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Simplification problems
1. If a + b = 8 and ab = 15, then what is the value of a3 + b3?
Options
A. 98
B. 152
C. 124
D. 260
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Correct Answer: 152
2. Point A (4 , 2) divides segment BC in the ratio 2:5. Co-ordinates of B are (2 , 6) and C are (7 , y). What is the value of y?
Options
A. 8
B. -8
C. 6
D. -6
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Correct Answer: -8
3. Tan 45° + Cosec 60° =
Options
A. (1 + 2?2)/2
B. (?3 + 2)/?6
C. 5/?3
D. (3 + 2?3)/3
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Correct Answer: (3 + 2?3)/3
4. ?XYZ is right angled at Y. If m?Z = 60°, then Cosec X =
Options
A. 2
B. 1/2
C. 1/?2
D. 1/?3
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Correct Answer: 2
5. If Cosec ? = 17/8, then Cot ? = ?
Options
A. 17/8
B. 15/8
C. 8/15
D. 17/15
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Correct Answer: 15/8
6. What is the area (in sq cm) of a regular hexagon of side 9 cm?
Options
A. 50?3
B. 300?3
C. 243?3/2
D. 200?3
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Correct Answer: 243?3/2
7. If 2/3(6x/5 - 1/4) + 1/3 = 9x/5, then what is the value of x?
Options
A. 1/6
B. -1/6
C. 1/5
D. -1/5
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Correct Answer: 1/6
8. What is the value of Cot 45°+ 1/3 Cosec 60° ?
Options
A. ?3 + 2
B. (9 + 2?3)/9
C. ?3
D. (2?2 + 3)/?6
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Correct Answer: (9 + 2?3)/9
9. ? DEF is right angled at E. If m?F = 45, then what is the value of Sin F x Tan F?
Options
A. ?2
B. 1/?3
C. 1/?2
D. 2/?3
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Correct Answer: 1/?2
10. If Cot ? = 21/20, then what is the value of Sec ??
Options
A. 29/21
B. 21/29
C. 29/20
D. 20/29
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Correct Answer: 29/21
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