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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 4 · Set 2 · Q21
Using matrices and determinants, find the value(s) of k for which the pair of equations 5 x - ky =2; 7 x -5 y =3 has a unique solution.
Using matrices and determinants, find the value(s) of k for which the pair of equations $\displaystyle 5 \mathrm{x}-\mathrm{ky}=2 ; 7 \mathrm{x}-5 \mathrm{y}=3$ has a unique solution.
Marking-scheme solution
For uniquesolution, $\displaystyle \left|\begin{array}{cc} 5 & -k \\ 7 & -5 \end{array}\right| \neq 0$
\[\Rightarrow-25+7 k \neq 0 \Rightarrow k \neq \frac{25}{7} \text { or } R-\left\{\frac{25}{7}\right\}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.