Q77.Statement-1: ∑nr=0(r + 1)nCr = (n + 2)2n−1 Statement -2: ∑nr=0(r + 1)nCrxr = (1 + x)n + nx(1 + x)n−1 . JEE Main 2008 JEE Main Previous Year Paper (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.
What This Question Tests
This question tests the understanding of properties of binomial coefficients and the ability to derive sums using differentiation of binomial series. Statement 2 is a more general identity from which Statement 1 can be derived by setting x=1, making Statement 2 a correct explanation for Statement 1.
Concepts Tested
Formulas Used
∑ nCr = 2^n
∑ r nCr = n * 2^(n-1)
d/dx (1+x)^n = n(1+x)^(n-1)
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📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Properties of Binomial Coefficients
- Year
- 2008
- Shift
- Unknown
- Q Number
- Q77
- Type
- Assertion Reasoning
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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