Mathematics - Class 12 Practice Test 2

1. Find the inverse of matrix A=\(\begin{bmatrix}5&1&3\\4&2&6\\5&4&2\end{bmatrix}\)

\(\begin{bmatrix}\frac{1}{3}&\frac{1}{6}&0\\\frac{11}{30}&\frac{1}{12}&\frac{3}{10}\\-\frac{1}{10}&\frac{1}{4}&\frac{1}{10}\end{bmatrix}\)

\(\begin{bmatrix}\frac{1}{3}&-\frac{1}{6}&0\\-\frac{11}{30}&\frac{1}{12}&\frac{3}{10}\\-\frac{1}{10}&\frac{1}{4}&-\frac{1}{10}\end{bmatrix}\)

\(\begin{bmatrix}0&-\frac{1}{6}&0\\-\frac{11}{30}&\frac{1}{12}&\frac{3}{10}\\-\frac{1}{10}&\frac{1}{4}&-\frac{1}{10}\end{bmatrix}\)

\(\begin{bmatrix}\frac{1}{3}&-\frac{1}{6}&0\\-\frac{11}{30}&1&\frac{3}{10}\\-\frac{1}{10}&\frac{1}{4}&-\frac{1}{10}\end{bmatrix}\)

2. How many elementary operations are possible on Matrices?

3. The inverse of the matrix A=\(\begin{bmatrix}1&2&4\\5&2&4\\3&6&2\end{bmatrix}\) is

\(\begin{bmatrix}\frac{-1}{4}&\frac{1}{4}&0\\ \frac{1}{40}&\frac{-1}{8}&\frac{1}{5}\\ \frac{3}{40}&1&\frac{-1}{10}\end{bmatrix}\)

\(\begin{bmatrix}\frac{-1}{4}&\frac{1}{4}&0\\ \frac{1}{40}&\frac{-1}{8}&\frac{1}{5}\\ \frac{3}{40}&0&\frac{-1}{10}\end{bmatrix}\)

\(\begin{bmatrix}\frac{-1}{4}&-\frac{1}{4}&0\\ \frac{1}{40}&\frac{1}{8}&\frac{-1}{5}\\ \frac{3}{40}&0&\frac{-1}{10}\end{bmatrix}\)

\(\begin{bmatrix}\frac{-1}{4}&\frac{1}{4}&1\\ \frac{1}{40}&\frac{-1}{8}&\frac{1}{5}\\ \frac{3}{40}&0&\frac{-1}{10}\end{bmatrix}\)

4. What will be the value of \(\begin{vmatrix}cos^2⁡ θ & cosθ \, sinθ & -sinθ \\cosθ\, sinθ & sin^2⁡θ & cosθ \\sinθ & -cosθ & 0 \end {vmatrix}\)?

-1

5. Which of the following elementary operations has been applied to the matrix A=\(\begin{bmatrix}8&5\\2&8\end{bmatrix}\) such that the new matrix is \(\begin{bmatrix}12&21\\2&8\end{bmatrix}\)?

R₁→R₁+2R₂

R₁→R₁-2R₂

R₁→R₂+R₁

R₁→2R₁+R₂

6. Evaluate \(\begin{vmatrix}8x+1&2x-2\\x^2-1&3x+5\end{vmatrix}\).

-2x³-26x²-45x+3

-2x³+26x²+45x-3

-2x³-26x²+45x+3

-2x³+26x²+45x+3

7. What will be the value of \(\begin{vmatrix}2bc - a^2 & c^2 & b^2 \\c^2 & 2ac - b^2 & a^2 \\b^2 & a^2 & 2ab - c^2 \end {vmatrix}\) if given another determinant \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?

(a³ + b³ + c³ – 3abc)²

–(a³ + b³ + c³ – 3abc)²

–(a³ + b³ + c³ + 3abc)²

(a³ + b³ + c³ + 3abc)²

8. If A'=\(\begin{bmatrix}8&2\\6&4\end{bmatrix}\) and B'=\(\begin{bmatrix}9&5\\7&3\end{bmatrix}\). Find (A+2B)'.

\(\begin{bmatrix}26&20\\10&12\end{bmatrix}\)

\(\begin{bmatrix}26&12\\20&10\end{bmatrix}\)

\(\begin{bmatrix}26&10\\20&12\end{bmatrix}\)

\(\begin{bmatrix}26&20\\12&10\end{bmatrix}\)

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

cos⁡2θ

cos⁡θ

cos²⁡θ

-cos²⁡θ

10. Evaluate \(\begin{vmatrix}cos⁡θ&-cos⁡θ&1\\sin^2⁡θ&cos^2⁡θ&1\\sin⁡θ&-sin⁡θ&1\end{vmatrix}\).

-sin⁡θ-cos²⁡⁡θ

sin⁡θ-cos²⁡⁡θ

sin⁡θ+cos²⁡θ

-sin⁡θ+cos²⁡⁡θ