JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q29

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MathematicsInteger+4 / -1Question 29 of 90

Let A be a $3\times3$ matrix having entries from the set $\{-1,0,1\}$ . The number of all such matrices A having sum of all the entries equal to 5, is ______.

Your answer

Answer and worked solution

Official answer: 414

Count. With $p$ ones and $m$ minus-ones, $p-m=5$ and $p+m\le9$ .

$m=0,p=5$ : $\binom95=126$ .
$m=1,p=6$ : $\dfrac{9!}{6!\,1!\,2!}=252$ .
$m=2,p=7$ : $\dfrac{9!}{7!\,2!}=36$ .

Total 414.

Answer: 414

Topics:Distribution and arrangements Matrix algebra

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 29