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  • Tell me? The number of terms in the expansion of (1 + x)101 (1 + x2 - x)100 in powers of x is :

 The number of terms in the expansion of  (1 + x)101 (1 + x2 - x)100 in powers of x is :

  • Option 1)

    302

  • Option 2)

    301

  • Option 3)

    202

  • Option 4)

    101

 

Answers (1)

As we have learned

Expression of Binomial Theorem -

\left ( x+a \right )^{n}= ^{n}\! c_{0}x^{n}a^{0}+^{n}c_{1}x^{n-1}a^{1}+^{n}c_{2}x^{n-2}a^{2}x-----^{n}c_{n}x^{0}a^{n}

 

- wherein

for n  +ve integral .

 

 

(1+x)^{101}(x^2+1-1)^{100}\\= (1+x)(x^3+1)^{100}\\(1+x) (^{100}C_0+^{100}C_1x^3+^{100}C_2x^6 + ....+ ^{100}C_{100}x^{300})

\Rightarrow No. \: \: of\: \: terms = 101+101 = 202

 

 

 

 

 


Option 1)

302

Option 2)

301

Option 3)

202

Option 4)

101

Posted by

Vakul

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