Problems on Binomial Theorem: CAT Quantitative Aptitude

CAT Quantitative Aptitude section has sometimes question on Binomial Theorem Concept.Go through the following application based problems on binomial expansion to see the kind of problems that may be created in this topic!

Example:

The term independent of x in the binomial expansion of   is:

Solution:

The general term of the given binomial expansion is:

Now, for this term to be independent of x, we know that:  (10 – 2r) = 0

Therefore, the correct option is [1].

Example:
If A is the sum of odd n terms and B is the sum of even terms in the expansion of (x + a)ⁿ . Then A² - B² (x² - a²)ⁿ = 0 , where k =

[1] 1

[2] 2

[3] -1

[4] 3

Solution:

= A + B

Where

Example:
The term that does not contain irrational expression in the expansions of is:

Solution:

General term 

For a term to be rational, the conditions are

24 - r = 5k

r = 7m

where k and m are non–negative integers.

Now, 

And 

The common value of r is 14.

Therefore Rational term =