I was going through a JSTSE paper, When I found this question...

How many points (x,y) exist in the 1st quadrant such that x+y=7 ?

I was going through a JSTSE paper, When I found this question...

How many points (x,y) exist in the 1st quadrant such that x+y=7 ?

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TopNewestThe formula for the number of Natural numbers satisfying \(x + y = k\) is always \(k-1\).

So in this case

k = 7. Hence number of points are6This formula is just a observation based. Please verify it @Azhaghu Roopesh M @Krishna Ar @Sravanth Chebrolu – Rajdeep Dhingra · 2 years, 4 months ago

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What do you say @Rajdeep Dhingra ??? – Sravanth Chebrolu · 2 years, 4 months ago

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– Sravanth Chebrolu · 2 years, 4 months ago

Going to class \(10\)Log in to reply

If it is not specified natural number or

kis a rational number with denominator \(\ne\) 1 then the answer is \(\infty\) – Rajdeep Dhingra · 2 years, 4 months agoLog in to reply

– Sravanth Chebrolu · 2 years, 4 months ago

Exactly. Then this might have been included in the question . . .Log in to reply

If the number of points(x,y) are said to be only whole numbers(not decimals), then there are 6, they are:

\( (1,6),(2,5),(3,4),(4,3),(5,2) and (6,2) \)

If it is mentioned, including decimals, then it is infinite . . .

What do you say Azhaghu Roopesh M ??? – Sravanth Chebrolu · 2 years, 4 months ago

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@Sravanth Chebrolu Do (0,7) and (7,0) not lie in any quadrant? Coz the definition of the point in the 1st quadrant is x,y>0. Anyways.. If included, they should be 8 in number , eh. I think there is a typo. – Mehul Arora · 2 years, 4 months ago

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axesnot thequadrants. – Sravanth Chebrolu · 2 years, 4 months agoLog in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Yeah , since the number 7 is quite small , we can count it out .Log in to reply

– Sravanth Chebrolu · 2 years, 4 months ago

Exactly. Is there any formula for these kind of problems???Log in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Look up the Generating Functions wiki here on B'ant . Anyway , I've got to go now, Bye :)Log in to reply

I guess there would have been more information provided. Most likely the question would have specified \(x,y\) to be integers. – Krishna Ar · 2 years, 4 months ago

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– Azhaghu Roopesh M · 2 years, 4 months ago

But it has been said that x,y belong to the first quadrant , so automatically \(x,y \geq 0\)Log in to reply

Is this the exact same question ? If so , it is a simple question of Generating Functions – Azhaghu Roopesh M · 2 years, 4 months ago

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– Siddhartha Srivastava · 2 years, 4 months ago

Generating functions? Are you sure? This is a JSTSE question, so its for classes 10 or below I think.Log in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Well , I think any class 10 student has the ability to count the number of solutions manually , it's just that the method of Generating Functions works for finding solutions of the type :\(x+y = N\) or other types .Log in to reply

– Mehul Arora · 2 years, 4 months ago

Not exactly below.. The maths questions were mainly Of class 10 level iincluding all AP, GP , Quadratics, Vieta's etc...Log in to reply