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Statement-1:Sum of the coefficients of last 30 terms in the expansion of `(1+x)^(49)`. When expanded in ascending powers of x, is `2^(48)`.
Statement-2: `P^(th)` term from the end in the expansion of `(x+y)^(n)` is `(n-P+2)^(th)` term from the beginninig.

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To solve the problem, we will analyze both statements provided in the question. ### Step 1: Analyze Statement 1 We need to find the sum of the coefficients of the last 30 terms in the expansion of \((1+x)^{49}\). 1. **Understanding the Expansion**: The expansion of \((1+x)^{49}\) has \(n + 1 = 49 + 1 = 50\) terms, which are: \[ \binom{49}{0}x^0, \binom{49}{1}x^1, \ldots, \binom{49}{49}x^{49} \] 2. **Sum of Coefficients**: To find the sum of the coefficients of the entire expansion, we substitute \(x = 1\): \[ (1 + 1)^{49} = 2^{49} \] 3. **Identifying Last 30 Terms**: The last 30 terms in the expansion correspond to the terms from \(\binom{49}{20}x^{20}\) to \(\binom{49}{49}x^{49}\). 4. **Sum of Coefficients of Last 30 Terms**: The sum of the coefficients of the last 30 terms can be expressed as: \[ \sum_{k=20}^{49} \binom{49}{k} \] This is equal to: \[ \sum_{k=0}^{49} \binom{49}{k} - \sum_{k=0}^{19} \binom{49}{k} = 2^{49} - \sum_{k=0}^{19} \binom{49}{k} \] 5. **Using Symmetry**: By the symmetry of binomial coefficients: \[ \sum_{k=0}^{19} \binom{49}{k} = \sum_{k=30}^{49} \binom{49}{k} \] Thus, the sum of the coefficients of the last 30 terms is: \[ \sum_{k=20}^{49} \binom{49}{k} = 2^{49} - \sum_{k=0}^{19} \binom{49}{k} = 2^{49} - \sum_{k=30}^{49} \binom{49}{k} \] 6. **Conclusion for Statement 1**: The sum of the coefficients of the last 30 terms is not equal to \(2^{48}\), therefore Statement 1 is **False**. ### Step 2: Analyze Statement 2 We need to verify if the \(P^{th}\) term from the end in the expansion of \((x+y)^{n}\) is the \((n-P+2)^{th}\) term from the beginning. 1. **Understanding the Terms**: The \(P^{th}\) term from the end can be expressed as: \[ T_{n-P+1} = \binom{n}{n-P} x^{n-P} y^{P} \] The \(P^{th}\) term from the beginning is: \[ T_{P} = \binom{n}{P-1} x^{n-(P-1)} y^{P-1} \] 2. **Identifying the Correspondence**: The \(P^{th}\) term from the end corresponds to the \((n-P+1)^{th}\) term from the beginning, not \((n-P+2)^{th}\). 3. **Conclusion for Statement 2**: Therefore, Statement 2 is also **False**. ### Final Conclusion Both statements are incorrect. Thus, the correct option is that both statements are false.
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