हिंदी

If in the Expansion of (A + B)N and (A + B)N + 3, the Ratio of the Coefficients of Second and Third Terms, and Third and Fourth Terms Respectively Are Equal, Then N is (A) 3 (B) 4 (C) 5 (D) 6

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प्रश्न

If in the expansion of (a + b)n and (a + b)n + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is

विकल्प

  • 3

  • 4

  •  5

  • 6

     
MCQ
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उत्तर

n = 5

\[\text{ Coefficients of the 2nd and 3rd terms in } (a + b )^n \text{ are } ^{n}{}{C}_1 \text{ and }  ^{n}{}{C}_2 \]

\[\text{ Coefficients of the 3rd and 4th terms in } (a + b )^{n + 3} \text{ are } ^{n + 3}{}{C}_2 \text{ and  }^{n + 3}{}{C}_3 \]

\[\text{ Thus, we have} \]

\[\frac{^{n}{}{C}_1}{^{n}{}{C}_2} = \frac{^{n + 3}{}{C}_2}{^{n + 3}{}{C}_3}\]

\[ \Rightarrow \frac{2}{n - 1} = \frac{3}{n + 1}\]

\[ \Rightarrow 2n + 2 = 3n - 3\]

\[ \Rightarrow n = 5\]

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अध्याय 18: Binomial Theorem - Exercise 18.4 [पृष्ठ ४६]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 18 Binomial Theorem
Exercise 18.4 | Q 4 | पृष्ठ ४६

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