An unbiased six-faced dice whose faces are marked with numbers $1,2,3,4,5$, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is $\_\_\_\_$
Which one of the following options is correct for the given data in the table?
| Iteration ($i$) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Input ($I$) | 20 | $-$4 | 10 | 15 |
| Output ($X$) | 20 | 16 | 26 | 41 |
| Output ($Y$) | 20 | $-$80 | $-$800 | $-$12000 |
In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.
What is the area (in $\mathrm{cm}^2$ ) of the rectangle PLMN?
Note: The figure shown is representative
In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point $P$ and line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?
Note: The figure shown is representative.
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