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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. The median for the data 2, 4, 6, 8, 10, 12, 14 is
Options- A. 6
- B. 8
- C. 9.5
- D. 10 Discuss
- 2. The value of 47 / 10000 is?
Options- A. .0047
- B. .0470
- C. .00047
- D. .000047 Discuss
- 3. If 4x = 18y, then the value of ( x/y - 1) is
Options- A. 1 3
- B. 7 2
- C. 2 3
- D. 3 2 Discuss
- 4. If the price of 23 toys is Rs. 276, then what will the price (Rs.) of 12 toys?
Options- A. 144
- B. 158
- C. 159
- D. 166 Discuss
- 5. .02 =(......?.....)%
Options- A. 20
- B. 2
- C. .02
- D. .2 Discuss
- 6. If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?
Options- A. 45
- B. 55
- C. 60
- D. 72 Discuss
- 7. 2?63 / 11 =233
Options- A. 4
- B. 3
- C. 6
- D. 5 Discuss
- 8. When 121012 is divided by 12, the remainder is
Options- A. 0
- B. 2
- C. 3
- D. 4 Discuss
- 9. Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?
Options- A. 18 days
- B. 21 days
- C. 3 days
- D. 6 days Discuss
- 10. 750.0003 ÷ 19.999 =?
Options- A. 49
- B. 18
- C. 22
- D. 38 Discuss
More questions
Correct Answer: 8
Explanation:
4th observation i.e., 8 is the median.
Correct Answer: .0047
Explanation:
47/10000 = .0047
Correct Answer: 7 2
Correct Answer: 144
Explanation:
Correct Answer: 2
Explanation:
.02 =(2/100) x 100% =2%
Correct Answer: 60
Explanation:
Correct Answer: 5
Explanation:
Let N / 11 = 233
Then, N = 233 x 11 = 2563
? Missing digit is 5.
Correct Answer: 4
Explanation:
121012 = 12 x 10084 + 4
? remainder = 4
Correct Answer: 18 days
Explanation:
We have the important relation, More work, More time (days)
? A piece of work can be done in 6 days.
? Three times of work of same type can be done in 6 x 3
= 18 days
Correct Answer: 38
Explanation:
? = 750.0003 ÷ 19.999
? ? ? 750 ÷ 20
? ? ? 375 ? 38
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