4 2 3 1 4 3 2  1 4  
           
QUE. 51 52 53 54 55 56 57 58 59 60 
ANS.  2 3  4 4 3 4 1 3 2 2 
  
          
QUE. 61 62 63 64 65 66 67 68 69 70 
ANS.  1 3 3 3 1 4 1 2 2 4 
  
          
QUE. 71 72 73 74 75 76 77 78 79 80 
ANS.  1 3 1 3 2 1 3 2 2 4 
  
          
QUE. 81 82 83 84 85 86 87 88 89 90 
ANS.  3 1 1 3 1 1 1 3 2 4 
  
          
QUE. 91 92 93 94 95 96 97 98 99 100 
ANS. 2  1 3 1 4 4 1 3 3 3 
 
SAT SOLUTIONS 
 
1. (4) 
 Theory :- Light bonds due to difference in R.I. of air layers. 
 
2. (2) 
General Knowledge 
 
3. (3) 
 Theory:-  Universal law of gravitation 
 
    
  
 
  
4. (1) 
 P = 
F
A
= 
2 6 2
6
50
N / m 100 10 N / m
0.5 10
?
? ?
?
  
 
5. (2) 
 Theory:- Property of human eye 
 
6. (1) 
Theory 
 
7. (3) 
 Theory 
 
8. (4) 
 Theory:- Filed lines originate from north pole and end on south pole outside magnet 
 
9. (4) 
 Theory:- Phenomenon is reflection 
 
10. (1) 
 Theory:- Electromagnetic Induction 
 
11. (3) 
 Q = it = 0.4 ? 3 ? 60 = 72C 
 
12. (2) 
 Theory:- Image formation by concave mirror 
 
13. (1) 
 Theory:- Circuit diagram for Ohm’s Law 
 
14. (3) 
 Ionisation energy decreases down the group and increases across the period. Hence K 
 
15. (4) 
 K 19 1 18
?
? ? ?  
 
2
Cl 17 1 18
Ca 20 2 18
?
?
? ? ?
? ? ?
  
 Hence Only K 
 
16. (3) 
 
2 4 2 4
Na SO BaCl BaSO 2NaCl ? ? ?  
 
17. (2) 
 
4
4 2 4
Blue white anhydrous CuSO
CuSO 5H O CuSO ? ?  
 
18. (4) 
 Ant sting contains methanoic acid also called formic acid. 
 
19. (1) 
 Na 2CO 3 is formed from NaOH and H 2CO 3 i.e. strong base and weak acid. 
 Hence Na 2CO 3. 
 
20. (2) 
 HCl . Rest all are ionic 
 
21. (1) 
 Copper lies below H in reactivity series. 
 
22. (2) 
 CH 3COOH and C 2H 5COOH 
 a difference of -CH 2 
 
23. (2) 
 
3 2
CH CH CH ? ?  
 
    
  
 
  
24. (1) 
 Stainless steel is a mixture of Iron, Nickel, Chromium and Carbon. 
 
25. (1) 
 Nonmetals form acidic oxides. 
 Hence aromic No. 7 
 
26. (2) 
 
n 2n 1
C H
?
 is alkyl 
 
27. (4) 
 CO 2 and water (CO 2 is reduced to C 6H 12O 6 and H 2O is oxidized to oxygen) 
 
28. (4) 
 Testis (Is male reproductive organ while others are female) 
 
29. (1) 
 50 decibel (in day time, 40 decibel at night in silent zone) 
  
30. (2) 
 114 (N 2O remains in the atmosphere for 114 years) 
 
31. (3) 
 Two (Deoxydenated blood enters the heart and then lungs, oxygenated blood enters the heart and pumped to 
other parts of the body (Pulmonary circulation and then systemic circulation)) 
 
32. (4) 
 Seisononastic movement (Nastic movement, nondirectional movement towards direction of touch) 
 
33. (2) 
 Regeneration is not truly a reproductive process, rather it’s a process of renewal, restoration and growth in 
organisms. 
 
