CAT Quant · Chapter Test
Binomial Theorem — 25-Question Test
A fresh, mixed-difficulty set drawn from the whole chapter — questions you haven't been asked before. Auto-graded with full solutions; your result is saved to your dashboard.
Building your 25-question test…
Formula Reference Sheet
This chapter
Expansion & general term
| Binomial expansion | (a+b)ⁿ = Σ nCr · a^(n−r) · b^r, r = 0…n |
|---|---|
| General term | T(r+1) = nCr · a^(n−r) · b^r |
| Number of terms | (a+b)ⁿ has (n+1) terms |
| Binomial coefficient | nCr = n! / [r!(n−r)!] |
| Symmetry of coefficients | nCr = nC(n−r) |
Middle term, sums & special cases
| Middle term (n even) | single term T(n/2 + 1) |
|---|---|
| Middle terms (n odd) | two terms T((n+1)/2) and T((n+3)/2) |
| Sum of all coefficients | put each variable = 1 ⇒ (sum of bases)ⁿ |
| Sum of binomial coefficients | nC0 + nC1 + … + nCn = 2ⁿ |
| Greatest coefficient | the middle coefficient: nC(n/2) (n even) |
CAT reference
🖩 Graphing Calculator