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Questions and Answers
For a sample data, mean = 60 and median = 48. What is the mode?
For a sample data, mean = 60 and median = 48. What is the mode?
- 8√3 cm
- 6√3 cm
- 4√3 cm (correct)
- 11√3 cm
Find the sum of the roots and the product of the roots in the following equation: $x^2 + 3x + 7 = 0$
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?
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?
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?
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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