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- Question
A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?
Options- A. (6/11, 9/11)
- B. (6/7, 9/7)
- C. (6/11, -9/11)
- D. (-6/7, 9/7)
- Correct Answer
- (6/11, 9/11)
- 1. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Options- A. 5 : 2
- B. 7 : 3
- C. 9 : 2
- D. 13 : 4 Discuss
- 2. 19 5 + 21 5 is divisible by
Options- A. Only 10
- B. Only 20
- C. Both 10 and 20
- D. Neither 10 nor 20 Discuss
- 3. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options- A. 35.55 km/hr
- B. 36 km/hr
- C. 71.11 km/hr
- D. 71 km/hr Discuss
- 4. A train takes 24 sec to cross a 480 m platform and 36 sec to cover a 900 m platform. what is the length of the train?
Options- A. 360 m
- B. 400 m
- C. 390 m
- D. 430 m Discuss
- 5. The numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio 3 : 4, the numbers are
Options- A. 3 , 6
- B. 4 , 8
- C. 6 , 8
- D. 6 , 4 Discuss
- 6.
The value of ( 2 3 ) 2/3 x ( 3 3 ) is : 3 2 2 2
Options- A. 64/3
- B. 82/3
- C. 62/3
- D. 91/3 Discuss
- 7. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Options- A.
9 1 days 5 - B.
9 2 days 5 - C.
9 3 days 5 - D. 10 Discuss
- 8. How many numbers can be formed from 1, 2, 3, 4, 5, ( without repetition), when the digit at the unit's place must be greater than that in the ten's place?
Options- A. 54
- B. 60
- C. 51/3
- D. 2 x 4! Discuss
- 9. A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is?
Options- A. 7
- B. 8
- C. 9
- D. 24 Discuss
- 10. An intelligence agency forms a code of two distinct digits selected from 0, 1, 2,....., 9 such that the first-digit of code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down, for examples the code 91 may appear as 16. how many codes are there for which no such confusion can arise?
Options- A. 80
- B. 78
- C. 71
- D. 69 Discuss
More questions
Correct Answer: 7 : 3
Explanation:
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⟹ 3x + 20 = 2x + 40
⟹ x = 20.
∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Correct Answer: Both 10 and 20
Explanation:
We can check divisibility of 195 + 215 by 10 by adding the unit digit of 95 + 15 which is equal to 9 + 1 = 10.
So it must be divisible by 10.
Now, for divisibility by 20 we add 19 and 21 which is equal to 40. So, it is clear that it is also divisible by 20.
So 195 + 215 is divisible by both 10 and 20
Correct Answer: 71.11 km/hr
Explanation:
| Total time taken = | ❨ | 160 | + | 160 | ❩hrs. | = | 9 | hrs. |
| 64 | 80 | 2 |
| ∴ Average speed = | ❨ | 320 x | 2 | ❩km/hr | = 71.11 km/hr. |
| 9 |
Correct Answer: 360 m
Explanation:
Let the length of the train be x meter and its speed be y m/sec
Then, (x + 480 m) / 24 sec = y ....(i)
and , (x + 720 m) / 36 sec = y ....(ii)
From Eqs (i) and (ii)
(x + 480) / 24 = (x + 900) / 36
? 3x + 1440 = 2x + 1800
? Length of train, x= 360m
Correct Answer: 6 , 8
Explanation:
Let us assume the ratio term is r.
then the number will be 3r and 4r.
According to question,
(4r)2 + 224 = 8 x (3r)2
16r2 + 224 = 8 x 9r2
16r2 + 224 = 72r2
72r2 - 16r2 = 224
56r2 = 224
r2 = 224/56
r2 = 4
r = 2
First number = 3r = 3 x 2 = 6
Second number = 4r = 4 x 2 = 8
Correct Answer: 62/3
Correct Answer:
| 9 | 3 | days |
| 5 |
Explanation:
| (A + B + C)'s 1 day's work = | 1 | , |
| 4 |
| A's 1 day's work = | 1 | , |
| 16 |
| B's 1 day's work = | 1 | . |
| 12 |
| ∴ C's 1 day's work = | 1 | - | ❨ | 1 | + | 1 | ❩ | = | ❨ | 1 | - | 7 | ❩ | = | 5 | . |
| 4 | 16 | 12 | 4 | 48 | 48 |
| So, C alone can do the work in | 48 | = 9 | 3 | days. |
| 5 | 5 |
Correct Answer: 60
Explanation:
The digit in the unit's place should be greater than that in the tens' place.
Hence, if digit 5 occupies the unit place, then remaining four digits need not to follow any order,hence required number = 4!
However, if digit 4 occupies the unit place then 5 cannot occupy the ten;s position. Hence, digit at the ten's place and it will be filled by the digit 1, 2 or 3. This can happen in 3 ways. The remaining 3 digit can be filled in the remaining three place in 3! ways.
Hence, in all, we have (3 x 3!) numbers ending in 4. Similarly, if we have 3 in the unit's place and it will be either 1 or 2. this can happen in 2 ways. Hence, we will have (2 x 3! ) number ending in 3 . Similarly, we can find that there will be 3! numbers ending in 2 and no number with 1. Hence, total number of numbers
= 4! + (3) x 3! + (2 x 3!) + 3!
= 4! + 6 x 3! = 24 + (6 x 6) = 60
Correct Answer: 24
Explanation:
To construct 2 roads, three towns can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third road goes from the third town to the first town, a triangle is formed and if it goes to the fourth town, a triangle is not formed, So there are 24 ways to form a triangle and 24 ways of avoiding the formation of triangle.
Correct Answer: 69
Explanation:
The available digits are 0, 1, 2,...., 9. The first digit can be chosen in 9 ways (0 not acceptable), the second digit can be accepted in 9 ways (digit repetition not allowed). Thus, the code can be made in 9 x 9 = 81 ways.
Now, there are only 4 digits which can create confusion 1, 6, 8, 9. The same can be given in the following ways
Total number of ways confusion can arise
= 4 x 3 = 12
Thus, the ways in which no such confusion arise = 81-12 =69
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