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123!  can be written in the form of 4n. how???

number of non-negative integral solutions of

a+b+c+d<=15 ?

any method to know prime numbers quickly

For a given (n,m,k)..

Using values in the range (0..k), how many different m-combos can be made which sum to n?

For example, if (n,m,k) = (3,3,2) there are 7 possible combinations. For (5,4,2) there seem to be 16.

I've been trying to approach this like the binomial formula, stars and bars sort of deal but the k-constraint is puzzling me and I'm not entirely sure of what to do.

give questions for ib acio

How I do spotting error 

how to solve inequality problems

In a triangle abc bd is the median drawn from vertes on the side of ac a line cf drawn from vertex c to the point f on the side ab bisects bd 1:1 at e if bf =6 units find ab

i am getting a fluctuating score in my mocks plz help how to improve even after analysing i am unable to achieve the score that i desire

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