\(\rm (2x - \frac {x} {2})^n\) के विस्तार के अंत से nवां पद क्या है?

  1. \(\rm - nx^n​​​. 2^{(n - 1)}\)
  2. \(\rm nx^n​​​. 2^{(n - 1)}\)
  3. \(\rm - nx^n​​​. 2^{(n - 2)}\)
  4. \(\rm nx^n​​​. 2^{(n - 2)}\)

Answer (Detailed Solution Below)

Option 3 : \(\rm - nx^n​​​. 2^{(n - 2)}\)
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Electric charges and coulomb's law (Basic)
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Detailed Solution

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संकल्पना:

सामान्य पद: (x + y)n के विस्तार में सामान्य पद को निम्न द्वारा ज्ञात किया गया है

\(\rm {T_{\left( {r\; + \;1} \right)}} = {\;^n}{C_r} \times {x^{n - r}} \times {y^r}\)

(x + y)के विस्तार में पदों की संख्या (n + 1) है। 

अंत से (n + 1)वां पद पहला पद है और nवां पद दूसरा पद है। 

गणना:

 \(\rm (2x - \frac {x} {2})^n\) के विस्तार में एक विस्तार के अंत से nवां पद दूसरा पद है। 

Tr+1 = nCr (2x)(n - r) \(\rm (\frac {-x} {2})^r\)

T2 =  nC1.(2x)(n - 1) \(\rm (\frac {-x} {2})\)

\(\rm - n \times 2^{(n - 1 - 1)} \times x^{(n - 1 +1)}\)

\(\rm - n \times 2^{(n - 2)} \times x^{n}\)

\(\rm - nx^n​​​. 2^{(n - 2)}\)

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