J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer
    The number of even numbers of three digits which can be formed with digits \[0,1,\text{ }2,\text{ }3,4\] and 5 (no digit being used more than once) is

    A)  \[60\]             

    B)  \[92\]

    C)  \[52\]             

    D)  \[48\]

    Correct Answer: C

    Solution :

    The three digit number is termed, if unit place is either 0, 2 or 4. Case I when 0 is in unit place, then number of ways \[{{=}^{5=20}}{{P}_{2}}\] Case II    When 2 or 4 in unit place, then number of ways \[{{=}^{5}}{{p}_{2}}{{\times }^{2}}{{C}_{1}}=40\] Now, we have to subtract those case in which 0 is in hundred place. If 0 is in hundred place and 2 or 4 in unit place, then number of ways \[{{=}^{4}}{{C}_{1}}{{\times }^{2}}{{C}_{1}}=8\] \[\therefore \] Required number of ways \[=20+40-8=52\]


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