General Term — Tr+1 in (a+b)ⁿ
Binomial Theorem
9
JEE Qs
8%
Hard
50
min
Master the correct identification of 'a', 'b', and 'n', and ensure meticulous calculation of powers and binomial coefficients to avoid common errors.
🧮 Key Formulas
✅ Key Points for JEE
- 1The term T_r+1 is the (r+1)-th term in the expansion of (a+b)^n, and 'r' is the exponent of the second term 'b'.
- 2Always correctly identify 'a', 'b', and 'n' from the given binomial expression, paying close attention to signs and any complex expressions.
- 3To find the k-th term (e.g., 5th term), set r+1 = k (e.g., r=4) and substitute into the general term formula.
- 4This formula is fundamental for solving various problems like finding coefficients of specific powers, terms independent of a variable, or middle terms.
⚠️ Common Mistakes
- ✕Confusing 'r' with the term number; T_r+1 is the (r+1)-th term, not the r-th term.
- ✕Sign errors when 'a' or 'b' are negative terms (e.g., (x-y)^n where b = -y).
- ✕Algebraic mistakes in simplifying the powers of 'a' and 'b', especially when 'a' or 'b' are expressions involving variables (e.g., (x^2 + 1/x)^n).
📝 Practice Questions
See allQ21.If ∑30r=1 r2(30Cr)230Cr−1
Q20.If the area of the region {(x, y) : −1 ≤x ≤1, 0 ≤y ≤a + e|x| −e−x, a > 0} is e2+8e+1e , then the value of is : (1) 8 (2) 7 (3) 5 (4) 6
Q22.If ∑5r=0 11C22r2r+2 = mn , gcd(m, n) = 1
Q3. Let α, β, γ and δ be the coefficients of x7, x5, x3 and x respectively in the expansion of 5 5 αu + βv = 18 + , x > 1. If u and v satisfy the equations then u + v equals : (x + √x3 −1) (x −√x3 −1) γu + δv = 20 (1) 5 (2) 3 (3) 4 (4) 8
Q24.The sum of all rational terms in the expansion of (1 + 21/2 + 31/2) 6 is equal to
Q6. The product of all the rational roots of the equation (x2 −9x + 11)2 −(x −4)(x −5) = 3, is equal to (1) 14 (2) 21 (3) 28 (4) 7
NCERT Chapters
- Class 11 Maths Ch 8: Binomial Theorem