2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced AIEEE Solved Paper-2003

  • question_answer
    If \[^{n}{{C}_{r}}\] denotes the number of combinations of n things taken r at a time, then the expression \[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r-1}}+2{{\times }^{n}}{{C}_{r}}\] equals     AIEEE  Solved  Paper-2003

    A)                         \[^{n+2}{{C}_{r}}\]                         

    B) \[^{n+2}{{C}_{r+1}}\]                    

    C) \[^{n+1}{{C}_{r}}\]                                         

    D) \[^{n+1}{{C}_{r+1}}\]

    Correct Answer: B

    Solution :

    \[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r}}{{=}^{n}}{{C}_{r+1}}\]. Now,         \[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r-1}}+{{2}^{n}}{{C}_{r}}\]                     \[{{=}^{n+1}}{{C}_{r+1}}{{+}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}\]                     \[{{=}^{n+1}}{{C}_{r+1}}{{+}^{n+1}}{{C}_{r}}\]                     \[{{=}^{n+2}}{{C}_{r+1}}\]


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