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Term Independent of x

If 1+2 x +3 x...

Question

If $(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20},$ then $a_{1}$ equals

A

10

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B

20

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C

210

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D

110

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Solution

The correct option is B $20$
$a_{1} = coefficient of x in (1 + 2 x + 3 x^{2})^{10}$
$= coefficient of x in ((1 + 2 x) + 3 x^{2})^{10}$
$= coefficient of x in (^{10} C_{0} (1 + 2 x)^{10} +^{10} C_{1} (1 + 2 x)^{9} (3 x^{2}) + \dots)$
$= coefficient of x in (1 + 2 x)^{10}$
$=^{10} C_{1} \cdot 2$
$= 20$

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Similar questions

(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20}

a_{1}

{(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . + a_{20} x^{20}

a_{1}

(1 + x + x^{2})^{20} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{40} x^{40},

then the value of

a_{0} + a_{1} + a_{2} + \dots + a_{19}

{(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . + a_{20} x^{20}

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3 a_{0} + 2 a_{1} + 3 a_{2} + 2 a_{3} + 3 a_{4} + 2 a_{5} + . . . 2 a_{19} + 3 a_{20}

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Term Independent of x

Standard XII Mathematics

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