In the expansion of , which term is independent of x ?

This question was previously asked in
RPSC 2nd Grade Mathematics (Held on 18th Feb 2019) Official Paper
View all RPSC Senior Teacher Grade II Papers >
  1. 10
  2. 8
  3. 9
  4. 11

Answer (Detailed Solution Below)

Option 3 : 9
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RPSC Senior Grade II (Paper I): Full Test 1
100 Qs. 200 Marks 120 Mins

Detailed Solution

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Concept: Binomial expansion.

The binomial (a + b) can be expanded to the power n (n is non-negative) in the following form:

(a + b)n = 

where , denotes the (r + 1)th term.

Solution:

We have 

⇒ a = 2x2, b = , n = 12

∴ 

⇒ 

⇒ 

Now, for the term to be independent of x, the power of x should be zero

⇒ 24 - 3r = 0

⇒ 3r = 24

⇒ r = 8

∴  is independent of x.

∴ The term independent of x is the 9th term.

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