34. (2) 
 23 pairs of chromosomes  (22 pairs of autosome and one pair of allosome) 
 
35. (1) 
 Darwin explained natural selection, Lamarck explained inheritance of acquired characters and Mendel is known 
for pioneering work in inheritance. 
 
36. (4) 
1, 2 and 3 belongs to Thallophyta and 4 belongs to Bryophyta 
 
37. (2) 
 Raphide crystals are sharp needle like crystals of calcium oxalate that dart and cause discomfort to throat, 
activates inflammatory reaction by production of histamines. 
 
38. (3) 
 Area A is for perception of touch, pain etc. 
 Area B is for perception of sound 
 Area C is occipital lobe of for brain for visual perception 
 Area D is for thinking, Intelligence etc. 
 
39. (2) 
 Estrogen is secreted by ovary 
 
40. (4) 
 1, 2 and 3 are pteridophytes and 4 is  bryophyte 
 
41. (2) 
 
42. (4) 
 
43. (2) 
 
44. (3) 
 
45. (1) 
 
46. (4) 
Page 4


     
  
  
  
 
 
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
 
SAT ANSWER KEY 
 
QUE. 1 2 3 4 5 6 7 8 9 10 
ANS.  4 2 3 1 2 1 3 4 4   1 
  
          
QUE. 11 12 13 14 15 16 17 18 19 20 
ANS.  3 2  1   3 4 3 2 4 1 2 
  
          
QUE. 21 22 23 24 25 26 27 28 29 30 
ANS. 1  2 2 1 1 2  4 4 1 2 
  
          
QUE. 31 32 33 34 35 36 37 38 39 40 
ANS.  3 4 2 2 1 4 2 3 2 4 
  
          
QUE. 41 42 43 44 45 46 47 48 49 50 
ANS.  2 4 2 3 1 4 3 2  1 4  
           
QUE. 51 52 53 54 55 56 57 58 59 60 
ANS.  2 3  4 4 3 4 1 3 2 2 
  
          
QUE. 61 62 63 64 65 66 67 68 69 70 
ANS.  1 3 3 3 1 4 1 2 2 4 
  
          
QUE. 71 72 73 74 75 76 77 78 79 80 
ANS.  1 3 1 3 2 1 3 2 2 4 
  
          
QUE. 81 82 83 84 85 86 87 88 89 90 
ANS.  3 1 1 3 1 1 1 3 2 4 
  
          
QUE. 91 92 93 94 95 96 97 98 99 100 
ANS. 2  1 3 1 4 4 1 3 3 3 
 
SAT SOLUTIONS 
 
1. (4) 
 Theory :- Light bonds due to difference in R.I. of air layers. 
 
2. (2) 
General Knowledge 
 
3. (3) 
 Theory:-  Universal law of gravitation 
 
    
  
 
  
4. (1) 
 P = 
F
A
= 
2 6 2
6
50
N / m 100 10 N / m
0.5 10
?
? ?
?
  
 
5. (2) 
 Theory:- Property of human eye 
 
6. (1) 
Theory 
 
7. (3) 
 Theory 
 
8. (4) 
 Theory:- Filed lines originate from north pole and end on south pole outside magnet 
 
9. (4) 
 Theory:- Phenomenon is reflection 
 
10. (1) 
 Theory:- Electromagnetic Induction 
 
11. (3) 
 Q = it = 0.4 ? 3 ? 60 = 72C 
 
12. (2) 
 Theory:- Image formation by concave mirror 
 
13. (1) 
 Theory:- Circuit diagram for Ohm’s Law 
 
14. (3) 
 Ionisation energy decreases down the group and increases across the period. Hence K 
 
15. (4) 
 K 19 1 18
?
? ? ?  
 
2
Cl 17 1 18
Ca 20 2 18
?
?
? ? ?
? ? ?
  
 Hence Only K 
 
16. (3) 
 
2 4 2 4
Na SO BaCl BaSO 2NaCl ? ? ?  
 
17. (2) 
 
4
4 2 4
Blue white anhydrous CuSO
CuSO 5H O CuSO ? ?  
 
18. (4) 
 Ant sting contains methanoic acid also called formic acid. 
 
