If 1-x n-C 0 n- C1nx -C 2 n x 2- Cnnxnthen the value of C 0 n-3 C 1 n-9 C 2 n-3 n CnnisA- 2nB- 3n C- 4 nD- 2 n -1

The correct option is C 4^nIf we substitute x=3 in the above expression, we get nbsp;(1 nbsp;+ nbsp;3)n nbsp;= nbsp; nbsp;C0n nbsp;30 nbsp;+ ...

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Byju's Answer

Standard XII

Mathematics

General Term of Binomial Expansion

If 1+x n=C 0 ...

Question

$If {(1 + x)}^{n} = n C 0 + n C 1 x + n C 2 x^{2} + . . . + n C n x^{n} then the value of n C 0 + 3 n C 1 + 9 n C 2 + . . . + 3^{n} n C n is$
______

2^{n}

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3^{n}

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2^{n - 1}

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4^{n}

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Solution

The correct option is D $4^{n}$
If we substitute $x = 3$ in the above expression, we get
${(1 + 3)}^{n} = n C 0 3^{0} + n C 1 3^{1} + n C 2 3^{2} + . . . + n C n 3^{n} = 4^{n}$
Hence, Option d.

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If {(1 + x)}^{n} = n C 0 + n C 1 x + n C 2 x^{2} + . . . + n C n x^{n} then the value of n C 0 + 3 n C 1 + 9 n C 2 + . . . + 3^{n} n C n is

______

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If (1 + x)n = nC0 + nC1x+ nC2x2 + ... + nCnxnthen the value of nC0 + 3 nC1 + 9 nC2+ ... + 3n nCnis ______

The correct option is D 4nIf we substitute x=3 in the above expression, we get (1 + 3)n = nC0 30 + nC1 31 + nC2 32 + ... + nCn3n = 4n Hence, Option d.

$If {(1 + x)}^{n} = n C 0 + n C 1 x + n C 2 x^{2} + . . . + n C n x^{n} then the value of n C 0 + 3 n C 1 + 9 n C 2 + . . . + 3^{n} n C n is$
______

The correct option is D $4^{n}$
If we substitute $x = 3$ in the above expression, we get
${(1 + 3)}^{n} = n C 0 3^{0} + n C 1 3^{1} + n C 2 3^{2} + . . . + n C n 3^{n} = 4^{n}$
Hence, Option d.