If a0 and the coefficient of x^2 in the expansion of (a x^3+ c x )^6 is 60, then a c^2=

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If a>0 and the coefficient of x^2 in the expansion of (a x^3+ c x )^6 is 60, then a c^2=

Quantrex Academy · Accepted Answer

Correct answer: A. 2

General term, aligned & T_ r+1 = ^6 C_r (a x^3 )^ 6-r ( c x )^r & = ^6 C_r a^ 6-r c^r x^ 18-3 r-r & = ^6 C_r a^ 6-r c^r x^ 18-4 r aligned According to the question, aligned 18-4 r & =2 4 r=16 r & =4 . aligned So, ^6 C₄ a⁶⁻⁴ c^4=60 15 a^2 c^4=60 array rlrl & & a^2 c^4=4 a c^2= 2 & a>0 & & a c^2=2 array

If a>0 and the coefficient of x^2 in the expansion of (a x^3+ c x )^6 is 60, then a c^2=

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