19. (1) 
 Na 2CO 3 is formed from NaOH and H 2CO 3 i.e. strong base and weak acid. 
 Hence Na 2CO 3. 
 
20. (2) 
 HCl . Rest all are ionic 
 
21. (1) 
 Copper lies below H in reactivity series. 
 
22. (2) 
 CH 3COOH and C 2H 5COOH 
 a difference of -CH 2 
 
23. (2) 
 
3 2
CH CH CH ? ?  
 
    
  
 
  
24. (1) 
 Stainless steel is a mixture of Iron, Nickel, Chromium and Carbon. 
 
25. (1) 
 Nonmetals form acidic oxides. 
 Hence aromic No. 7 
 
26. (2) 
 
n 2n 1
C H
?
 is alkyl 
 
27. (4) 
 CO 2 and water (CO 2 is reduced to C 6H 12O 6 and H 2O is oxidized to oxygen) 
 
28. (4) 
 Testis (Is male reproductive organ while others are female) 
 
29. (1) 
 50 decibel (in day time, 40 decibel at night in silent zone) 
  
30. (2) 
 114 (N 2O remains in the atmosphere for 114 years) 
 
31. (3) 
 Two (Deoxydenated blood enters the heart and then lungs, oxygenated blood enters the heart and pumped to 
other parts of the body (Pulmonary circulation and then systemic circulation)) 
 
32. (4) 
 Seisononastic movement (Nastic movement, nondirectional movement towards direction of touch) 
 
33. (2) 
 Regeneration is not truly a reproductive process, rather it’s a process of renewal, restoration and growth in 
organisms. 
 
34. (2) 
 23 pairs of chromosomes  (22 pairs of autosome and one pair of allosome) 
 
35. (1) 
 Darwin explained natural selection, Lamarck explained inheritance of acquired characters and Mendel is known 
for pioneering work in inheritance. 
 
36. (4) 
1, 2 and 3 belongs to Thallophyta and 4 belongs to Bryophyta 
 
37. (2) 
 Raphide crystals are sharp needle like crystals of calcium oxalate that dart and cause discomfort to throat, 
activates inflammatory reaction by production of histamines. 
 
38. (3) 
 Area A is for perception of touch, pain etc. 
 Area B is for perception of sound 
 Area C is occipital lobe of for brain for visual perception 
 Area D is for thinking, Intelligence etc. 
 
39. (2) 
 Estrogen is secreted by ovary 
 
40. (4) 
 1, 2 and 3 are pteridophytes and 4 is  bryophyte 
 
41. (2) 
 
42. (4) 
 
43. (2) 
 
44. (3) 
 
45. (1) 
 
46. (4) 
    
  
 
  
 
47. (3) 
 
48. (2) 
 
49. (1) 
 
*50. (4) (Correction in question - League of nation) 
 
51. (2) 
 
52. (3) 
 
53. (4) 
 
54. (4) 
 
55. (3) 
 
56. (4) 
 
57. (1) 
 
58. (3) 
 
59. (2) 
 
60. (2) 
 
61. (1) 
 
62. (3) 
 
63. (3) 
 
64. (3) 
 
65. (1) 
 
66. (4) 
 
67. (1) 
 
68. (2) 
 
69. (2) 
 
70. (4) 
 
71. (1) 
 
72. (3) 
 
73. (1) 
 
74. (3) 
 
75. (2) 
 
76. (1) 
 
77. (3) 
 
78. (2) 
 
79. (2) 
 
80. (4) 
 
81. (3) 
Page 5


     
  
  
  
 
 
