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- Question
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
- Correct Answer
- Each fraction is equal to 1/2 or -1
Explanationa/(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
- 1. What is the simplified value of (cos4 A ? sin4 A) ?
Options- A. 0
- B. 2 cos2 A
- C. cos2A
- D. 1 Discuss
- 2. 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 Discuss
- 3. 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 Discuss
- 4. 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 Discuss
- 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 Discuss
- 6. If 3x= 4y= 12 , then z is equal to
Options- A. xy
- B. x + y
- C. xy/x+Y
- D. 4x +3y Discuss
- 7. If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct ?
Options- A. a/b = c/d
- B. a/d = c/b
- C. a/b = d/c
- D. none Discuss
- 8. What is the value of 2+2+2+2.......
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9. A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?
Options- A. 12/?+4
- B. 6/?+4
- C. 3/?+4
- D. 6/?+2?2 Discuss
- 10. Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10?3 cm, then what is the diameter of the circle?
Options- A. 10 cm
- B. 15 cm
- C. 20 cm
- D. 30 cm Discuss
Simplification problems
Search Results
Correct Answer: cos2A
Correct Answer: 1
Correct Answer: 1
Correct Answer: 4/3
Correct Answer: 154/27
Correct Answer: xy/x+Y
Explanation:
Correct Answer: a/b = c/d
Explanation:
(4a+7b)(4c-7d) = (4a-7b)(4c+7d)
(4a+7b)/(4a-7b) = (4c+7d)/(4c-7d)
Using componendo and dividendo
(4a+7b)+(4a-7b) / (4a+7b)-(4a-7b)
= (4c+7d)+(4c-7d) / (4c+7d)-(4c-7d)
Or 8a/14b = 8c/14d
Or a/b = c/d
Correct Answer: 4
Explanation:
Let 2+?2+?2..... = t
2+?t = t
t - 2 = ?t
t = 4
Correct Answer: 6/?+4
Explanation:
Correct Answer: 20 cm
Explanation:
Let there be 2 circles with centre O1 and OAB is the common chord
Since both passes through the center of each other as shown in figure
So O1O is the radius of both
Let O1O = r = AO1= AO
AX = AB / 2 = 5?3 cm (since OX perpendicular to chord bisects it)
AOO1 forms an equilateral triangle with on side = radius = r
Sin 60 = ?3/2 = AX / AO = 5?3/r
So r = 10 cm
So diameter = 20 cm
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