The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)⁴ and of (1−αx )⁶ is the same if α equals

-5/3

3/5

-3/10

10/3

Solution

-3/10

The coefficient of x in the middle term of expansion of (1+ αx)⁴= ⁴C₂.α²
The coefficient of x in middle term of the expansion of 3(1− αx) = ⁶C₃ (−α)³
According to question
$straight C presuperscript 4 subscript 2 straight alpha squared space equals space to the power of 6 straight C subscript 3 space left parenthesis negative straight alpha right parenthesis cubed fraction numerator 4 factorial over denominator 2 factorial 2 factorial end fraction straight alpha squared space equals space minus space fraction numerator 6 factorial over denominator 3 factorial 3 factorial end fraction straight alpha cubed 6 straight alpha squared space equals space minus space 20 straight alpha cubed straight alpha space equals space minus space 6 over 20 straight alpha space equals space minus 3 over 10$

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Binomial Theorem

The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)⁴ and of (1−αx )⁶ is the same if α equals

-5/3

3/5

-3/10

10/3

Some More Questions From Binomial Theorem Chapter

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Binomial Theorem

The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)4 and of (1−αx )6 is the same if α equals -5/3 3/5 -3/10 10/3

Some More Questions From Binomial Theorem Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)⁴ and of (1−αx )⁶ is the same if α equals

-5/3

3/5

-3/10

10/3