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Jee Main 2025Medium JEE math MCQ

Let the coefficients of three consecutive terms \( T_r, T_{r+1}, \) and \( T_{r+2} \) in the binomial expansion of \( (a + b)^{\frac{1}{2}} \) 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 \( (\sqrt{3} + \sqrt{4})^{\frac{1}{2}} \). Then \( p + q \) is equal to
  1. A. 283
  2. B. 287
  3. C. 295
  4. D. 299

Solution

The correct option is **A**. (A. 283)

MATH

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Question
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Let the coefficients of three consecutive terms Tr,Tr+1, T_r, T_{r+1}, and Tr+2 T_{r+2} in the binomial expansion of (a+b)12 (a + b)^{\frac{1}{2}} be in a G.P. and let p p be the number of all possible values of r r . Let q q be the sum of all rational terms in the binomial expansion of (3+4)12 (\sqrt{3} + \sqrt{4})^{\frac{1}{2}} . Then p+q p + q is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep