General And Middle Terms

Step 1: Concept
In , the independent term is the middle term, where the powers of cancel out.
Step 2: Analysis
Independent term . . .
Step 3: Conclusion
.
Final Answer: (A)

Concept: General term and power of

Step 1: General term:

Step 2: Power of :

Step 3: For constant term:

Step 4: Substitute :

Step 5: Equate to 405: Conclusion:

Concept: Perfect square identity

Step 1:

Step 2:

Step 3: Middle term in expansion:

Step 4: Conclusion:
Middle term =

Concept: For , middle term when is:

Step 1:General term.


Step 2:Middle term (r = 3).


Step 3:Simplify.

Concept: General term:

Step 1: Power of x.
For constant term:

Step 2: Compute term.

Concept: Middle term in when is even:

Step 1: Find middle term.


Step 2: Simplify.


Step 3: Correct form.

Concept: Middle term:

Step 1: For .
Middle term:

Step 2: For .
Middle term:

Step 3: Equate coefficients.