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Mathematical Induction and Binomial Theorem

Section: Mathematics

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Question : 3

Total: 8

For nonnegative integers s and r, let
(

For positive integers m and n, let
g(m,n)=

where for any nonnegative integer p,
f(m,n,p)=

)
Then which of the following statements is/are TRUE?

[JEE Adv 2020 P2]

g(m, n) = g(n, m) for all positive integers m, n
g(m, n + 1) = g(m + 1, n) for all positive integers m, n
g(2m, 2n) = 2g(m, n) for all positive integers m, n
g(2m, 2n) = (g(m, n))2 for all positive integers m, n

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