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JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    Direction: (Q. Nos. 90) For the following questions, the correct answers from the codes (a), (b), (c) and (d) defined as follows.
    In onto functions, each image must be assigned at least one preimage. Statement I Let \[E=\,\{1,\,\,2,\,\,3,\,\,4\}\] and \[F=\,\{\,a,\,\,b\},\] then the number of onto function from E to F is 14. Statement II Number of ways in which 4 distinct object can be distribution in two different boxes is 14, if no box remain empty.

    A)  Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.

    B)  Statement I is true, Statement II is also true and Statement II is not the correct explanation of Statement I.

    C)  Statement I is true, Statement II is false.

    D)  Statement I is false, Statement II is true.

    Correct Answer: A

    Solution :

     Now, if we consider the images a and b as two diffent boxes, then four distinct objects 1, 2, 3, and 4 (preimage) can be distributed in \[{{2}^{4}}{{-}^{4}}{{C}_{1}}{{(2-1)}^{4}}=16-2=14\]. Hence, both statements are true and statement II is the correct explanation of statement I.


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