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Mathematics · JEE | BINOMIAL THEOREM
हिन्दीConsider the properties of binomial coefficients: (I) \( {^n\text{C}_r} + {^n\text{C}_{r-1}} = {^{n+1}\text{C}_r} \) (II) \( {^n\text{C}_r} = \frac{n}{r} {^{n-1}\text{C}_{r-1}} \) (III) \( \sum_{r=0}^n {^n\text{C}_r} = 2^n - 1 \) (IV) \( {^n\text{C}_x} = {^n\text{C}_y} \implies x = y \) or \( x + y = n \) How many of the above statements are correct?
View Answer & Solution
Correct answer · Option C
Only three
Explanation
Statements (I), (II), and (IV) are standard correct formulas. Statement (III) is incorrect because \( \sum_{r=0}^n {^n\text{C}_r} = 2^n \), not \( 2^n - 1 \). Thus, exactly three statements are correct.
