Constant term in the expansion of x-1-x2-x-1-x-1-x-x10 is

The correct option is A 210Let x^1/6 = t.. Then given expression becomes [ (t^2+1)(t^4 t^2+1)/t^4 t^2+1 (t^3 1)(t^3+1)/t^3(t^3 1) ]^10 = [ (t^2+1) (1+t^ 3) ...

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Standard XII

Mathematics

Middle Terms

Constant term...

Question

Constant term in the expansion of ${(\frac{x + 1}{\sqrt[3]{x^{2}} - \sqrt[3]{x} + 1} - \frac{x - 1}{x - \sqrt{x}})}^{10}$ is

210

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252

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120

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Solution

The correct option is A 210
Let $x^{\frac{1}{6}} = t$ .. Then given expression becomes
${[\frac{(t^{2} + 1) (t^{4} - t^{2} + 1)}{t^{4} - t^{2} + 1} - \frac{(t^{3} - 1) (t^{3} + 1)}{t^{3} (t^{3} - 1)}]}^{10}$

$= {[(t^{2} + 1) - (1 + t^{- 3})]}^{10} = [t^{2} - t^{- 3}]^{10}$
$T_{r} =^{10} C_{r} t^{2 (10 - r)} (- 1)^{4} t^{- 3 r}$
Coefficient of $t = 20 - 5 r = 0 \Rightarrow r = 4$ . Constant term = $^{10} C_{4} = 210$

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Constant term in the expansion of (x+13√x2−3√x+1−x−1x−√x)10 is

The correct option is A 210Let x16=t.. Then given expression becomes [(t2+1)(t4−t2+1)t4−t2+1−(t3−1)(t3+1)t3(t3−1)]10 =[(t2+1)−(1+t−3)]10=[t2−t−3]10 Tr=10Cr t2(10−r)(−1)4t−3r Coefficient oft=20−5r=0⇒r=4. Constant term = 10C4=210

Constant term in the expansion of ${(\frac{x + 1}{\sqrt[3]{x^{2}} - \sqrt[3]{x} + 1} - \frac{x - 1}{x - \sqrt{x}})}^{10}$ is