 
NATIONAL TALENT SEARCH EXAMINATION, 2017-18 
 
SAT ANSWER KEY 
 
QUE. 1 2 3 4 5 6 7 8 9 10 
ANS.  4 2 3 1 2 1 3 4 4   1 
  
          
QUE. 11 12 13 14 15 16 17 18 19 20 
ANS.  3 2  1   3 4 3 2 4 1 2 
  
          
QUE. 21 22 23 24 25 26 27 28 29 30 
ANS. 1  2 2 1 1 2  4 4 1 2 
  
          
QUE. 31 32 33 34 35 36 37 38 39 40 
ANS.  3 4 2 2 1 4 2 3 2 4 
  
          
QUE. 41 42 43 44 45 46 47 48 49 50 
ANS.  2 4 2 3 1 4 3 2  1 4  
           
QUE. 51 52 53 54 55 56 57 58 59 60 
ANS.  2 3  4 4 3 4 1 3 2 2 
  
          
QUE. 61 62 63 64 65 66 67 68 69 70 
ANS.  1 3 3 3 1 4 1 2 2 4 
  
          
QUE. 71 72 73 74 75 76 77 78 79 80 
ANS.  1 3 1 3 2 1 3 2 2 4 
  
          
QUE. 81 82 83 84 85 86 87 88 89 90 
ANS.  3 1 1 3 1 1 1 3 2 4 
  
          
QUE. 91 92 93 94 95 96 97 98 99 100 
ANS. 2  1 3 1 4 4 1 3 3 3 
 
SAT SOLUTIONS 
 
1. (4) 
 Theory :- Light bonds due to difference in R.I. of air layers. 
 
2. (2) 
General Knowledge 
 
3. (3) 
 Theory:-  Universal law of gravitation 
 
    
  
 
  
4. (1) 
 P = 
F
A
= 
2 6 2
6
50
N / m 100 10 N / m
0.5 10
?
? ?
?
  
 
5. (2) 
 Theory:- Property of human eye 
 
6. (1) 
Theory 
 
7. (3) 
 Theory 
 
8. (4) 
 Theory:- Filed lines originate from north pole and end on south pole outside magnet 
 
9. (4) 
 Theory:- Phenomenon is reflection 
 
10. (1) 
 Theory:- Electromagnetic Induction 
 
11. (3) 
 Q = it = 0.4 ? 3 ? 60 = 72C 
 
12. (2) 
 Theory:- Image formation by concave mirror 
 
13. (1) 
 Theory:- Circuit diagram for Ohm’s Law 
 
14. (3) 
 Ionisation energy decreases down the group and increases across the period. Hence K 
 
15. (4) 
 K 19 1 18
?
? ? ?  
 
2
Cl 17 1 18
Ca 20 2 18
?
?
? ? ?
? ? ?
  
 Hence Only K 
 
16. (3) 
 
2 4 2 4
Na SO BaCl BaSO 2NaCl ? ? ?  
 
17. (2) 
 
4
4 2 4
Blue white anhydrous CuSO
CuSO 5H O CuSO ? ?  
 
18. (4) 
 Ant sting contains methanoic acid also called formic acid. 
 
19. (1) 
 Na 2CO 3 is formed from NaOH and H 2CO 3 i.e. strong base and weak acid. 
 Hence Na 2CO 3. 
 
20. (2) 
 HCl . Rest all are ionic 
 
21. (1) 
 Copper lies below H in reactivity series. 
 
22. (2) 
 CH 3COOH and C 2H 5COOH 
 a difference of -CH 2 
 
23. (2) 
 
3 2
CH CH CH ? ?  
 
    
  
 
  
24. (1) 
 Stainless steel is a mixture of Iron, Nickel, Chromium and Carbon. 
 
25. (1) 
 Nonmetals form acidic oxides. 
 Hence aromic No. 7 
 
26. (2) 
 
n 2n 1
C H
?
 is alkyl 
 
27. (4) 
 CO 2 and water (CO 2 is reduced to C 6H 12O 6 and H 2O is oxidized to oxygen) 
 
28. (4) 
 Testis (Is male reproductive organ while others are female) 
 
29. (1) 
 50 decibel (in day time, 40 decibel at night in silent zone) 
  
30. (2) 
 114 (N 2O remains in the atmosphere for 114 years) 
 
31. (3) 
 Two (Deoxydenated blood enters the heart and then lungs, oxygenated blood enters the heart and pumped to 
other parts of the body (Pulmonary circulation and then systemic circulation)) 
 
32. (4) 
 Seisononastic movement (Nastic movement, nondirectional movement towards direction of touch) 
 
33. (2) 
 Regeneration is not truly a reproductive process, rather it’s a process of renewal, restoration and growth in 
organisms. 
 
