2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Solved Paper-2017

  • question_answer
    The value of  \[({{\,}^{21}}{{C}_{1}}-{{\,}^{10}}{{C}_{1}})+({{\,}^{21}}{{C}_{2}}-{{\,}^{10}}{{C}_{2}})+\] \[({{\,}^{21}}{{C}_{3}}-{{\,}^{10}}{{C}_{3}})+({{\,}^{21}}{{C}_{4}}-{{\,}^{10}}{{C}_{4}})+....+\] \[({{\,}^{21}}{{C}_{10}}-{{\,}^{10}}{{C}_{10}})\]is:-     JEE Main Solved Paper-2017

    A)  \[{{2}^{20}}-{{2}^{10}}\]                              

    B)  \[{{2}^{21}}-{{2}^{11}}\]

    C)  \[{{2}^{21}}-{{2}^{10}}\]                              

    D)  \[{{2}^{20}}-{{2}^{9}}\]

    Correct Answer: A

    Solution :

     \[({{\,}^{21}}{{C}_{1}}{{+}^{21}}{{C}_{2}}.....+{{\,}^{21}}{{C}_{10}})\]                 \[-({{\,}^{10}}{{C}_{1}}{{+}^{10}}{{C}_{2}}.....{{\,}^{10}}{{C}_{10}})\]              \[=\frac{1}{2}[({{\,}^{21}}{{C}_{1}}+....+{{\,}^{21}}{{C}_{10}})+({{\,}^{21}}{{C}_{11}}+....{{\,}^{21}}{{C}_{20}})]\]                 \[-({{2}^{10}}-1)\]                 \[=\frac{1}{2}[{{2}^{21}}-2]-({{2}^{10}}-1)\] \[=({{2}^{20}}-1)-({{2}^{10}}-1)={{2}^{20}}-{{2}^{10}}\]


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