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Question 1. Asked on :17 June 2019:11:25:45 PM

Show that one and only one out of n, n+2 or n+4 is divisible by 3, where n is any positive integer. 

-Added by ATP Admin Mathematics » Real Numbers

Answer:

Solution: Using Euclid's division lemma any positive integer can be written in the form of a = bq + r where r = 0, 1, 2 ...... and q is quotients. 

Let the number which is divisible by 3 be 3q + 0 or 3q + 1 or 3q + 2 where [0 <= r < b] 

Now n = 3q or n = 3q + 1 or n = 3q + 2 

Case I, 

When n = 3q  .......... (i) 

⇒ n = 3(q) where n is divisible by 3

Adding 2 both sides in equ. (i) 

We have,

    n + 2 = 3q + 2 Where n + 2 is not divisible by 3 

Now adding 4 both side in equ. (i) 

We have,

    n + 4 = 3q + 4 Where n + 4 is not divisible by 3 


Case II  

  Taking n = 3q + 1 ........ (ii) where n is not divisible by 3

Adding 2 both sides in equ. (ii) 

We have, 

n + 2 = 3q + 1 + 2 = 3q + 3 

n + 2 = 3(q + 1) where n + 2 is divisible by 3 

Now adding 4 both sides in equ. (ii) 

n + 4 = 3q + 1 + 4 = 3q + 5 where n + 4 is not divisible by 3 


Case III  

taking n = 3q + 2 .... (iii) where n is not divisible by 3 

Adding 2 both sides in equ. (iii) 

We have,

n + 2 = 3q + 2 + 2 = 3q + 4 where n + 2 is not divisible by 3

Now adding 4 both sides in equ. (iii) 

We have, 

n + 4 = 3q + 2 + 4 = 3q +6 

n + 4 = 3(q + 2) where n + 4 is divisible by 3 

Hence in all these three cases we have seen that either one and only one n or n + 2 or n + 4 is divisible by 3. 

 

 



-Answered by ATP Admin On 17 June 2019:11:28:43 PM

Question 2. Asked on :17 June 2019:01:11:58 AM

 पेरिस शांति संधि कब हुई ? 

-Added by ATP Admin History » इंडोचाइना

Answer:

 पेरिस शांति संधि 1974 में हुई थी ? 

-Answered by ATP Admin On 17 June 2019:01:14:19 AM

Question 3. Asked on :17 June 2019:12:34:11 AM

 Name the physical quantities which can change the state of matters.

-Added by ATP Admin Science » Matters And Its States

Answer:

There are two physical quantities by which state of matter can be changed.

these are - 

(i) Temperature 

(ii) Pressure 

-Answered by ATP Admin On 17 June 2019:12:41:12 AM

Question 4. Asked on :08 June 2019:06:42:35 PM

 sukh and dukh kya hai

-Added by SUDHANSHU KUMAR Other » Aadhyatam

Answer:

 सुख दुःख जीवन की अवस्था है जो जीवन में आभाव के कारण अनुभव किये जाते हैं | जीवन में किसी इच्छित वस्तु के आभाव होने पर दुःख का अनुभव होता है जबकि आभाव रहित जीवन सुख का अनुभव करता है | 

-Answered by ATP Admin On 17 June 2019:12:35:52 AM

Question 5. Asked on :14 May 2019:11:53:18 AM

 What is the term used for specialised cultivation of fruits and vegetables?

-Added by Himanshi Verma Geography » Agriculture

Answer:

 Horticulture is the term used for specialized cultivation of fruits and vegetables. 

-Answered by Shalu Shukla On 19 May 2019:09:53:11 AM

Question 6. Asked on :14 May 2019:11:52:30 AM

 Which country does produce 13% of the world's vegetables?

-Added by Himanshi Verma Geography » Agriculture

Answer:

 India produce 13% of the world's vegetables.

-Answered by Himanshi Verma On 07 June 2019:05:48:53 PM

Question 7. Asked on :14 May 2019:11:47:25 AM

 What is money?

-Added by Rohit rajput Economics » Money And Credit

Answer:

 Money refers to a medium of exchange used in economic transactions or in exchange of goods and services.

-Answered by Shalu Shukla On 14 May 2019:11:48:54 AM

Question 8. Asked on :14 May 2019:11:46:22 AM

 Who compiled folk- tales in Germany?

-Added by Rohit rajput History » Ch-7

Answer:

 The Grimm Brothers compiled folk tales in Germany.

-Answered by Himanshi Verma On 07 June 2019:05:50:45 PM

Question 9. Asked on :14 May 2019:11:46:01 AM

 Who wrote Jungle Book?

-Added by Rohit rajput History » History

Answer:

 Rudyard Kipling wrote Jungle Book.

-Answered by Himanshi Verma On 07 June 2019:05:53:51 PM

Question 10. Asked on :14 May 2019:11:43:09 AM

 Who was Walter Scott?

-Added by Himanshi Verma History » Novels, Society, History

Answer:

 Walter Scott was the Inventer and the greatest practitioner of the historical novel.

-Answered by Himanshi Verma On 07 June 2019:05:54:36 PM


 

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