10 Question MCQ (including Assertion)

If \(\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 7 & 3\end{array}\right|\), then value of \(x\) is

Let \(f(t)=\left|\begin{array}{ccc}\cos t & t & 1 \\ 2 \sin t & t & 2 t \\ \sin t & t & t\end{array}\right|\), then \(\lim _{t \rightarrow 0} \frac{f(t)}{t^2}\) is equal to

There are two values of \(a\) which makes determinant, \(\Delta=\left|\begin{array}{ccc}1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a\end{array}\right|=86\), then sum of these number is

If A, B and C are angles of a triangle, then the determinant \(\left|\begin{array}{ccc}-1 & \cos \mathrm{C} & \cos \mathrm{B} \\ \cos \mathrm{C} & -1 & \cos \mathrm{~A} \\ \cos \mathrm{~B} & \cos \mathrm{~A} & -1\end{array}\right|\) is equal to

The number of distinct real roots of \(\left|\begin{array}{ccc}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\) in the interval \(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is

If A and B are invertible matrices, then which of the following is not correct?

The value of the determinant \(\left|\begin{array}{ccc}x & x+y & x+2 y \\ x+2 y & x & x+y \\ x+y & x+2 y & x\end{array}\right|\) is

If \(f(x)=\left|\begin{array}{ccc}0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0\end{array}\right|\), then

If \(x, y, z\) are all different from zero and \(\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z\end{array}\right|=0\), then value of \(x^{-1}+y^{-1}+z^{-1}\) is