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    Question

    A student is required to answer 4 questions out of 12

    questions in an English paper, which are divided into two sections of 6 questions each. If the student is not permitted to attempt more than 3 questions from either of the sections, then in ‘N’ number of ways can the student choose the 4 questions. Which of the following option/s will satisfy the value of (N-43)
    A 20² + 1 Correct Answer Incorrect Answer
    B 256 Correct Answer Incorrect Answer
    C Both a and b Correct Answer Incorrect Answer
    D 1441 Correct Answer Incorrect Answer
    E 400 Correct Answer Incorrect Answer

    Solution

    Case (1) when student attempted 1 question from one section and from another, he attempted 3 questions Number of ways = 6C1 × 6C3 = 6 × 20 = 120 Case (2) when student attempted 2 questions from one section and from another, he attempted 2 questions Number of ways =     6C2 × 6C2 = 15 × 15 = 225 Case (3) when student attempted 3 questions from one section and from another, he attempted 1 question Number of ways =  6C1 × 6C3 = 6 × 20 = 120 N = 120 + 225 + 120 = 465 Required value = 465 – 64 =401

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