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- Question
Consider the following statements: 1) The perimeter of a triangle is greater than the sum of its three medinas. 2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
- Correct Answer
- Both 1 and 2
ExplanationLet ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)Hence in ?ABD, AD is a median?AB + AC > 2(AD)Similarly, we getBC + AC > 2CFBC + AB > 2BEOn adding the above inequations, we get(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE2(AB + BC + AC) > 2(AD + BE + CF)?AB + BC + AC > AD + BE +CF2.To prove: AB + BC + CA > 2ADConstruction: AD is joinedProof: In triangle ABD,AB + BD > AD [because, the sum of any two sides of a triangle is always greater than thethird side]----1In triangle ADC,AC + DC > AD [because, the sum of any twosides of a triangle is always greater than thethird side]----2Adding 1 and 2 we get,AB + BD + AC + DC > AD + AD=> AB + (BD + DC) + AC > 2AD=> AB + BC + AC > 2ADHence proved - 1. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:
Options- A. 48 km/hr
- B. 54 km/hr
- C. 66 km/hr
- D. 82 km/hr Discuss
- 2. Find out the wrong number in the series 5, 15, 30, 135, 405, 1215, 3645?
Options- A. 3645
- B. 1215
- C. 405
- D. 30 Discuss
- 3. What will be the average of even numbers between 11 to 63.
Options- A. 37.5
- B. 47
- C. 42
- D. 37 Discuss
- 4. Ashok took a loan of Rs. 15000 for 3 years at simple interest . If the total interest paid is Rs. 2700. What is the rate of interest per annum?
Options- A. 18
- B. 5.4
- C. 9
- D. 6 Discuss
- 5. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Options- A. 648
- B. 1800
- C. 1700
- D. 1080 Discuss
- 6. A speed of 22.5 m/sec. is the same as?
Options- A. 40.5 km/hr.
- B. 81 km/hr.
- C. 36.8 km/hr .
- D. 72 km/hr. Discuss
- 7. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
Options- A. 69
- B. 78
- C. 96
- D. Cannot be determined
- E. None of these Discuss
- 8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options- A. 40 sec
- B. 42 sec
- C. 45 sec
- D. 48 sec Discuss
- 9. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Options- A. Rs. 2160
- B. Rs. 3120
- C. Rs. 3972
- D. Rs. 6240
- E. None of these Discuss
- 10. A contract is to be complete in 50 days and 105 men were set to work, each working 8 h a day. After 25 days, 2/5th of the work is finished. How many additional men be employed, so that the work may be completed on time, each man now working 9 h a day?
Options- A. 34
- B. 36
- C. 35
- D. 37 Discuss
More questions
Correct Answer: 82 km/hr
Explanation:
Let the speed of the second train be x km/hr.
| Relative speed | = (x + 50) km/hr | |||||||
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Distance covered = (108 + 112) = 220 m.
| ∴ | 220 | = 6 | ||
|
⟹ 250 + 5x = 660
⟹ x = 82 km/hr.
Correct Answer: 30
Explanation:
Multiply each term by 3 to obtain the next term. Hence, 30 is a wrong number.
Correct Answer: 37
Explanation:
Even numbers between 11 to 63
= 12,14,16,18,20,..........,62.
Clearly, this is a series of consecutive even number
According to the formula
Average of consecutive even numbers = (First number + Last number)/2
= (12 + 62)/2
= 74/2
= 37
Correct Answer: 6
Explanation:
? Rate = [(interest x 100) / (Principal x Time) ] %
? Rate = (2700 x 100) / (15000 x 3) %
? Rate = 6%
Correct Answer: 1800
Explanation:
Since 6 identical machines in 1 minute can produce a total of 270 bottles.
? 1 identical machines in 1 minute can produce a total of 270 / 6 bottles.
? 10 identical machines in 1 minute can produce a total of 270 x 10 / 6 bottles.
? 10 identical machines in 4 minute can produce a total of 270 x 10 x 4 / 6 bottles.
? 10 identical machines in 4 minute can produce a total of 45 x 10 x 4 bottles.
? 10 identical machines in 4 minute can produce a total of 1800 bottles.
Correct Answer: 81 km/hr.
Explanation:
Speed in km/hr = speed in m/sec x (18 / 5 )
Speed in km/hr = (22.5 x 18 /5 ) km/hr
= 81 km/hr.
Correct Answer: Cannot be determined
Explanation:
Then, x + y = 15 and x - y = 3 or y - x = 3.
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69.
Hence, the number cannot be determined.
Correct Answer: 40 sec
Explanation:
| Formula for converting from km/hr to m/s: X km/hr = | ❨ | X x | 5 | ❩ | m/s. |
| 18 |
| Therefore, Speed = | ❨ | 45 x | 5 | ❩m/sec | = | 25 | m/sec. |
| 18 | 2 |
Total distance to be covered = (360 + 140) m = 500 m.
| Formula for finding Time = | ❨ | Distance | ❩ |
| Speed |
| ∴ Required time = | ❨ | 500 x 2 | ❩sec | = 40 sec. |
| 25 |
Correct Answer: Rs. 3972
Explanation:
| ∴ R = | ❨ | 100 x 60 | ❩ | = 10% p.a. |
| 100 x 6 |
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
| ∴ C.I. |
|
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| = 3972. |
Correct Answer: 35
Explanation:
According to the formula
M1D1T1/W1= M2D2T2/W2
Given M1 = 105 D1 = 25 T1 = 8 W1 = 2/5
Now let the additional men be N
Then, M2 = 105 + N, T2 = 9, D2 = 25 and W2 =1 - (2/5) = 3/5
On putting these value in the above formula
(105 x 25 x 8) / (2/5) = [(105 + N) x 25 x 9] / (3/5)
? (105 x 8) / 2 = (105 + N) x (9/3)
? 105 x 4 = (105 + N) x 3
? 105 x 4 = 105 x 3 +3N
? 3N = 105
? N = 35 men
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