Q1QP3 Math Question.No 89

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Shinas MN

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Dec 3, 2020, 1:03:20 AM12/3/20
to Discussion forum for Mathematics for Data Science I, sup...@onlinedegree.iitm.ac.in
Respected Sir/Ma'am,
     I request your attention to Question No 89 of Mathematics Paper 3(Q1QP3).If we substitute Lambda with 0 we will get the points as (0,0)(0,0)(-1,1).In which the first two points turns out to be the same which is at the Origin. And the other point is at (-1,1).We can very easily draw a straight line among that two point. And two points are always collinear. 
The question no 89 was The points (..)(..)& (..) are collinear if, Since there are no other condition said in the  question, Even the Option 2-Zero(0) also satisfies the condition, Hence it seems to be right answer.

Request IITMOD Support team to kindly loo into this and revert at the earliest.

Ps:-Please find the below attached screenshot of the question and some reference from web which says the two points are always collinear.

Regards,
Shinas Moideen M N

Nutan Patil

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Dec 3, 2020, 5:39:21 AM12/3/20
to Shinas MN, Discussion forum for Mathematics for Data Science I, sup...@onlinedegree.iitm.ac.in
Yes absolutely right...please give marks to all students


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

Amrit Raj

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Dec 3, 2020, 6:13:41 AM12/3/20
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Well collinearity is generally defined for three points, so that way lambda=-1 makes more sense.
Two points are always linear. But even in that case, people who have marked lambda =0 should be given marks. Not all.

Pritika Hirebet

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Dec 3, 2020, 6:41:10 AM12/3/20
to Amrit Raj, Discussion forum for Mathematics for Data Science I, nutanp...@gmail.com, sup...@onlinedegree.iitm.ac.in, Shinas MN
When the question of collinearity comes we equate the area of 3 points to zero. So when we do so by applying the formula, We get a quadratic equation which gives solution either 0 or -1, since the word distinct is not mentioned in the question both options hold true. Having mentioned distinct, we could rule out 0. Hence 0 cannot be completely ruled out.

Regards,
Pritika

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Kaushik Deka

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Dec 3, 2020, 6:56:44 AM12/3/20
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Dear Amrit,

Geometric collinearity is defined for more than one point - two points are, by default (trivially), always collinear. So, it is mathematically wrong to think that collinearity is not defined for 2 points. Also, coordinates refer to positions, so one can also visualize 2 points overlapping at (0,0), which are collinear with the 3rd point at a distinct location (-1,1), for lambda = 0.

Ref:


It is about objectivity of mathematical definitions, not just about marks!

Don't you agree ?

Regards,
Kaushik

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Nutan Patil

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Dec 3, 2020, 7:00:46 AM12/3/20
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Very nice .  .I agree with you..

Manish Bibhu

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Dec 4, 2020, 3:07:26 AM12/4/20
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I have also sended a email to support team. But support team says you have to raise your doubt related to course only on discussion forum.
But we are not getting any response from IITM here as well. What can we do now.....

Manish Bibhu

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Dec 4, 2020, 3:11:57 AM12/4/20
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All of you please raise a query for same question on main page at least two times so that it will noticed easily by IITM.

On Thursday, 3 December, 2020 at 5:30:46 pm UTC+5:30 nutanp...@gmail.com wrote:

Avipsa Dey

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Dec 4, 2020, 3:27:15 AM12/4/20
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Mathematics Support Team we humbly request you to reply at the earliest. We are eagerly waiting to hear back from you.

Amrit Raj

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Dec 4, 2020, 3:38:10 AM12/4/20
to Nutan Patil, Kaushik Deka, Discussion forum for Mathematics for Data Science I, sup...@onlinedegree.iitm.ac.in, Shinas MN
My point was not about lambda=0 not being correct, but the point was , that people who have either marked lambda= (-1 or 0 ) could be given marks.
I marked -1 despite getting 0 also as the answer because the question paper gave me a feeling that it was not set by somebody very experienced, so he/she would go for the traditional answers. I had found ambiguity in a lot of other questions in terms of language.

1. On the point of zero being correct. I don't think it is wrong at all.

2. Also people telling that the quadratic equation gave them two solutions i.e probably from the area of triangle formula which in itself is considering three points. That is one of the methods of solving.If you used the slope method, you would get linear solutions.My point is that methods do not/should not supersede the definition/concept(if collinearity is defined for three or more points or any no of points). So we should keep this in mind. That is why we check extraneous roots in quadratic equations or remove answers which do not fall in the domain of a function.

3.The problem here was the question did not have enough explanation, they should have mentioned "three distinct points" or even mention of " three" gives the clarity.

Avipsa Dey

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Dec 4, 2020, 3:50:43 AM12/4/20
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You are cent percent correct in your opinion Mr. Amrit. The Mathematics Section of QP3 was too ambiguous to understand because of the language usage in framing the questions. It becomes a strenuous exercise to solve such papers when you are hard pressed on time as well. I urge Mathematics Support Team to at least come forward and provide a proper reply.

