Q4. Let the coefficients of three consecutive terms Tr, Tr+1 and Tr+2 in the binomial expansion of (a + b)12 be in a G.P. and let p be the number of all possible values of r. Let q be the sum of all rational terms in the binomial expansion of (4√3 + 3√4)12 . Then p + q is equal to : (1) 283 (2) 287 (3) 295 (4) 299
What This Question Tests
This question tests the understanding of binomial coefficients and their properties when in G.P., along with the ability to identify and sum rational terms in a binomial expansion with irrational bases.
Concepts Tested
Formulas Used
C_r = n! / (r! * (n-r)!)
For a,b,c in G.P., b^2 = ac
General term T_r+1 = nCr * a^(n-r) * b^r
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📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Properties of binomial coefficients, Rational terms in expansion
- Year
- 2025
- Shift
- 28 Jan Shift 2
- Q Number
- Q4
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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