Last Minute Key Notes for CAT

[gautam41in]

The values of n for which n! is a perfect square are -- 0 and 1 --> only 2 values.

Any prime number greater than 3 will be of the form 6k+1 or 6k-1

[gautam41in]

For a right Angled triangle

Circum-radius -- hyp/2

In-radius -- (base x hgt) / (base+hgt+hyp)

[anarchy]

now if someone can tell me how to find out the last non zero digit of n! without using Euler or any such complex method, I'll b eternally grateful!!

[maverickisneo]

Originally Posted by anarchy

now if someone can tell me how to find out the last non zero digit of n! without using Euler or any such complex method, I'll b eternally grateful!!

hey this method was posted by sumit in the thread entitled "math trips and trick..."

just posting the crux:
z(n)-> denotes the last non zero digit in in expansion of n factorial
L(n)-> denotes the last digit(unit digit) of n.
z(n)=L[4^(number of tens in n)] * Z[n/5]
eg.Z(100) = L(4^10)*Z(20)
Z(20)=L(4^2)*Z(4)
Z(4)=4
L(4^2)=6
Z(20)=4
so Z(100) = 6*4 = 24, hence last non zero digit in 100! is 4

for a detailed discussion, please read his post

[anarchy]

Originally Posted by maverickisneo

hey this method was posted by sumit in the thread entitled "math trips and trick..."

just posting the crux:
z(n)-> denotes the last non zero digit in in expansion of n factorial
L(n)-> denotes the last digit(unit digit) of n.
z(n)=L[4^(number of tens in n)] * Z[n/5]
eg.Z(100) = L(4^10)*Z(20)
Z(20)=L(4^2)*Z(4)
Z(4)=4
L(4^2)=6
Z(20)=4
so Z(100) = 6*4 = 24, hence last non zero digit in 100! is 4

for a detailed discussion, please read his post

got it!!!
So after getting the last digit in this form.. all we have to do is multiply the remaining numbers to find the last digit (just for the sake of generality)!!

sahi..
I had gone thru that earlier but dint get it..
suddenly, the fog seems to have lifted!!

[ajay_citm]

Originally Posted by maverickisneo

This one is related with conditional probability.
Here mainly we have 2 formulas:
1.Simple conditional probability.(Remember when A is an event depended on events E1 and E2, where E1 and E2 are mutually exclusive events??)

2.Bayes Theorem.

Use former when data are given for present and asked about future and use latter when datas are given for present and asked about past.

hope am clear, if not then will explain with examples.

dude pls elaborate

[sheth_pranav]

Here is a contribution from me

Sum of all numbers formed by n digits (a,b,c,d...n) = (n-1)! * (Sum of all digits) * 11...n times

For eg
sum of all numbers formed by 2, 3, 4 & 5

= (4-1)! * (2+3+4+5) * 1111
= 3! * 14 * 1111 = 93324

[Prakash_max]

Hey this is simple one, but useful...

Set of numbers whose value differ from sum of its factor (including 1 & the number itself) is the set of all PRIME no.s.

Numbers which are equal to no.s of its factors.... 1 & 2

________________________


I am what I AM

[sheth_pranav]

Originally Posted by Prakash_max

Hey this is simple one, but useful...

Set of numbers whose value differ from sum of its factor (including 1 & the number itself) is the set of all ODD no.s.

Numbers which are equal to no.s of its factors.... 1 & 2

Can u pls give an example for the same

[sheth_pranav]

Meanwhile, here's another 1

No of possible diagonals for a n sided polygon = nC2 - n