Q65.The value of -15๐ถ1 + 2 ยท 15๐ถ2 - 3 ยท15 ๐ถ3 + . . . . . - 15 ยท 15๐ถ15 + 14๐ถ1 + 14๐ถ3 + 14๐ถ5 + . . . . + 14๐ถ11 is equal to (1) 214 (2) 213 - 13 (3) 216 - 1 (4) 213 - 14
What This Question Tests
This problem involves applying properties of binomial coefficients, specifically the sum of products of r and nCr with alternating signs, and the sum of alternate binomial coefficients.
Concepts Tested
Formulas Used
Sum (r * nCr) = n * 2^(n-1)
Sum ((-1)^r * r * nCr) = 0
nC1 + nC3 + ... = 2^(n-1)
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๐ Question Details
- Chapter
- Binomial Theorem
- Topic
- Properties of Binomial Coefficients
- Year
- 2021
- Shift
- 24 Feb Shift 1
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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