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