JEE Main20245 Apr 2024Evening ShiftMathematicsBinomial TheoremActual

If the constant term in the expansion of ( [5] 3 x + 2 x [3] 5 )¹², x 0 , is 2^8 [5] 3 , then 25 is equal to :

Options

A724
B742
C639
D693

Correct answer

D. 693

Step-by-step solution

aligned & T _ r +1 = ¹² C _ r ( 3^ 1 / 5 x )^ 12- r ( 2 x 5^ 1 / 3 )^ r & T _ r +1 = ¹² C _ r (3)^ 12- r 5 (2)^ r ( x )^ 2 r -12 (5)^ r / 3 & r =6 & ~T ₇= ¹² C ₆(3)^ 6 / 5 (2)^6 5^2 = ( 9 11 7 25 ) 2^8 3^ 1 / 5 & 25 =693 aligned

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