JEE Main & Advanced JEE Main Paper (Held On 10 April 2015)

  • question_answer
    Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is : JEE Main Online Paper (Held On 10 April 2015)

    A) \[\frac{({{2}^{10}}-1)}{{{2}^{20}}}\]                         

    B) \[\frac{({{2}^{10}}-1)}{{{2}^{10}}}\]

    C) \[\frac{^{20}{{C}_{10}}}{{{2}^{10}}}\]                     

    D) \[\frac{^{20}{{C}_{10}}}{{{2}^{20}}}\]

    Correct Answer: D

    Solution :

                     Required probability is\[\frac{{{\left( ^{10}{{C}_{0}} \right)}^{2}}+{{\left( ^{10}{{C}_{1}} \right)}^{2}}{{\left( ^{10}{{C}_{2}} \right)}^{2}}+.........{{\left( ^{10}{{C}_{10}} \right)}^{2}}}{{{2}^{10}}}\] \[\frac{^{20}{{C}_{10}}}{{{2}^{10}}}\]


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