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JEE MAIN Mathematics QUESTION #963
Question 1
In a group of 3 girls and 4 boys, there are two boys \(B_1\) and \(B_2\). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \(B_1\) and \(B_2\) are not adjacent to each other, is:
  • 96
  • 144✔️
  • 120
  • 72
Correct Answer Explanation
Girls together: \(3!\) ways. Boys together: \(4!\) ways. Two blocks arranged: \(2!\) ways. Total \(= 2! \times 3! \times 4! = 2 \times 6 \times 24 = 288\). Cases where \(B_1, B_2\) adjacent: treat them as one unit → \(2! \times 3! \times 3! \times 2! = 144\). Required \(= 288 - 144 = 144\).