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JEE Main20246 Apr 2024Morning ShiftMathematicsBinomial TheoremActual

If the second, third and fourth terms in the expansion of (x+y)^n are 135,30 and 10 3 , respectively, then 6 (n^3+x^2+y ) is equal to _______

Correct answer

0

Step-by-step solution

^ n C ₁ x ^ n -1 y =135 ....(i) ^n C₂ x^ n-2 y^2=30 ....(ii) ^ n C ₃ x ^ n -3 y ^3= 10 3 ....(iii) aligned & By (i) ( ii) & ^n C₁ ^n C₂ x y = 9 2 ...(iv) & By ( ii) ( iii) & ^n C₂ ^n C₃ x y =9....(v) aligned aligned & By ( iv ) (v) & ^n C₁ ^n C₃ ^n C₂ ^n C₂ = 1 2 & 2 n^2(n-1)(n-2) 6 = n(n-1) 2 n(n-1) 2 & 4 n-8=3 n-3 & n=5 & put in (v) aligned aligned & x y =9 & x=9 y & put in (i) & ^5 C₁ x^4 ( x 9 )=135 & x^5=27 9 & x=3, y= 1 3 & 6 (n^3+x^2+y ) & =6 (125+9+ 1 3 ) & =806 aligned

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