Core5 mapped NDA questions
Build the idea
Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.
Concept
The binomial theorem expands (a+b)ⁿ as a sum of n+1 terms whose coefficients are the binomial coefficients nCr. It is used to find a particular term, a coefficient, or the term independent of x.
The general (r+1)th term lets you target any specific term without full expansion.
Key Points & Formulas
- (a+b)ⁿ = Σ_{r=0}^{n} nCr a^(n−r) b^r.
- General term: T_{r+1} = nCr a^(n−r) b^r.
- Number of terms = n+1; middle term is the ((n/2)+1)th if n is even.
- Sum of all binomial coefficients = 2ⁿ.
Worked Example
Q. Find the term independent of x in the expansion of (x + 1/x)⁸.
General term T_{r+1} = 8Cr x^(8−r) (1/x)^r = 8Cr x^(8−2r).
Independent of x ⇒ 8−2r = 0 ⇒ r = 4.
Term = 8C4 = 70.