MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Signals Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For the following set of simultaneous equations 1.5x-0.5y=2, 4x+2y+3z=9, 7x+y+5=10. |
| A. | The solution is unique |
| B. | Infinitely many solutions exist |
| C. | The equations are incompatible |
| D. | Finite number of multiple solutions exist |
| Answer» B. Infinitely many solutions exist | |
| 2. |
If a square matrix B is skew symmetric then. |
| A. | BT = -B |
| B. | BT = B |
| C. | B-1 = B |
| D. | B-1 = BT |
| Answer» B. BT = B | |
| 3. |
Given A=\(\begin{bmatrix}2 & -0.1 \\0 & 3 \\\end{bmatrix} A^{-1} = \begin{bmatrix}1/2 & a \\0 & b \\\end{bmatrix}\) then find a + b. |
| A. | \(\frac{6}{20}\) |
| B. | \(\frac{7}{20}\) |
| C. | \(\frac{8}{20}\) |
| D. | \(\frac{5}{20}\) |
| Answer» C. \(\frac{8}{20}\) | |
| 4. |
The rank of the matrix (m × n) where m |
| A. | m |
| B. | n |
| C. | m*n |
| D. | m-n |
| Answer» B. n | |
| 5. |
Find the rank of the matrix A=\(\begin{bmatrix}1 & 3 & 5\\4 & 6 & 7\\1 & 2 & 2\\\end{bmatrix}\). |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» B. 2 | |
| 6. |
Find the adjacent A as A=\(\begin{bmatrix}1 & 7 & -3\\5 & 4 & -2\\6 & 8 & -6\\\end{bmatrix}\). |
| A. | \(\begin{bmatrix}1 & 1 & 1\\1 & 2 & 3\\2 & 3 & 4\\\end{bmatrix}\) |
| B. | \(\begin{bmatrix}31 & 39 & 80\\39 & 45 & 74\\80 & 74 & 136\\\end{bmatrix}\) |
| C. | \(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\\\end{bmatrix}\) |
| D. | \(\begin{bmatrix}35 & 34 & 32\\56 & 67 & 48\\98 & 74 & 52\\\end{bmatrix}\) |
| Answer» C. \(\begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\\\end{bmatrix}\) | |
| 7. |
Given the equations are 4x+2y+z=8, x+ y+ z=3, 3x+y+3z=9. Find the values of x, y and z. |
| A. | 5/3, 0, 2/3 |
| B. | 1, 2, 3 |
| C. | 4/3, 1/3, 5/3 |
| D. | 2, 3, 4 |
| Answer» B. 1, 2, 3 | |
| 8. |
Find the inverse of the matrix \(A = \begin{bmatrix}8 & 5 & 2\\4 & 6 & 3\\7 & 4 & 2\\\end{bmatrix}\). |
| A. | \(\frac{1}{13}*\begin{bmatrix}90 & 65 & 80\\65 & 61 & 54\\80 & 58 & 69\\\end{bmatrix}\) |
| B. | \(\frac{1}{14}*\begin{bmatrix}93 & 68 & 80\\68 & 61 & 58\\80 & 58 & 69\\\end{bmatrix}\) |
| C. | \(\frac{1}{13}*\begin{bmatrix}94 & 67 & 80\\67 & 60 & 56\\80 & 58 & 69\\\end{bmatrix}\) |
| D. | \(\frac{1}{13}*\begin{bmatrix}93 & 68 & 80\\68 & 61 & 58\\80 & 58 & 69\\\end{bmatrix}\) |
| Answer» E. | |
| 9. |
The matrix A is represented as \(\begin{bmatrix}1 & 4 \\-2 & 9 \\-3 & -8 \\\end{bmatrix}\). The transpose of the matrix of this matrix is represented as? |
| A. | \(\begin{bmatrix}1 & 4 \\-2 & 9 \\\end{bmatrix}\) |
| B. | \(\begin{bmatrix}1 & 4 \\-2 & 9 \\-3 & 8 \\\end{bmatrix}\) |
| C. | \(\begin{bmatrix}1 & -2 & -3\\4 & 9 & 8\\\end{bmatrix}\) |
| D. | \(\begin{bmatrix}-1 & 2 & 3\\-4 & -9 & 8\\\end{bmatrix}\) |
| Answer» D. \(\begin{bmatrix}-1 & 2 & 3\\-4 & -9 & 8\\\end{bmatrix}\) | |
| 10. |
Find the values of x, y, z and w from the below condition.\(5\begin{bmatrix}x & z \\y & w \\\end{bmatrix} = \begin{bmatrix}2 & 10 \\3 & 2x+y \\\end{bmatrix} + \begin{bmatrix}z & 5 \\7 & w \\\end{bmatrix} \). |
| A. | x=1, y=3, z=4, w=0 |
| B. | x=2, y=3, z=8, w=1 |
| C. | x=1, y=2, z=3, w=1 |
| D. | x=1, y=2, z=4, w=1 |
| Answer» E. | |