Q33 / 60 · JEE Advanced 2009 (Paper 1) · Mathematics

Paragraph: Let $A$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are 0 .Question: The number of matrices in $A$ is

  • Correct answer
    A
    12
  • B
    6
  • C
    9
  • D
    3

Solution

Case $I$ When all three diagonal elements are 1 , then Number of matrices $={ }^3 C_1=3$ Case II When two diagonal elements are zero and one element is one no, then Number of matrices $={ }^3 C_1 \cdot{ }^3 C_1=9$ $\therefore$ Total matrices $=3+9=12$

Hence, the correct answer is option: 'A'.

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