In the expansion of (x2– 2x)10 , the coefficient of x16 is(A) -1680(

1.	In the expansion of (x2– 2x)10 , the coefficient of x16 is(A) -1680(B) 1680(C) 3360(D) 6720
Answer» (C) 3360 (x² – 2x)¹⁰ = x¹⁰ (x – 2)¹⁰ To get the coefficient of x¹⁶ in (x – 2x)¹⁰, we need to check coefficient of x⁶ in (x – 2)¹⁰ ∴ Required coefficient = ¹⁰C₆ (-2)⁴ = 210 × 16 = 3360

In the expansion of (x2– 2x)10 , the coefficient of x16 is(A) -1680(B) 1680(C) 3360(D) 6720

Answer»

(C) 3360

(x² – 2x)¹⁰ = x¹⁰ (x – 2)¹⁰

To get the coefficient of x¹⁶ in (x – 2x)¹⁰,

we need to check coefficient of x⁶ in (x – 2)¹⁰

∴ Required coefficient = ¹⁰C₆ (-2)⁴

= 210 × 16

= 3360