The positive value of for which the coefficient of in the expression is 720, is
- A.3
- B.
- C.
- D.4
Show answer and solution
Correct option: D
Solution
The general term of (√x + λ/x²)10 is C(10,r)(√x)^(10-r)(λ/x²)r = C(10,r)λr · x^((10-r)/2 - 2r).
Multiplying by x² (from the x² outside), the power of x becomes (10-r)/2 - 2r + 2 = (14-5r)/2.
For coefficient of x², set (14-5r)/2 = 2 → 14-5r = 4 → r = 2.
The coefficient is C(10,2)·λ² = 45λ² = 720 → λ² = 16 → λ = 4.
Multiplying by x² (from the x² outside), the power of x becomes (10-r)/2 - 2r + 2 = (14-5r)/2.
For coefficient of x², set (14-5r)/2 = 2 → 14-5r = 4 → r = 2.
The coefficient is C(10,2)·λ² = 45λ² = 720 → λ² = 16 → λ = 4.
[JEE Main 2019 · 10 Jan · Shift II]