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If $^{n - 1} C_{r} = {(k^{2} - 3)}^{n} C_{r + 1},$ then k is belongs to

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(−∞,−2]

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detailed solution

Correct option is D

∵k2−3= n−1Cr nCr+1= n−1Crnr+1n−1Cr=r+1n -----(i)∵ 0≤r≤n−1⇒ 1≤r+1≤n⇒1n≤r+1n≤1⇒ 1n≤k2−3≤1⇒ 3+1n≤k2≤4When n→∞,3

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If n−1Cr=k2−3nCr+1, then k is belongs to

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If $^{n - 1} C_{r} = {(k^{2} - 3)}^{n} C_{r + 1},$ then k is belongs to