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प्रश्न
Complite the following table given that x varies directly as y .
| x | 3 | 5 | 7 | 9 |
| y | ... | 20 | 28 | ... |
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उत्तर
\[\text{ Here, x and y vary directly } . \]
\[ \therefore x = ky\]
\[x = 5 \text{ and } y = 20\]
\[i . e . , 5 = k \times 20\]
\[ \Rightarrow k = \frac{5}{20} = \frac{1}{4}\]
\[\text{ For x = 3 and } k = \frac{1}{4}, \text{ we have:} \]
\[3 = \frac{1}{4} \times y\]
\[ \Rightarrow y = 4 \times 3 = 12\]
\[\text{ For } x = 9, k = \frac{1}{4}, \text{ we have: } \]
\[x = ky\]
\[ \Rightarrow 9 = \frac{1}{4} \times y\]
\[ \Rightarrow y = 9 \times 4 = 36\]
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A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of the base that need to be added.
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| parts of base | 8 | .... | .... | .... | .... |
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| Mixture C | Mixture D |
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Match each of the entries in Column I with the appropriate entry in Column II
| Column I | Column II |
| 1. x and y vary inversely to each other | A. `x/y` = Constant |
| 2. Mathematical representation of inverse variation of quantities p and q |
B. y will increase in proportion |
| 3. Mathematical representation of direct variation of quantities m and n |
C. xy = Constant |
| 4. When x = 5, y = 2.5 and when y = 5, x = 10 | D. `p oo 1/q` |
| 5. When x = 10, y = 5 and when x = 20, y = 2.5 | E. y will decrease in proportion |
| 6. x and y vary directly with each other | F. x and y are directly proportional |
| 7. If x and y vary inversely then on decreasing x | G. `m oo n` |
| 8. If x and y vary directly then on decreasing x | H. x and y vary inversely |
| I. `p oo q` | |
| J. `m oo 1/n` |
