The coefficient of $x^{7}$ in the expansion of $(1 - x - x^{2} + x^{3})^{6}$ is

- 132

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 144

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

132

No worries! We‘ve got your back. Try BYJU‘S free classes today!

144

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $- 144$
Coff. of $x^{7}$ in exp. of $(1 - x - x^{2} + x^{3})^{6}$ is

$(1 - x - x^{2} + x^{3})^{6} = [(1 - x) - x^{2} (1 - x)]^{6}$

$\Rightarrow (1 - x - x^{2} + x^{3})^{6} = (1 - x^{2})^{6} (1 - x)^{6}$

$\Rightarrow (1 - 6 x^{2} +^{6} C_{2} x^{4} - 6^{6} C_{3} x^{6} +^{6} C_{4} x^{8} -^{6} C_{5} x^{10} + x^{12}) (1 - 6 x +^{6} C_{2} x^{2} -^{6} C_{3} x^{3} +^{6} C_{4} x^{4} - 6 x^{5} + x 6)$

$∴$ Coff. of $x^{7}$ is $(- 6) (-^{6} C_{3}) +^{6} C_{2} (-^{6} C_{3}) + (- 6) (- 6)$

$\Rightarrow 6 \times 20 - 15 \times 20 + 36$

Coff. $(x^{2}) = - 144$

Suggest Corrections

Similar questions

x^{7}

(1 - x - x^{2} + x^{3})^{6}

{(1 - x - x^{2} + x^{3})}^{6},

x^{7}

x^{7}

{(1 - x - x^{2} + x^{3})}^{6}

The coefficient of $x^{7}$ in $(1 - x - x^{2} + x^{3})^{6}$ is

x^{7}

{(1 - 2 x + x^{3})}^{6}

Join BYJU'S Learning Program