The Math Factory
1. Quadratic equation in one variable
2. Simple interest calculation
3. Theorems related to circles
4. Cuboid
5. Ratio and proportion
6. Compound interest and growth rate
7. Theorem related to angle in a circle
8. Right circular cylinder
9. Quadratic factorization
10. Theorem related to cyclic quadrilateral
11. Construction: Drawing the circumcircle and incircle of a triangle
12. Sphere
13. Variation
14. Partnership business
15. Theorem related to tangent to a circle
16. Right circular cone
17. Construction: Drawing a tangent to a circle
18. Similarity
19. Real-life problems related to different solid shapes
20. Trigonometry: Concept of angle measurement
21. Construction: Finding the mean proportional
22. Pythagoras theorem
23. Trigonometric ratios and trigonometric identities
24. Trigonometric ratios of complementary angles
25. Application of trigonometric ratios: Height and distance
26. Statistics: Mean, Median, Ogive, Mode
🧠Challenge | Solve Random 10 | Refresh To Regenerate
Q1.
15 farmers can cultivate 18 bighas of land in 5 days. Using the theory of proportion, determine how many days 10 farmers will take to cultivate 12 bighas of land.
Q2.
Find the median from the following data: | Class Interval | 5–10 | 10–15 | 15–20 | 20–25 | 25–30 | 30–35 | 35–40 | 40–45 | |----------------|------|-------|-------|-------|-------|-------|-------|-------| | Frequency | 5 | 6 | 15 | 10 | 5 | 4 | 3 | 2 |
Q3.
Write whether the number \(\sqrt{7}\) is a rational number or an irrational number, with explanation.
Q4.
If \((\sqrt{a} + \sqrt{b}) \propto (\sqrt{a} - \sqrt{b})\), then show that \((a + b) \propto \sqrt{ab}\).
Q5.
If \(x = y(\csc\theta + \cot\theta)\) and \(z = y(\csc\theta - \cot\theta)\), then which of the following relationships is correct?
Q6.
If five times a positive integer is 3 less than twice its square, then what is the value of that number?
Q7.
If \(\alpha\) and \(\beta\) are the two roots of the quadratic equation \(3x^2 + 2x - 5 = 0\), then find the value of \(\cfrac{\alpha^2}{\beta} + \cfrac{\beta^2}{\alpha}\).
Q8.
Two equal chords of a circle are equidistant from the center.
Q9.
Due to a decrease in the annual simple interest rate from 4% to 3\(\cfrac{3}{4}\)%, Mr. Amal's annual income is reduced by ₹60. Find Mr. Amal's principal.
Q10.
The simple interest on ₹400 for 5 years and on ₹600 for 4 years together amounts to ₹132. If the rate of interest is the same in both cases, find the rate of interest.