Hi guys,I request you all to share any shortcuts and tricks that you knw in quant, as it will be useful for all of us.Thanks and Regards,
Hi guys,
I request you all to share any shortcuts and tricks that you knw in quant, as it will be useful for all of us.
Thanks and Regards,
Few days back I learnt this.
PICK'S THEOREM
To find no of points in the Region described by the lines x/a+y/b=0 and y>=0
but HCF(a,b)=1 ( a and b both shud be co primes)
No of integer points inside the regions will be = [(a-1)*(b-1) - h]/2
where, h= No of points coinciding with the hypotenuse
when HCF(a,b)=1
h=0
Sum of perpendicular sides of ryt triangle given area A and semiperimeter S is given by S + A/S
Dind some file attached 😁
Area of rt angled traingle : when incentre =r
circum cetnre =R
A= r(r+2R)
Has come in handy in various places now !!
Positive integral solutions of 1/M + 1/N =1/P is No of factors of p^2.
Ex. 1/M + 1/N = 1/12 will have total of 15 +ve integral solns.
Total no. of integral coordinates inside including boundary |x|+|y|
If the boundary is not included then put n-1 in the eq...
Angle between the hands of clock : 30h-(11/2)m
@pankaj1988 said:Positive integral solutions of 1/M + 1/N =1/P is No of factors of p^2.Ex. 1/M + 1/N = 1/12 will have total of 15 +ve integral solns.
bhai isko thoda explain karna... not clear
@pankaj1988 said:Total no. of integral coordinates inside including boundary |x|+|y|If the boundary is not included then put n-1 in the eq...Will it be also applicable for the case, say, |x-a| + |y-b|
@rachit_28 said:Will it be also applicable for the case, say, |x-a| + |y-b|i guess it shud be... coz the area remain the same... so as the cordinates...
@maddy2807 Bhai jaise take p=12 so p^2=144 factors will be 2^4 * 3^2 . So the number of factors would be (4+1) * ( 2+1)=15 which is same as no of +ve integral soln of 1/M + 1/N= 1/12.
explanation : Eq can be written as (N-12) (M-12) =144
When done with counting (1,144) (2, 72) (3, 48) (4,36) ( 6,24) (8, 18) (9, 16) (12,12) of which previous 7 can be interchanged so total solns will be 2*7+1.
@rachit_28 said:Will it be also applicable for the case, say, |x-a| + |y-b|Bro I am not sure abt it. Though area remains the same but integral coordinates?? Let others throw some light on it......
@pankaj1988 said:Bro I am not sure abt it. Though area remains the same but integral coordinates?? Let others throw some light on it......
No of integral cordinates also remains the same. in case of |x-a|+|y-b|=p
the only change from |x|+|y|=p is the change in the no of coordinates to (a,b) from (0,0)
Rest thing remains the same
No of Triangle that can be formed with perimeter n will be
[(n+3)^2/48] when n is odd
[n^2/48] when n is even,
[] is the nearest integer function.
1.sum of all the co-primes of N which are less than N = N/2 * E(N)
2.The probability that an interval broken at n-1 points chosen uniformly at random is broken into pieces which can be rearranged to form an n-gon is :
P =1- (n/2^(n-1)) - aizen sir ka vardan
@billamin said:@maddy2807can u elaborate your first trick using the equation say, x/3+y/5=1?
here a=3 and b=5
h=0 as HCF(3,5)=1
so No of integer points= 4