Post mathematic related questions here

[rst]

Re: mathematic related questions

BTW if I had to solve such questions i would have probably applied hit and trial using the following conditions :

But you can use this method only with number giving remainder 3 (when divided by 4)
If a number gives remainder 0,1,2 ,then x² + y²=number may have solution or not
Also with this method we can't find number of solutions of x² + y²=number (in case it has solution)

offtopic : do you guys know what is the shortcut key for subscript and superscript here in this forum ?
have to go advanced everytime

see my first post (page 1)

 

[mastercool8695]

Re: mathematic related questions

^^ so we are supposed to copy and paste ???

 

[rst]

Re: mathematic related questions

Yeah
I use copy and paste

 

[Niilesh]

Re: mathematic related questions

The number of different positive integral solutions (x,y,z) such that x+y+z = 10

A) 36
B) 121
C) 10[SUP]3[/SUP] -10
D) [SUP]10[/SUP]C[SUB]3[/SUB] - [SUP]10[/SUP]C[SUB]2[/SUB]

offtopic : do you guys know what is the shortcut key for subscript and superscript here in this forum ?
have to go advanced everytime

Is it 9C2 = 36?

 

[rst]

Re: mathematic related questions

yeah
it is the correct answer

 

[Niilesh]

Re: mathematic related questions

But you can use this method only with number giving remainder 3 (when divided by 4)
If a number gives remainder 0,1,2 ,then x² + y²=number may have solution or not
Also with this method we can't find number of solutions of x² + y²=number (in case it has solution)

I was referening to questions in which remainder is other than 3 only
You can get solutions with hit and trial and also prove that their will be no solution with logic

 

[rst]

Re: mathematic related questions

I was referening to questions in which remainder is other than 3 only
You can get solutions with hit and trial and also prove that their will be no solution with logic

OK
No doubt,this is better method in case number has remainder 3

Is it 9C2 = 36?

Can you explain your work ??

 

[mastercool8695]

Re: mathematic related questions

yup..
guys please dont just give answers.
give method and theories too..

 

[rst]

Re: mathematic related questions

The number of different positive integral solutions (x,y,z) such that x+y+z = 10

A) 36
B) 121
C) 10[SUP]3[/SUP] -10
D) [SUP]10[/SUP]C[SUB]3[/SUB] - [SUP]10[/SUP]C[SUB]2[/SUB]

offtopic : do you guys know what is the shortcut key for subscript and superscript here in this forum ?
have to go advanced everytime

x+y+z = 10
possibilities are
1) 1,1,8
2) 1,2,7
3)1,3,6
.
.
.
8) 1,8,1

here I fixed 1 in first place

similarly I can fix 2 in first place
1) 2,1,7
2) 2,2,6
3)2,3,5
.
.
.
7) 2,7,1

similarly I can fix 3 in first place
1) 3,1,6
2) 3,2,5
3)3,3,4
.
.
.
6) 3,6,1

so in this way
we get = 8+7+6...+1
=36ways

-------------------------------------------------------------------------------------------------------------
Another method

This question is same as no. of ways of distributing 10 items among 3 persons such that each receive atleast one item
So ⁹C ₂ = 36

[As no. of ways of distributing n items among r persons such that each receive atleast one item=ⁿ⁻¹ Cr-1 ]

 

[Niilesh]

Re: mathematic related questions

OK
No doubt,this is better method in case number has remainder 3



Can you explain your work ??

I just realised we can also use multinomial theorem(also known as coefficient method)



Not now, i am online from mobile. BTW i had just recalled general result which is (n-1) C(r-1). It is useful to solve a lot of questions.

 

[mastercool8695]

Re: mathematic related questions

^^ can you guys post as many results relating to P&M like the one you gave..

 

[rst]

Re: mathematic related questions

1) No. of ways of distributing n items among r persons such that one can receive 0 item = n+r-1 C r-1

Example : Find number of different non negative integral solutions (x,y,z) such that x+y+z = 10
Solution:- This question is same as no. of ways of distributing 10 items among 3 persons such that one can receive 0 item
So we get ¹² C ₂

 

[Amit Digga]

Re: mathematic related questions

What will be the remainder when
3^2002 +7^2002 + 2002 is divided by 29?

 

[mastercool8695]

Re: mathematic related questions

found this :
MBA|CAT|CAT 2011|CAT 2012|CAT Online|MBA 2012|MBA Entrance Exams|CAT Test|Preparation|CAT Questions

3.3^2001 + 25^1001
=>3.27^667 + 25^1001
=>3.1^667 + (-1)^1001
=> 3-1
=> 2 which should be the answer .

the answer for the second one is 28 .
it would convert to 28 ! / 29 .....
also (p-1)!+1 is divisible by p and so on .

its related to the above one..
but i still cannot get the explaination in that forum (answer in Quote tags)

 

[©mß]

Re: mathematic related questions

I think remainder is 1.

 

[mastercool8695]

Re: mathematic related questions

^^ Explain..

 

[rst]

Re: mathematic related questions

remainder is 1

 

[TheSloth]

Re: mathematic related questions

damn. you guys are too much. I am very poor in these stuff. If someone explain the solution of above question i'll be thankful.

 

[mastercool8695]

Re: mathematic related questions

^^ exactly..
just writing the answer doesn't do anything

 

[©mß]

Re: mathematic related questions

I just used Python to solve it.
I don't know the explanation.