के विस्तार में केंद्रीय पद क्या है?

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Agniveer Vayu Science (Group X) 18 Jan 2023 Memory Based Paper
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  1. - 10C4
  2. 10C4 
  3. 10C5 
  4. - 10C5 

Answer (Detailed Solution Below)

Option 4 : - 10C5 
Free
Electric charges and coulomb's law (Basic)
10 Qs. 10 Marks 10 Mins

Detailed Solution

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अवधारणा:

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

 

मध्य पद: मध्य पद n के मान पर आधारित (x + y) n का विस्तार है। 

यदि n सम है, तो (x + y) n के विस्तार में पदों की कुल संख्या n +1 है। इसलिए केवल एक मध्य पद है अर्थात् \(\rm \left( {\frac{n}{2} + 1} \right){{\rm{\;}}^{th}}\) पद मध्य पद है। 

यदि n विषम है, तो (x + y) n के विस्तार में पदों की कुल संख्या n +1 है। इसलिए दो मध्य पद हैं अर्थात् औरदो मध्य पद हैं।

गणना:

दी गई अभिव्यक्ति  के लिए n = 10 (सम)।

∴ केंद्रीय पद  = T6 = 10C5 (2x)10-5

= - 10C5 

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