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JEE Main 7-April-2025 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 7-April-2025 Paper - Shift 14 Marks
Question
The number of singular matrices of order 2, whose elements are from the set $\{2,3,6,9\}$ is
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Answer

36
$\left|\begin{array}{ll}\mathrm{a} & \mathrm{d} \\ \mathrm{b} & \mathrm{c}\end{array}\right|=\mathrm{ad}-\mathrm{bc} \Rightarrow \mathrm{ad}=\mathrm{bc}$
Case-I Exactly 1 no. is used
$\Rightarrow$ All singular $={ }^{4} C_{1}$
Case-II Exactly 2 no. is used
$\Rightarrow{ }^{4} \mathrm{C}_{2} \times 2 \times 2$
Case-III Exactly 3 no. is used
None will be singular
Case-IV Exactly 4 No. is used
$\mathrm{ad}=\mathrm{bc}$
$\Rightarrow 2 \times 9=3 \times 6$
$\left|\begin{array}{cc}9 & - \\ - & 2\end{array}\right| \Rightarrow{ }^{4} \mathrm{C}_{1} \times 21$
Total $=36$

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