If the term independent of x in the expansion of ( a x 2 + 2 x 3 1 ) 10 is 105 , then a 2 is equal to :

( a x 2 + 2 x 3 1 ) 10 General term = 10 C r ( a x 2 ) 10 − r ( 2 x 3 1 ) r 20 − 2 r − 3 r = 0 r = 4 10 C 4 a 3 ⋅ 16 1 = 105 a 3 = 8 a 2 = 4 SECTION - B

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MathematicsBinomial TheoremGeneralEasy2 minPYQ_2024

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If the term independent of $x$ in the expansion of $(a x^{2} + \frac{1}{2 x ^{3}})^{10}$ is 105 , then $a^{2}$ is equal to :

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$(a x^{2} + \frac{1}{2 x ^{3}})^{10}$ General term $=^{10} C_{r} (a x^{2})^{10 - r} (\frac{1}{2 x ^{3}})^{r}$ $20 - 2 r - 3 r = 0 r = 4^{10} C_{4} a^{3} \cdot \frac{1}{16} = 105 a^{3} = 8 a^{2} = 4$
SECTION - B

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:General

⏱ 2mℹ️ Source: PYQ_2024

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