A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with \( U \leq 4 \) is:

We are asked to find how many pixels have intensities less than or equal to 4.
Let’s go through the matrix and count the number of pixels that satisfy \( U \leq 4 \).
The given matrix of pixel intensities is:

Row 1: 0, 1, 0, 2 (all are $\leq 4$) - Count: 4 Row 2: 4, 7, 3, 3 (4, 3, 3 are $\leq 4$) - Count: 3 Row 3: 5, 5, 4, 4 (4, 4 are $\leq 4$) - Count: 2 Row 4: 6, 7, 3, 2 (3, 2 are $\leq 4$) - Count: 2 \end{itemize} Total count: $4 + 3 + 2 + 2 = 11$
A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with \( U \leq 4 \) is:

The error matrix resulting from randomly selected test pixels for a classified image is given below. The Producer’s accuracy of class 1 is __________ % (rounded off to 1 decimal place).
| Reference Data | |||||
|---|---|---|---|---|---|
| Class 1 | Class 2 | Class 3 | Class 4 | ||
| Classified Data | Class 1 | 320 | 8 | 7 | 3 |
| Class 2 | 12 | 270 | 6 | 2 | |
| Class 3 | 9 | 6 | 410 | 5 | |
| Class 4 | 14 | 2 | 3 | 350 | |
The brightness values of four pixels in the input image are shown in the table below. The image is rectified using nearest neighbor intensity interpolation, and the pixel at location \( (5, 4) \) in the output image is to be filled with the value from coordinate \( (5.3, 3.7) \) in the input image. The brightness value of the pixel at location \( (5, 4) \) in the rectified output image is __________ (Answer in integer).
| Location of pixels in input image (Row, Column) | Brightness Value |
|---|---|
| (5, 3) | 9 |
| (5, 4) | 11 |
| (6, 3) | 14 |
| (6, 4) | 12 |
Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is _________ (rounded off to two decimal places).
A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is _________ (rounded off to two decimal places).
A prismatic vertical column of cross-section \( a \times 0.5a \) and length \( l \) is rigidly fixed at the bottom and free at the top. A compressive force \( P \) is applied along the centroidal axis at the top surface. The Young’s modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of \( P \) for yielding and for buckling of the column are equal, the value of \( \frac{l}{a} \) is __________ (rounded off to one decimal place).
A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is ___________ rad/s (answer in integer).
A jet-powered airplane is steadily climbing at a rate of 10 m/s. The air density is 0.8 kg/m³, and the thrust force is aligned with the flight path. Using the information provided in the table below, the airplane’s thrust to weight ratio is ___________ (rounded off to one decimal place). 