Kaushik Deka

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Dec 4, 2020, 4:39:33 AM12/4/20
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Amrit,

With regard to your point 2, even if you equate the slopes, you will arrive at a quadratic equation unless you trivially eliminate the quadratic term. If lambda/lambda is reduced to 1, one of the roots, the trivial solution (lambda = 0), is inadvertently eliminated. Try it again! 

amrit raj

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Dec 4, 2020, 5:26:17 AM12/4/20
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Bro, I was not making that point, I already said I got both the answers. I know what you are saying, one of the equations from the slope thing will be a quadratic equation as well. (One part of it will give you a linear solution.) I was just saying to be conscious about the definition. And start from the definition. Processes should reflect the definition. That is my point nothing else.
Let me make it very clear for you, because it seems I am not able to explain you my point.

1. Definition 1: Collinearity is defined for three or more points.
                         We can use any of the methods but we need to see there are at least three distinct points.

2. Definition 2: Collinearity is defined for two or more points.
                        We can use any of the methods, but we need to see if the method does not remove the two point condition.

I am just trying to say methods/process, should be able to reflect the exact definition and not exclude any set from the definition.

Kinjal Dave

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Dec 4, 2020, 7:30:40 AM12/4/20
to Shinas MN, Discussion forum for Mathematics for Data Science I, sup...@onlinedegree.iitm.ac.in
yes please give full marks to all

On Thu, Dec 3, 2020, 11:33 AM Shinas MN <mnsh...@gmail.com> wrote:

Kaushik Deka

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Dec 4, 2020, 8:47:54 AM12/4/20
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Amrit, I still don't understand your point. There is one and only one definition of collinearity: two or more points that share a line are collinear - it is not subject to variable interpretation! For two points, you just don't have to prove it; in formal mathematical language such a statement is called trivial or a degenerate case. That is, area enclosed by two points is always 0, and slope of the line through the two points is unique for them! For more than two points, a proof is necessary. So, in the context of Q89, collinearity is satisfied for two values of the unknown: -1 gives 3 collinear points, 0 gives 2 (trivially collinear) points, irrespective of the test used.  

Anubhav kumar Jha

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Dec 4, 2020, 9:11:35 AM12/4/20
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Thanks guys for raising issue both answer are correct.

Anubhav kumar Jha

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Dec 4, 2020, 11:42:59 AM12/4/20
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It is not about marks. 

Abhighyan Sinha

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Dec 4, 2020, 12:34:29 PM12/4/20
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Certainly no two points are same and has same coordinates, and that can be proven easily as follows:

Let us consider that two of the given points has the same coordinates. 
If the above statement is true, the slope of the (nonexistent) line connecting the two points(defined as change in y-axis/change in x-axis) should be zero(or rather undefined as the denominator is also zero).
In the given points, we can see that the above statement does not hold true in any combination of the points.

Therefore, we can conclude that the three given points are distinct.


Anubhav kumar Jha

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Dec 4, 2020, 12:58:14 PM12/4/20
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Slope of the line connecting the two points should be zero??Can you Explain?

Abhighyan Sinha

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Dec 4, 2020, 1:01:04 PM12/4/20
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It is better to say that the slope will be undefined, as both the numerator and denominator will be zero.

If the two points have the same coordinates(essentially the same point), the slope will be undefined (0/0).
 As an illustration, we can consider the point (3,3).Now if we try to find the slope, it will come out as 3-3/3-3 which is 0/0. And this will hold true for any point on the cartesian plane.
As an extension of this we can also say that, two points on the cartesian plane are distinct if and only if their slope is not equal to 0/0


It was a mistake in my previous post to say that slope will be zero, the correct way to express it is to mention that slope will be undefined as it will be 0/0

Kaushik Deka

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Dec 4, 2020, 1:59:11 PM12/4/20
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Sir Abhighyan Sinha, 0/0 slope for a point means infinite lines through the point! This is the case for the first two points for lambda = 0.

Abhighyan Sinha

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Dec 4, 2020, 2:07:32 PM12/4/20
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0/0 slope denotes that the points are the same, and not distinct. And definitely that means infinite lines through the point, as it is a single point!

If you go hrough my first post, that is essentialy a proof of why lambda cannot be 0 for the first two points, as it will give the points as (0,0).
For both the points to be (0,0), the slope must be undefined (0/0), which clearly is not the case here as we can see by taking the slope of the given points. Therefore it is clear by basic logical deductions that the three points are distinct.

Anubhav kumar Jha

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Dec 4, 2020, 9:24:22 PM12/4/20
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"two points on the cartesian plane are distinct if and only if their slope is not equal to 0/0 " Chill brother  
RECHECK YOUR LOGIC

Anubhav kumar Jha

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Dec 4, 2020, 9:38:40 PM12/4/20
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Please Review the Options 
0
-1 both are correct

Geetaanjali GNS

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Dec 4, 2020, 9:42:34 PM12/4/20
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Don't worry so much, all this will be reviewed.
And if not, like JEE they may allow us to point out any wrong answers after the result, there's no point trying to highlight the same thing again again.
Be patient.
We might get the normalised scores in a day or two.
All the best !

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Anubhav kumar Jha

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Dec 4, 2020, 10:55:24 PM12/4/20
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Ok :) 
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