JEE Main & Advanced Sample Paper JEE Main - Mock Test - 7

  • question_answer
    If the coefficient of 4th term in the expansion of \[{{\left( x+\frac{\alpha }{2x} \right)}^{n}}\]is 20, then the respective values of \[\alpha \]and n are

    A) \[2,7\]                          

    B) \[5,8\]     

    C) \[3,6\]                          

    D) \[2,6\]

    Correct Answer: D

    Solution :

    \[{{T}_{4}}{{=}^{n}}{{C}_{3}}\,{{x}^{n-3}}{{\left( \frac{\alpha }{2x} \right)}^{3}}{{\Rightarrow }^{n}}{{C}_{3}}\,{{x}^{n-6}}{{\left( \frac{\alpha }{2} \right)}^{3}}=20\] If \[n=6,\] then \[^{6}{{C}_{3}}{{\left( \frac{\alpha }{2} \right)}^{3}}=20\Rightarrow \alpha =2\]


You need to login to perform this action.
You will be redirected in 3 sec spinner