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Mathematics: Post your doubts here!

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View attachment 59537
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Ok so i know how to solve it but the thing is here they have classed them as 0-9 then 10-19 then 20-34 and so on so the midpoints will be 4.5 and 14.5 and 27 etc...
Why can't you split the data like 0≤X<10 and 10≤X<20 and 20≤X<35 and so on??
The first data says <10 which means 10 is excluded therefore it should be read as 0-9 only.
 
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There're 6 colors. Select three colors from these 6. This can be done in 6C3 ways.

Now from those three colors that have been selected, there's one colour which is repeated. So select 1 colour from the 3 colous selected which is to be repeated. This can be done in 3C1 ways.

Now the selections have been made, so arrange them in the four places.

So the total arrangements possible will be:

6C3 * 3C1 * 4!/2! = 720 arrangements
 
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In the (v) part there are three different possibilities:
1. All the pegs are of different colors.
2. Three different colors.
3. Two different colors.

Deal these possibilities, one by one:

All different colours:

Select 4 colours from the 6 colours given. This will done in 6C4 ways. Then arrange these in the 4 places (4!).
So the total no. of ways will be : 6C4 * 4! = 360

Three different colours:
We've already done that in the previous part. There're 720 arrangements for this.

2 different colours:
Select two colours from the given 6. This will done in 6C2 ways. Now arrange the 4 pegs, keeping in mind that there are two pairs of pegs, each pair having a similar colour.
So the total possible arrangements will be: 6C2 * 4!/(2!*2!) = 90

Sum all of these cases, you'll get the required result:

360 + 720 + 90 = 1170 arrangements.
 
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Is there a mark for solving simultaneous equations? I mean, in the ms they give a method mark for "solving simultaneously". Does that mean if we skip the step and use the calc to do it directly, we will lose a mark?
Yes. working has a separate mark and answer has a separate one mark. Writing answer directly will give you just 1 mark.
 
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There're 6 colors. Select three colors from these 6. This can be done in 6C3 ways.

Now from those three colors that have been selected, there's one colour which is repeated. So select 1 colour from the 3 colous selected which is to be repeated. This can be done in 3C1 ways.

Now the selections have been made, so arrange them in the four places.

So the total arrangements possible will be:

6C3 * 3C1 * 4!/2! = 720 arrangements
In the (v) part there are three different possibilities:
1. All the pegs are of different colors.
2. Three different colors.
3. Two different colors.

Deal these possibilities, one by one:

All different colours:

Select 4 colours from the 6 colours given. This will done in 6C4 ways. Then arrange these in the 4 places (4!).
So the total no. of ways will be : 6C4 * 4! = 360

Three different colours:
We've already done that in the previous part. There're 720 arrangements for this.

2 different colours:
Select two colours from the given 6. This will done in 6C2 ways. Now arrange the 4 pegs, keeping in mind that there are two pairs of pegs, each pair having a similar colour.
So the total possible arrangements will be: 6C2 * 4!/(2!*2!) = 90

Sum all of these cases, you'll get the required result:

360 + 720 + 90 = 1170 arrangements.
Thanks a ton!!!!
 
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Oops! You're right. :D



Differential equations are pretty easy. Vectors and complex numbers - the first sub-questions are generally easy but the further sub-questions require good thinking and practice.
I dont find them that difficult, its just thinking a bit and that's all, but my marks goes only in this parts :p Hence I am poor at it.. :p Anyways... :D
 
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I dont find them that difficult, its just thinking a bit and that's all, but my marks goes only in this parts :p Hence I am poor at it.. :p Anyways... :D
Hahaha ... That's what I'm talking about. Practice more and you will hopefully get it. Complex numbers and vectors also require a bit of imagination, or rather, visualisation.
 
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