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प्रश्न
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
उत्तर
Use `""^"n""C"_r` has maximum value if,
(a) r = `"n"/2` when n is even
(b) r = `("n" - 1)/2 "or" ("n" + 1)/2` when n is odd
`""^14"C"_r "and" ""^12"C"_r`
Maximum value of `""^14"C"_r "occurs at" r = 14/2` = 7
∴ Maximum value of `""^14"C"_r = ""^14"C"_7`
= `(14 xx 13 xx 12 xx 11 xx 10 xx 9 xx 8)/(7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)`
= 3432
Maximum value of `""^12"C"_r "occurs at" r = 12/2` = 6
∴ Maximum value of `""^12"C"_r = ""^12"C"_6`
= `(12 xx 11 xx 10 xx 9 xx 8 xx 7)/(8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2)`
= 924
∴ The difference between the maximum values of `""^14"C"_r "and" ""^12"C"_r`
= 3432 – 924
= 2508.
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