34. (2) 
 23 pairs of chromosomes  (22 pairs of autosome and one pair of allosome) 
 
35. (1) 
 Darwin explained natural selection, Lamarck explained inheritance of acquired characters and Mendel is known 
for pioneering work in inheritance. 
 
36. (4) 
1, 2 and 3 belongs to Thallophyta and 4 belongs to Bryophyta 
 
37. (2) 
 Raphide crystals are sharp needle like crystals of calcium oxalate that dart and cause discomfort to throat, 
activates inflammatory reaction by production of histamines. 
 
38. (3) 
 Area A is for perception of touch, pain etc. 
 Area B is for perception of sound 
 Area C is occipital lobe of for brain for visual perception 
 Area D is for thinking, Intelligence etc. 
 
39. (2) 
 Estrogen is secreted by ovary 
 
40. (4) 
 1, 2 and 3 are pteridophytes and 4 is  bryophyte 
 
41. (2) 
 
42. (4) 
 
43. (2) 
 
44. (3) 
 
45. (1) 
 
46. (4) 
    
  
 
  
 
47. (3) 
 
48. (2) 
 
49. (1) 
 
*50. (4) (Correction in question - League of nation) 
 
51. (2) 
 
52. (3) 
 
53. (4) 
 
54. (4) 
 
55. (3) 
 
56. (4) 
 
57. (1) 
 
58. (3) 
 
59. (2) 
 
60. (2) 
 
61. (1) 
 
62. (3) 
 
63. (3) 
 
64. (3) 
 
65. (1) 
 
66. (4) 
 
67. (1) 
 
68. (2) 
 
69. (2) 
 
70. (4) 
 
71. (1) 
 
72. (3) 
 
73. (1) 
 
74. (3) 
 
75. (2) 
 
76. (1) 
 
77. (3) 
 
78. (2) 
 
79. (2) 
 
80. (4) 
 
81. (3) 
    
  
 
  
 11, 15, 19, . . . 299 
 299 = 11 + (n – 1)4 
 ? n = 73 
 
82. (1) 
 
2
x 2 x 6 0 ? ? ?  
 ? ? ? ?
2
x 3 2x 2x 6 0
x 2 x 3 2 0
x 2, 3 2
? ? ? ? ?
? ? ? ?
? ?
  
 
83. (1) 
 50 ? 10,000/- 
 100 ? 20,000/- 
 
84. (3) 
 Speed x km/hr distance = y km 
 Speed = (x + 15) 
 
y y
2
x 15 x
? ?
?
  
 
? ? ? ?
2
2
xy x 15 y 2x
xy xy 15y 2x 30x
15y 2x 30x
? ? ? ?
? ? ? ? ?
? ? ?
  
 Speed = (x – 15) km/hr 
 
y y
1
x 5 x
? ?
?
  
 
? ? ? ?
2
2
2
xy x 5 y x
xy xy x 5y 5x
5y x 5x
15y 3x 15x
? ? ?
? ? ? ? ?
? ? ?
? ? ?
  
 
2 2
2
3x 15x 2x 30x
x 45x 0
? ? ? ?
? ? ?
  
 x = 0, x = 45 
 ? y = 
? ?
2
45
45
5
? = 405 – 45 = 360 km 
 
85. (1) 
 ? ? ? ?
3 3 3 3 3
3 2 9 4 6 ? ? ?  
 
3 3 3 3 3 3
27 12 18 18 8 12 ? ? ? ? ? ?  
 = 3 + 2 = 5 
 
86. (1) 
 x + 12 = 160 ? 
1
x
  
 
? ? ? ?
2
2
2
x 12x 160
x 12x 160 0
x 20x 8x 160 0
x x 20 8 x 20 0
? ? ?
? ? ? ?
? ? ? ? ?
? ? ? ? ?
  
 X = 8, x = -20 
 X = 8 
 ? Number = 8 + 12 = 20 
 
87. (1) 
 n(S) = 50 
 E = {2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 31, 37, 41, 43, 47} 
 n(E) = 15 
 ? P(E) = 
15
50
 = 
3
10
  
 
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