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Home ‣ Aptitude ‣ Linear Equation See What Others Are Saying!
- Question
- The graph of ax + by = c, dx + ey = f will be
I. parallel, if the system has no solution.
II. coincident, if the system has finite number of solutions.
III. intersecting. if the system has only one solution.
Which of the above statements are correct?
Options- A. Only I and II
- B. Only II and II
- C. Only I and III
- D. I, II and III
- Correct Answer
- Only I and III
Explanationax + by = c and dx + ey = f
a1/a2 = a/d, b1/b2 = b/e, c1/c2 = c/f
? b1/b2 ? c1/c2
? b/e ? c/f
it represent a pair of parallel lines.
? a1/a2 ? b1/b2
? a/d ? b/e
Therefore, system has unique solutions and represents a pair of intersecting lines. - 1. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
Options- A. 4 days
- B. 6 days
- C. 8 days
- D. 18 days Discuss
- 2. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
Options- A. 145°
- B. 150°
- C. 155°
- D. 160° Discuss
- 3. Find the perimeter of a triangle with sides equal to 6 cm, 4 cm and 5 cm.
Options- A. 14 cm
- B. 18 cm
- C. 20 cm
- D. 15 cm Discuss
- 4. In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
Options- A. 22.75 m
- B. 25 m
- C. 19.5 m
- D.
7 4 m 7
Discuss
- 5. A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Options- A. 10
- B. 20
- C. 21
- D. 25 Discuss
- 6. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Options- A. 26.34 litres
- B. 27.36 litres
- C. 28 litres
- D. 29.16 litres Discuss
- 7. A tower stands at the end of a straight road. The angles of elevation of the top of the tower from two points on the road 500 m apart are 45° and 60°, respectively. Find out the height of the tower.
Options- A. 500 ?3 ?3 - 1
- B. 5000 ?3
- C. 500 ?3 ?3 + 1
- D. None of these Discuss
- 8. Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women.?
Options- A. 30
- B. 20
- C. 10
- D. 25 Discuss
- 9. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Options- A. 23 days
- B. 37 days
- C. 37½
- D. 40 days Discuss
- 10. The average weight of 4 men, A, B, C and D is 67 kg. The 5th man E is included and the average weight decreses by 2 kg. A is replaced by F. The weight of F is 4 kg more then E . Average weight decreases because of the replacement of A and now the average weight is 64 kg. Find the weight of A.
Options- A. 78 kg
- B. 66 kg
- C. 75 kg
- D. 58 kg Discuss
More questions
Correct Answer: 4 days
Explanation:
So, ratio of times taken = 1 : 2.
| B's 1 day's work = | 1 | . |
| 12 |
| ∴ A's 1 day's work = | 1 | ; (2 times of B's work) |
| 6 |
| (A + B)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 3 | = | 1 | . |
| 6 | 12 | 12 | 4 |
So, A and B together can finish the work in 4 days.
Correct Answer: 155°
Explanation:
| Angle traced by hour hand in 5 hrs 10 min. i.e., | 31 | hrs = | ❨ | 360 | x | 31 | ❩ | ° | = 155°. |
| 6 | 12 | 6 |
Correct Answer: 15 cm
Explanation:
Given that, a = 6 cm, b = 4 cm and c = 5 cm
Required perimeter = a + b + c
= 6 + 4 + 5 cm
= 15 cm
Correct Answer: 25 m
Explanation:
A : C = 200 : 182.
| C | = | ❨ | C | x | A | ❩ | = | ❨ | 182 | x | 200 | ❩ | = 182 : 169. |
| B | A | B | 200 | 169 |
When C covers 182 m, B covers 169 m.
| When C covers 350 m, B covers | ❨ | 169 | x 350 | ❩m | = 325 m. |
| 182 |
Therefore, C beats B by (350 - 325) m = 25 m.
Correct Answer: 21
Explanation:
| Quantity of A in mixture left = | ❨ | 7x - | 7 | x 9 | ❩ | litres = | ❨ | 7x - | 21 | ❩ litres. |
| 12 | 4 |
| Quantity of B in mixture left = | ❨ | 5x - | 5 | x 9 | ❩ | litres = | ❨ | 5x - | 15 | ❩ litres. |
| 12 | 4 |
| ∴ |
|
= | 7 | |||||
|
9 |
| ⟹ | 28x - 21 | = | 7 |
| 20x + 21 | 9 |
⟹ 252x - 189 = 140x + 147
⟹ 112x = 336
⟹ x = 3.
So, the can contained 21 litres of A.
Correct Answer: 29.16 litres
Explanation:
| Amount of milk left after 3 operations = | [ | 40 | ❨ | 1 - | 4 | ❩ | 3 | ] litres |
| 40 |
| = | ❨ | 40 x | 9 | x | 9 | x | 9 | ❩ | = 29.16 litres. |
| 10 | 10 | 10 |
Correct Answer: 500 ?3 ?3 - 1
Explanation:
Correct Answer: 30
Explanation:
The number of ways of selecting 3 men and 3 women out of 6 men and 5 women = 6C3 x 5C3
= 6!/(3! x 3!) + 5/(3! x 2!)
= 20 + 10 = 30
Correct Answer: 37½
Explanation:
| Whole work is done by A in | ❨ | 20 x | 5 | ❩ | = 25 days. |
| 4 |
| Now, | ❨ | 1 - | 4 | ❩ | i.e., | 1 | work is done by A and B in 3 days. |
| 5 | 5 |
Whole work will be done by A and B in (3 x 5) = 15 days.
| A's 1 day's work = | 1 | , (A + B)'s 1 day's work = | 1 | . |
| 25 | 15 |
| ∴ B's 1 day's work = | ❨ | 1 | - | 1 | ❩ | = | 4 | = | 2 | . |
| 15 | 25 | 150 | 75 |
| So, B alone would do the work in | 75 | = 37 | 1 | days. |
| 2 | 2 |
Correct Answer: 66 kg
Explanation:
Sum of the weight of A, B, C and D = 67 x 4 = 268 kg
and average weight of A, B , C , D and E = 67 - 2 = 65kg
? Sum of the weight of A, B, C, D and E = 65 x 5 = 325 kg
? Weight of E = 325 - 268 = 57 kg
? Weight of F = 57 + 4 = 61 kg
Now, average weight of F, B, C, D and E = 64 kg
? Sum of the weight of F, B, C, D and E = 64 x 5 = 320 Kg
? Sum of the weights of B, C and D = 320 - 57 - 61 = 202 kg
? Weight of A = 268 - 202 = 66 kg
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