List of practice Questions

A well of 3 meter in diameter is dug to a depth of 14 meter. An embankment is made by spreading the soil out of it, making a circular ring of 4 meters wide, evenly around the well. Find the height of the embankment.
A hollow sphere whose inner and outer diameters are 4 cm and 8 cm respectively is melted to form a cone whose base is 8 cm in diameter. Find the slant height and curved surface area of the cone.
Discriminant of the quadratic equation \( 3x^2 - 6x + 4 = 0 \) will be:
Solution of equations \( 3x + 2y = 6 \) and \( y = 0 \) will be:
Find the median of the following data:
Find the coordinates of the point which divides the line segment formed by joining the points \( (-1, 7) \) and \( (4, -3) \) in the ratio \( 2 : 3 \).
For what value of \( K \), points \( (K, -1) \), \( (2, 1) \), and \( (4, 5) \) will be on the same line?
Show through graphical method that the linear equation system \( 3x - y = 2 \) and \( 9x - 3y = 6 \) have infinite number of solutions.
The sum of the digits of a two-digit number is 9. If the digits of the number are interchanged, then the new number will exceed the original number by 27. Find the number.
Construct \( \triangle ABC \) in which \( BC = 6 \, \text{cm} \), \( AB = 3 \, \text{cm} \), and \( \angle ABC = 45^\circ \). Construct a similar triangle \( A'B'C' \) whose corresponding sides are \( \frac{3}{4} \) of the sides of \( \triangle ABC \). Write the steps of construction in brief.
In the figure, if \( BD \perp AC \) and \( CE \perp AB \), prove that \( \triangle AEC \sim \triangle ADB \).
Find the arithmetic mean from the following frequency table:
Find the mode of the following data:
Which one of the following is not a measure of central tendency?
The arithmetic mean of natural numbers 1 to 9 will be:
In a given frequency distribution, if the mean is 15 and the median is 16, then its mode will be:
Median of the first 10 natural numbers will be:
Prove that \(5 + \sqrt{3}\) is an irrational number.
If \( \cos A = \frac{\sqrt{3}}{2} \), then find the value of \( \sin 2A \).
Prove that the twice of the volume of a cylinder is equal to the product of its radius of base and curved surface.
If the corresponding sides of two similar triangles are in the ratio 3:5, the ratio of their areas will be:
If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the triangle will be:
The perimeter of two similar triangles are 10 cm and 15 cm respectively, find the ratio of their areas.
If \( \tan \theta = \frac{8}{15} \), then the value of \( \csc \theta \) will be:
If \( 2 \cos 3\theta = 1 \), then the value of \( \theta \) will be: