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Questions and Answers
For a sample data, mean = 60 and median = 48. What is the mode?
Find the sum of the roots and the product of the roots in the following equation: $x^2 + 3x + 7 = 0$
Sum = -3, Product = 7
If a and $eta$ are the roots of the quadratic equation $x^2 - 5x + k = 0$ and $a - eta = 1$, what is k?
k = 6
If the length of each median of an equilateral triangle is $6√3$ cm, what is the perimeter of the triangle?
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A cube has a length of 25 cm. How many cubes with sides 5 cm fit inside it?
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Study Notes
Circle in a Square
- A circle is inscribed in a square whose diagonal is 12√2 cm.
- An equilateral triangle is inscribed in the circle.
- The length of the side of the triangle needs to be calculated.
Roots of a Quadratic Equation
- The sum and product of the roots of the equation x² + 3x + 7 = 0 are needed.
- The equation x² - 5x + k = 0 has roots α and β.
- Given that α - β = 1, the value of k needs to be determined.
Equal Roots of a Quadratic Equation
- The value of k needs to be found for which the roots of the quadratic equation 9x² + 8(k - 5)x + 64 = 0 are equal.
Median of an Equilateral Triangle
- The length of each median of an equilateral triangle is given as 6√3 cm.
- The perimeter of the triangle needs to be determined.
Mode of a Distribution
- For a data set, the mean is 60 and the median is 48.
- The mode of the distribution needs to be determined.
Famine Relief Fund
- A group of boys raised ₹400 for a famine relief fund.
- Each boy contributed as many 25 paise coins as there were boys.
- The number of boys needs to be determined.
Cube Dimensions
- A cube has a side length of 25 cm.
- The number of smaller cubes with sides of 5 cm that can be made from the larger cube needs to be calculated.
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Description
Test your knowledge on advanced geometry and quadratic equations. This quiz covers topics such as calculating side lengths in inscribed shapes, solving for roots, and exploring properties of triangles and distributions. Challenge your comprehension of these mathematical concepts!
