Question

The coefficient of x¹³ in the expansion of (1 – x)⁵ (1 + x + x² + x³) 4 is

(a)  4 

(b)  –4 

(c)   0 

(d)   none of these 

Answer 1

Correct option  (a)  4

Explanation:

Coefficient of x¹³ in = (1 – x)⁵ (1 + x + x² + x³) 4 = (1 – x)⁵ ((1 + x)(1 + x²))⁴

= (1 – x) {(1 – x)(1 + x)(1 + x² )}4

= (1 – x) {(1 – x⁴)⁴ 

= (1 – x) (1 – 4x⁴  + 6x⁸ – 4x¹² + x¹⁶) 

∴  coefficient of x¹³ is  –1 x – 4 = 4