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Let's go through the mathematical problems visible in the image:

### Question 21:
**"How many pairs of intersecting lines are there in the given figure?"**
- The figure shows five lines: \( p, q, r, s, t \). To count the intersecting pairs of lines, we can observe that each pair of distinct lines can potentially intersect once, given the general position.

There are five lines, and the number of ways to choose 2 lines from 5 is calculated using combinations:
\[
\text{Number of pairs} = \binom{5}{2} = \frac{5(5-1)}{2} = 10
\]
Therefore, **the correct answer is 10**. However, the options only go up to "more than 6", so the correct answer would be **D. More than 6**.

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### Question 22:
**"Which of the following is TRUE about the shaded fraction of the given figures?"**
- Two triangular grids are shown. In each triangle, several smaller triangles are shaded.

- In the first triangle, there are **16 small triangles in total**, and **4 of them are shaded**.
- In the second triangle, there are **36 small triangles in total**, and **9 of them are shaded**.

Therefore, for both figures:
- The fraction of shaded triangles in the first figure is \( \frac{4}{16} = \frac{1}{4} \).
- The fraction of shaded triangles in the second figure is \( \frac{9}{36} = \frac{1}{4} \).

Hence, the shaded fraction is **the same for both figures**, so the correct answer is **C. X = Y**.

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### Question 23:
**"Which of the following options shows the number written in the International system of numeration?"**
- The options provided are:
    - A. 54,683,391
    - B. 985,200,003
    - C. 575,318,200
    - D. 530,911,712

The correct answer depends on the proper comma placement according to the International numeration system, which groups digits in sets of three, starting from the right. All of the numbers provided are correctly formatted in the International system, but since the question likely asks for the largest number, the correct choice is **B. 985,200,003**.

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Would you like more detailed explanations for any specific question, or any further clarifications?

Here are some additional related questions to explore:
1. How are combinations calculated for intersecting lines in complex figures?
2. What are the differences between the International and Indian number systems?
3. How do we calculate fractions for irregularly shaded shapes?
4. Can you explain the concept of pairwise intersections in geometry?
5. How does the placement of commas differ in various numeral systems?

**Tip:** When calculating intersections, always ensure that the lines intersect in distinct points to avoid overcounting intersections that coincide at a single point.

How many pairs of intersecting lines are there in the given figure? Which of the following is TRUE about the shaded fraction of the given figures? Which of the following options shows the number written in the International system of numeration?

Explore the mathematical solution to counting pairs of intersecting lines, understanding shaded fractions in figures, and identifying numbers in the International system of numeration. This problem involves geometry, fractions, and numeral systems, suitable for students in Grades 6-8.

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