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- Question
- The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m high is?
Options- A. 12 m
- B. 14 m
- C. 17 m
- D. 21 m
- Correct Answer
- 17 m
ExplanationLength of longer rod = ?l2 + b2 + h2
= ?122 + 92 + 82
= ?144 + 81 + 64
= ?289
= 17 m - 1. A train overtake two persons walking along a railway track. The first one walks at 4.5 km/h and the other one walks at 5.4 km/h. The train needs 8.4 s and 8.5 s respectively , to overtake them. What is the speed of the train, if both the persons are walking in the same direction as the train?
Options- A. 66 kkm/h
- B. 72 km/h
- C. 78 km/h
- D. 81 km/h Discuss
- 2. Maneela, Raghu and Aravind have some jems with each of them. Five times the number of jems with Raghu equals seven times the number of jems with Maneela while five times the number of jems with Maneela equals seven times the number of jems with Aravind. What is the minimum number of jems that can be there with all three of them put together ?
Options- A. 108
- B. 107
- C. 109
- D. 110 Discuss
- 3. Two trains A and B starts from Howrah and Patna towards Patna and Howrah respectively at the same time. After passing each other, they take 4, h, 48 min and 3 h, 20 min to reach Patna and Howrah, respectively. If the train from Howrah is moving at 45 km/h, then the speed of the other train is?
Options- A. 60 km/h
- B. 45 km/h
- C. 35 km/h
- D. 54 km/h Discuss
- 4. Two solutions have milk & water in the ratio 7:5 and 6:11. Find the proportion in which these two solutions should Be mixed so that the resulting solution has 1 part milk and 2 parts water ?
Options- A. 7 : 12
- B. 8 : 13
- C. 9 : 4
- D. 2 : 5 Discuss
- 5. A train travelling at 36 kmph completely crosses another train having half its length and travelling in the opposite direction at 54 kmph, in 12 second, If it also passes a railway platform in 1 1/ 2 minutes, the length of the platform is?
Options- A. 560 metres
- B. 620 metres
- C. 700 metres
- D. 750 metres Discuss
- 6. A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°, when he retires 40 meters from the bank then he find the angle to be 30°. Then the breadth of the river is?
Options- A. 40 m
- B. 60 m
- C. 20 m
- D. 30 m Discuss
- 7. The angle of elevation of the top of two vertical towers as seen from the middle point of the line joining the foot of the towers are 60° and 30° respectively. The ratio of the heights of the towers is?
Options- A. 2 : 1
- B. ?3 : 1
- C. 3 : 2
- D. 3 : 1 Discuss
- 8. On the ground level the angle of elevation of the top of a tower is 30°, On moving 20 m nearer the tower, the angle of elevation found to be 60°. The height of the tower is?
Options- A. 10 m
- B. 10?3 m
- C. 15 m
- D. 20 m Discuss
- 9. From the top of h meter high cliff the angles of depression of the top and the button of a tower are observed to be 30° and 60° respectively. The height of the tower is?
Options- A. h?3
- B. 2h?3
- C. h/3
- D. 2h/3 Discuss
- 10. The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of ?
Options- A. 4:5
- B. 6:5
- C. 3:2
- D. 1:3 Discuss
More questions
Correct Answer: 81 km/h
Explanation:
Speed of the person = 4 km/h = 4.5 x (5/18) = m/s = 5/4 m/s = 1.25 m/s
Speed of 2nd person = 5.4 km/h = 5.4 x (5/18) m/s = 3/2 m/s = 1.5 m/s
Let speed of train be x m/s.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
? 8.4x - 10.5 = 8.5x - 12.75
? 0.1x = 2.25
? x = 22.5
? Speed of the train = 225 x (18/5 ) = 81 km/h .
Correct Answer: 109
Explanation:
From given data,
R : M = 5 : 7
M : A = 5 : 7
R : M : A = 25 : 35 : 49
25 + 35 + 49 = 109
Correct Answer: 54 km/h
Explanation:
Given, a = 45 km/h, y = ?, t1 = 4 h 48 min and t2 = 3 h 20 min
Using y = a?t1 / t2= 45?4 h and 48 min /3 h and 20 min
= 45?(24/5h) / (10/3 h) = 45?24 x 3/5 x 10
= 45 x ?1.44 = 45 x 12 = 54 km/h
Correct Answer: 8 : 13
Explanation:
To get the solution that contains 1 part of milk and two parts of water,
they must be mixed in the ratio as
7x+6x/5y+11y = 1/2
26x = 16y
x/y = 16/26
x/y = 8/13
Correct Answer: 700 metres
Explanation:
Let the length of slower train be L meters and the
length of faster train be (L/2) meters
Their relative speed = (36 + 54) km/hr
= 90 x (5/18)
= 25 m/sec
? 3L / (2 x 25) = 12
? 3L = 600
? L = 200
? Length of slower train = 200 meters
Let the length of platform by M meters
Then, 200 + M/[36 x (5/18)] = 90 sec.
? 200 + M = 900
? M = 700 meters
Length of platform = 700 meters.
Correct Answer: 20 m
Explanation:
Let us draw a figure below as per given question.
Let A be the position of a person on the bank of a river and OP the tree on the opposite bank and ?OAP = 60°. When the person retires to the position B, then AB = 40 meter and ?OBP = 30°
Let us assume OA(Breadth of the river) = x meter and height of tree OP = h meter
In ?OAP, Use the trigonometry formula
Tan60° = P/B = Perpendicular distance / Base distance
? Tan60° = OP / OA
? OP = OA Tan60°
Put the value of OP and OA, We will get
? h = x?3 ..............(1)
Now in the triangle ?OBP
Tan30° = OP / OB
? OP = OB Tan30°
? OP = (x + 40)/?3
? h = (x + 40)/?3 ...................(2)
From Equation (1) and (2), We will get
? (x + 40)/?3 = x?3
? (x + 40) = x?3 X ?3
? (x + 40) = 3x
? 3x - x = 40
? x = 20 m
Correct Answer: 3 : 1
Explanation:
Let AB and CD be two towers of height h1 and h2 respectively and O the mid-point of the line joining the foots A and C of the towers.
Let OA = OC = x
Then h1 = x tan 60° = x?3
and h2 = x tan 30° = x/?3
? h1 /h2= 3/1.
Hence, h1 : h2 = 3 : 1
Correct Answer: 10?3 m
Explanation:
Let us draw a figure below from the given question.
Let AB = h meter be the height of the towers. B and C are two points such that BC = 20 m; ?ADB = 30° and ?ACB = 60° BC = x meter (let us assume)
Now, from right triangle ABC,
x = h cot 60°
? x = h/?3 meter
Again, from right triangle ABD,
h = (20 + x) tan 30°
put the value of x in above equation.
? x = h/?3
? h = (20 + h/?3) x 1/?3 ( ? tan 30° = 1/?3 )
? h - h/3 = 20/?3 ? 2h/3 = 20/?3
? h = 20 x 3/2?3 = 10?3 m
Correct Answer: 2h/3
Explanation:
Let us draw a figure below as per given question.
Let AB = h meter be the height of cliff and CD = x meter be the height of the tower and also ? ADB = 60° and ?ACE = 30° ,
Now, from the figure, AE = (h - x) meter
From right triangle ABD, BD = h cot 60° = h/?3 m
From right triangle CEA. (h - x) = EC tan 30° = BD tan 30°
? h - x = h/?3 X 1/?3
? x = h - h/3 = 2h/3 meter
Correct Answer: 6:5
Explanation:
4:5
3:2
-------
=> 12:15:10
12:10
=> 6:5
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