Find the 5th term of 2x2-4-x311

5th term is ^ 11 C _ 4 ( 2x ^ 2 ) #160; ^ 7 ( 4 x ^ 3 #160; ) #160; ^ 4 = 11! 7!4! 2^7x^14× 4 ^ 4 x ^ 12 =330× 2^15× x^2 Hence, the ...

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Standard XII

Mathematics

General Term of Binomial Expansion

Find the 5t...

Question

Find the $5^{t h}$ term of $(2 x^{2} + \frac{4}{x^{3}})^{11}$

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Solution

5th term is ${^{11} C}_{4} {({2 x}^{2})}^{7} {(\frac{4}{x^{3}})}^{4}$
$= \frac{11!}{7! 4!} 2^{7} x^{14} \times \frac{4^{4}}{x^{12}}$
$= 330 \times 2^{15} \times x^{2}$
Hence, the answer is $330 \times 2^{15} \times x^{2} .$

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Find the 5th term of (2x2+4x3)11

5th term is 11C4(2x2)7(4x3)4=11!7!4!27x14×44x12=330×215×x2Hence, the answer is 330×215×x2.

Find the $5^{t h}$ term of $(2 x^{2} + \frac{4}{x^{3}})^{11}$

5th term is ${^{11} C}_{4} {({2 x}^{2})}^{7} {(\frac{4}{x^{3}})}^{4}$
$= \frac{11!}{7! 4!} 2^{7} x^{14} \times \frac{4^{4}}{x^{12}}$
$= 330 \times 2^{15} \times x^{2}$
Hence, the answer is $330 \times 2^{15} \times x^{2} .$