If the coefficients of x7 in {\left( {{x^2} + {1 \over {bx}}} ight)^{11}} and x-7 in {\left( {{x} - {1 \over {bx^2}}} ight)^{11}}, b
e 0, are equal, then the value of b is equal to :

Question

If the coefficients of x7 in {\left( {{x^2} + {1 \over {bx}}} ight)^{11}} and x-7 in {\left( {{x} - {1 \over {bx^2}}} ight)^{11}}, b 
e 0, are equal, then the value of b is equal to :

Accepted Answer

Answer: C. 1 Coefficient of x7 in {\left( {{x^2} + {1 \over {bx}}} ight)^{11}} : General Term = {}^{11}{C_r}{({x^2})^{11 - r}}.{\left( {{1 \over {bx}}} ight)^r} = {}^{11}{C_r}{x^{22 - 3r}}.{1 \over {{b^r}}} 22 - 3r = 7 r = 5 	herefore Required Term = {}^{11}{C_5}.{1 \over {{b^5}}}.{x^7} Coefficient of x-7 in {\left( {x - {1 \over {b{x^2}}}} ight)^{11}} : General Term = {}^{11}{C_r}{(x)^{11 - r}}.{\left( { - {1 \over {b{x^2}}}} ight)^r} = {}^{11}{C_r}{x^{11 - 3r}}.{{{{( - 1)}^r}} \over {{b^r}}} 11 - 3r = - 7 	herefore r = 6 	herefore Required Term = {}^{11}{C_6}.{1 \over {{b^6}}}{x^{ - 7}} According to the question, {}^{11}{C_5}.{1 \over {{b^5}}} = {}^{11}{C_6}.{1 \over {{b^6}}} Since, b 
e 0 	herefore b = 1

If the coefficients of x7 in $${\left( {{x^2} + {1 \over {bx}}} \right)^{11}}$$ and x$$-$$7 in $${\left( {{x} - {1 \over {bx^2}}} \right)^{11}}$$, b $$\ne$$ 0, are equal, then the value of b is equal to :

Answer

Explanation

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