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JEE Main202331 Jan 2023Evening ShiftMathematicsBinomial TheoremActual

The coefficient of x - 6 , in the expansion of 4 x 5 + 5 2 x 2 9 , is

Correct answer

5040

Step-by-step solution

Given, 4 x 5 + 5 2 x 2 9 Now r t h term of the expression is given by, T r + 1 = C r 9 4 x 5 9 - r 5 2 x 2 r ⇒ T r + 1 = C r 9 4 5 9 - r 5 2 r x 9 - r - 2 r Now equating 9 - r - 2 r = - 6 ⇒ r = 5 So, coefficient of x - 6 will be, = C 5 9 4 5 9 - 5 5 2 5 = 9 × 8 × 7 × 6 4 × 3 × 2 × 1 × 4 5 4 5 2 5 = 5040

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