Q121. What will be the value of x if \( \begin{vmatrix} 1-x & 2 \\ 2 & 5-x \end{vmatrix} =0 \)

Q122. For a given system of equations if \(|A|=0\) and \((adj A)B≠O\) (zero matrix), then which of the following is correct regarding the solutions of the given equations?

Q123. \(\Rightarrow\) Let \(A_{a\times b}\) and \(B_{c\times d}\) be two matrices, then if \(AB\) exists, the order of \(AB\) is \(_{-----------}\).

Q124. Let \(A=[a_{ij} ]\) be an \(m\times n\) matrix and \(k\) be a scalar then \(kA\) is equal to \(_{-----------}\).

Q125. Find the minor and cofactor respectively for the element 3 in the determinant \( \Delta = \begin{vmatrix} 1 & 5 \\ 3 & 2 \end{vmatrix} \).

Q126. Find the \(\frac{d}{dx} (log_e \sqrt{x^2+a^2})\).

Q127. If \(A = \begin{bmatrix}1 & 4 \\ 3 & 2 \end{bmatrix}\) and \(B = \begin{bmatrix}1 & 4 \\ 2 & 3 \end{bmatrix} \) find \(2A-3B \)

Q128. What is the derivative of the function \(f(x) = x^3+4^x+2^3\) with respect to \(x\)?

Q129. Value of \( \begin{vmatrix} \log_{12}4 & -1 \\ \log_{12}3 & 1 \end{vmatrix} = _{----------}\)

Q130. Which of the following property of matrix multiplication is correct?