If the coefficients of x^7 in (x^2 + 1/x)^11 and x ^-7 in (x^2-+1/bx)^11 are equal, then the value of b is equal to:

Question

If the coefficients of x⁷ in \(\left({\text{x}} ^2 + \frac{1}{{\text{x}}}\right)^{11}\) and x^–7 in \(\left({\text{x}} ^2 + \frac{1}{b{\text{x}}}\right)^{11}\) are equal, then the value of b is equal to:

(1) 2

 (2) -1

(3) 1

(4) -2

Answer 1

Correct option (3) 1

Coefficient of x⁷ in \(\left( x^2 + \frac{1}{bx} \right)^{11}\)

Coefficient of x^–7 in \(\left( x + \frac{b}{bx^2} \right)^{11}\)

Since b \(\neq\) 0 \(\therefore\) b = 1