Simplification problems
- 1. If x = (?2 + 1)/(?2 ? 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?
Options- A. 5
- B. 2
- C. 2?3
- D. 2?2 Also asked in: Bank Exams
Correct Answer: 2?3
- 2. If 27x + 27[x?(1/3)] = 972, then what is the value of x?
Options- A. 2
- B. 3
- C. 4
- D. 5 Also asked in: Bank Exams
Correct Answer: 2
- 3. The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?
Options- A. 5
- B. 10?3
- C. 20
- D. 20?3 Also asked in: Bank Exams
Correct Answer: 20
- 4. If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 ? 3abc ?
Options- A. 365
- B. 444
- C. 666
- D. 999 Also asked in: Bank Exams
Correct Answer: 666
- 5. If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3) ?
Options- A. 70/9
- B. 154/27
- C. 349/27
- D. 349/7 Also asked in: Bank Exams
Correct Answer: 154/27
- 6. If x ? (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 ? 3x + 2) / (3x4 + 3) ?
Options- A. 1/3
- B. 2/3
- C. 4/3
- D. 5/3 Also asked in: Bank Exams
Correct Answer: 4/3
- 7. What is the simplified value of sec6 A ? tan6 A ? 3 sec2 A tan2 A ?
Options- A. -1
- B. 0
- C. 1
- D. sec A tan A Also asked in: Bank Exams
Correct Answer: 1
- 8. What is the simplified value of (cosec A ? sin A)(sec A ? cos A)(tan A + cot A)?
Options- A. -1
- B. 0
- C. 1
- D. 2 Also asked in: Bank Exams
Correct Answer: 1
- 9. What is the simplified value of (cos4 A ? sin4 A) ?
Options- A. 0
- B. 2 cos2 A
- C. cos2A
- D. 1 Also asked in: Bank Exams
Correct Answer: cos2A
- 10. If ab+c=bc+a=Cb+a then which one of the following statements is correct?
Options- A. Each fraction is equal to 1 or -1
- B. Each fraction is equal to 1/2 or 1
- C. Each fraction is equal to 1/2 or -1
- D. Each fraction is equal to 1.2 only Also asked in: Bank Exams
Correct Answer: Each fraction is equal to 1/2 or -1
Explanation:
a/(b+c) = b/(c+a) = c/(a+b)
Taking reciprocal and adding 1 to each ratio we get;
(b+c)/a + 1 = b/(c+a) + 1 = c/(a+b) + 1
Or (a+b+c)/a = (a+b+c)/b = (a+b+c)/c
So this can only be equal when a=b=c or a+b+c = 0
When a=b=c we get
a/(b+c)= ½When a+b+c = 0 we get
b+c = -a
So a/(b+c) = -1
So the ratios are ½ or -1
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