Mathematics – Class 12 Mock Test 2

1. Evaluate \(\begin{vmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{vmatrix}\)

2. Find the value of x, if \(\begin{vmatrix}2&5\\3&x\end{vmatrix}\)=\(\begin{vmatrix}x&-1\\5&3\end{vmatrix}\).

3. Which among the below matrices has the inverse A^-1=\(\begin{bmatrix}1&-\frac{5}{8}\\0&\frac{1}{8}\end{bmatrix}\)

4. What is the value of \(\begin{vmatrix}sin^2 ⁡a & sina\, cosa & cos^2 ⁡a \\sin^2 ⁡b & sinb\, cosb & cos^2 ⁡b \\sin^2⁡ c & sinc\, cosc & cos^2⁡ c \end {vmatrix}\)?

5. The following operation is applied on a matrix A=\(\begin{bmatrix}2&3\\6&4\end{bmatrix}\)
R₁→R₁+R₂
Which of the following will be the resulting new matrix?

6. If A=\(\begin{bmatrix}cos⁡x&-sin⁡x&-cos⁡x\\sin⁡x&-cos⁡x&sin⁡x \end{bmatrix}\). Find A'A.

7. Evaluate |A|²-5|A|+1, if A=\(\begin{bmatrix}7&4\\5&5\end{bmatrix}\)

8. If A=\(\begin{bmatrix}1&0\\0&1\end{bmatrix}\), then which of the following statement is incorrect?

9. Evaluate \(\begin{vmatrix}5&4&3\\3&4&1\\5&6&1\end{vmatrix}\).

10. Evaluate \(\begin{vmatrix}-sinθ&-1\\1&sin⁡θ\end{vmatrix}\).