CUET · MATHS · PYQ PAPER 2025
If \(A=\left[\begin{array}{cc}3 & 2 a \\ 1 & 5\end{array}\right]\) and \(B=\left[\begin{array}{ll}2 & 3 \\ b & 5\end{array}\right]\) are singular matrices, then \(a+b\) is :
- A \(\frac{6}{65}\)
- B \(\frac{67}{6}\)
- C \(\frac{65}{6}\)
- D \(\frac{1}{66}\)
Answer & Solution
Correct Answer
(C) \(\frac{65}{6}\)
Step-by-step Solution
Detailed explanation
\(\det(A) = (3)(5) - (2a)(1) = 0\) \(15 - 2a = 0 \implies a = \frac{15}{2}\) \(\det(B) = (2)(5) - (3)(b) = 0\) \(10 - 3b = 0 \implies b = \frac{10}{3}\) \(a+b = \frac{15}{2} + \frac{10}{3}\) \(a+b = \frac{45 + 20}{6}\) \(a+b = \frac{65}{6}\)
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