How many terms are there in the expansion of ((a^2)/(b^2)+(b^2)/(a^2)+2 )^21 where a ≠ 0, b ≠ 0 ?

Correct answer: (D) 43. ((a^2)/(b^2)+(b^2)/(a^2)+2 )^21= ((a^4+b^4+2 a^2 b^2)/(a^2 b^2) )^21 = ( ((a^2+b^2)/(a b) )^2 )^21= (a/b+b/a )^42 ∴ Number ofterms =42+1=43 .

Q200 / 270 · NDA 2021 (Phase 2) · Mathematics

How many terms are there in the expansion of $\left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}$ where $a \neq 0, b \neq 0$ ?

A
21
B
22
C
42
Correct answer
D
43

Solution

$\begin{aligned} & \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}=\left(\frac{a^4+b^4+2 a^2 b^2}{a^2 b^2}\right)^{21} \\ & \quad=\left(\left(\frac{a^2+b^2}{a b}\right)^2\right)^{21}=\left(\frac{a}{b}+\frac{b}{a}\right)^{42} \\ & \therefore \quad \text { Number ofterms }=42+1=43 . \end{aligned}$

Hence, the correct answer is option: 'D'.

How many terms are there in the expansion of $\left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}$ where $a \neq 0, b \neq 0$ ?

Solution

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