Discussion
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- Question
If x = 3 + 2√2, then the value of ❨ √x - 1 ❩ is: √x
Options- A. 1
- B. 2
- C. 2√2
- D. 3√3
- Correct Answer
- 2
Explanation❨ √x - 1 ❩ 2 = x + 1 - 2 √x x = (3 + 2√2) + 1 - 2 (3 + 2√2) = (3 + 2√2) + 1 x (3 - 2√2) - 2 (3 + 2√2) (3 - 2√2) = (3 + 2√2) + (3 - 2√2) - 2
= 4.
∴ ❨ √x - 1 ❩ = 2. √x - 1. (17)3.5 x (17)? = 178
Options- A. 2.29
- B. 2.75
- C. 4.25
- D. 4.5 Discuss
- 2. (0.04)-1.5 =?
Options- A. 25
- B. 125
- C. 250
- D. 625 Discuss
- 3. (256)0.16 x (256)0.09 =?
Options- A. 4
- B. 16
- C. 64
- D. 256.25 Discuss
- 4.
1 + 1 + 1 =? 1 + x(b - a) + x(c - a) 1 + x(a - b) + x(c - b) 1 + x(b - c) + x(a - c)
Options- A. 0
- B. 1
- C. xa - b - c
- D. None of these Discuss
- 5. If 5a = 3125, then the value of 5(a - 3) is:
Options- A. 25
- B. 125
- C. 625
- D. 1625 Discuss
- 6. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Options- A. 1
- B. 11⁄40
- C. 40
- D. 80 Discuss
- 7. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Options- A. 12
- B. 18
- C. 22
- D. 24
- E. None of these Discuss
- 8. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Options- A. 9
- B. 10
- C. 11
- D. 12 Discuss
- 9. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
Options- A. 4
- B. 8
- C. 12
- D. 16 Discuss
- 10. A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:
Options- A. 10 m
- B. 12.5 m
- C. 17.5 m
- D. 21.25 m Discuss
Surds and Indices problems
Search Results
Correct Answer: 4.5
Explanation:
Let (17) 3.5 x (17) x = 17 8
Then, (17)3.5 + x = 178.
∴ 3.5 + x = 8
⟹ x = (8 - 3.5)
⟹ x = 4.5
Correct Answer: 125
Explanation:
| (0.04)-1.5 = | ❨ | 4 | ❩ | -1.5 |
| 100 |
| = | ❨ | 1 | ❩ | -(3/2) |
| 25 |
= (25)(3/2)
= (52)(3/2)
= (5)2 x (3/2)
= 53
= 125.
Correct Answer: 4
Explanation:
(256) 0.16 x (256) 0.09 = (256) (0.16 + 0.09)
= (256)0.25
= (256)(25/100)
= (256)(1/4)
= (44)(1/4)
= 44(1/4)
= 41
= 4
Correct Answer: 1
Explanation:
| Given Exp. = |
|
| = | xa | + | xb | + | xc |
| (xa + xb + xc) | (xa + xb + xc) | (xa + xb + xc) |
| = | (xa + xb + xc) |
| (xa + xb + xc) |
= 1.
Correct Answer: 25
Explanation:
5 a = 3125 ⟺ 5 a = 5 5
⟹ a = 5.
∴ 5(a - 3) = 5(5 - 3) = 52 = 25.
Correct Answer: 40
Explanation:
Let the required number of days be x
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
| Cows | 1 | : | 40 | ] | :: 40 : x |
| Bags | 40 | : | 1 |
∴ 1 x 40 x x = 40 x 1 x 40
⟹ x = 40.
Correct Answer: 24
Explanation:
Let the required number of days be x
Less men, More days (Indirect Proportion)
∴ 27 : 36 :: 18 : x ⟺ 27 x x = 36 x 18
| ⟹ x = | 36 x 18 |
| 27 |
⟹ x = 24.
Correct Answer: 12
Explanation:
Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
| Pumps | 4 | : | 3 | ] | :: 8 : x |
| Days | 1 | : | 2 |
∴ 4 x 1 x x = 3 x 2 x 8
| ⟹ x = | (3 x 2 x 8) |
| (4) |
⟹ x = 12.
Correct Answer: 16
Explanation:
Let the required number of bottles be x
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
| Wavers | 4 | : | 8 | ] | :: 4 : x |
| Days | 4 | : | 8 |
∴ 4 x 4 x x = 8 x 8 x 4
| ⟹ x = | (8 x 8 x 4) |
| (4 x 4) |
⟹ x = 16.
Correct Answer: 12.5 m
Explanation:
Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)
∴ 40.25 : 28.75 :: 17.5 : x ⟺ 40.25 x x = 28.75 x 17.5
| x = | 28.75 x 17.5 |
| 40.25 |
⟹ x = 12.5
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