IIT-JEE 2009 · Paper 1 · Mathematics Q33

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MathematicsSingle correct+4 / -1Question 33 of 60

Passage

Paragraph for Question Nos. 33 to 35

Let $\mathcal A$ be the set of all $3\times3$ symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices in $\mathcal A$ is

Answer and worked solution

Official answer: A

Count. In a symmetric matrix, off-diagonal 1s come in pairs. With $d$ ones on the diagonal and $p$ off-diagonal pairs, $d+2p=5$ :

$d=1$ , $p=2$ : $3\times\binom32=9$ ;
$d=3$ , $p=1$ : $1\times3=3$ .

Total 12.

(A)

Topics:Special matrices Combinations

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IIT-JEE 2009 · Paper 1, Mathematics question 33