1. If Δ = \(\left[\begin{array}{cc}10 & 2 \\30 & 6\end{array}\right]\) then A =

2. A = \(\left[\begin{array}{ll}\alpha & q \\q & \alpha\end{array}\right]\) |A³| = 125 then α =

3. The area of a triangle with vertices (-3, 0) (3, 0) and (0, k) is 9 sq. units. The value of k will be

4. Let f(t) = \(\left[\begin{array}{ccc}cot t & t & 1 \\2 sin t & t & 2t \\sin t & t & t\end{array}\right]\) then \(_{t→0}^{lim}\) \(\frac{f(t)}{t^2}\) is equal to

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

6. If x, y, z are all different from zero and

7. Evaluate the determinant Δ = \(\left|\begin{array}{cc}log_{3}512 & log_{4}3 \\log_{3}8 & log_{4}9\end{array}\right|\)

8. \(\left|\begin{array}{cc}x & -7 \\x & 5 x+1\end{array}\right|\)

9. \( \left|\begin{array}{cc}\cos \theta & -\sin \theta \\\sin \theta & \cos \alpha\end{array}\right|\)

10. \( \left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\\sin 75^{\circ} & \cos 75^{\circ}\end{array}\right|\)