JEE Main 202229 Jun, Evening shiftMathematicsHardBinomial Theorem and Its Simple Applications131× since 2002Let n ≥\ge≥ 5 be an integer. If 9^n −-− 8n −-− 1 = 64α\alphaα and 6^n −-− 5n −-− 1 = 25β\betaβ, then α\alphaα −-− β\betaβ is equal toAOption A. 1 + ^nC₂ (8 −-− 5) + ^nC₃ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 1 −-− 5^n −-− 1)BOption B. 1 + ^nC₃ (8 −-− 5) + ^nC₄ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 2 −-− 5^n −-− 2)COption C. ^nC₃ (8 −-− 5) + ^nC₄ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 2 −-− 5^n −-− 2)DOption D. ^nC₄ (8 −-− 5) + ^nC₅ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 3 −-− 5^n −-− 3)CheckSkip · show solution
