List of top Mathematics Questions

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around the well in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then prove that the two triangles are similar.
Solve: \[ \frac{4}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 3 \] \[ \frac{8}{\sqrt{x}} - \frac{9}{\sqrt{y}} = 1 \]
The distance of the point \( (-3, 5) \) from the y-axis will be:
BL and CM are medians of a triangle ABC, right-angled at A. Prove that \( 4(BL^2 + CM^2) = 5BC^2 \).
A motor boat, whose speed is 18 km/hour in still water, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Find the mean of the following frequency distribution:
In the figure, AB and CD are two perpendicular diameters of a circle with center O. OD is the diameter of the smaller circle. If OA = 7 cm, find the ratio of the areas of the smaller and larger circles.
Find the coordinates of the points which divide the line segment \( AB \) joining points \( A (-2, 2) \) and \( B (2, 8) \) into four equal parts.
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of new fraction and the original fraction is \( \frac{29}{20} \). Find the original fraction.
The sum of the digits of a two-digit number is 9. Nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at the angle of depression of \( 30^\circ \), which is approaching the foot of the tower with a uniform speed. After 6 seconds the angle of depression of the car is found to be \( 60^\circ \). Find the time taken by the car to reach the foot of the tower from this point.
Find the H.C.F. of 867 and 255 using Euclid's division algorithm.
Show that any positive odd integer is of the form \( 4q + 1 \) or \( 4q + 3 \), where \( q \) is some integer.
Find the mode of the following data:
Draw a circle of radius 3.0 cm. From a point 7.0 cm away from its centre, construct the pair of tangents to the circle. Write the steps of the construction in brief.
The roots of the quadratic equation $x^2 - 3x - 10 = 0$ are:
Find the discriminant of the quadratic equation \( 4x^2 - 6x + 5 = 0 \) and hence find the nature of its roots.
If \( \triangle ABC \) is an equilateral triangle such that \( AD \perp BC \), then \( AD^2 \) is equal to:
The number of solid spheres, each of diameter $6$ cm, that can be made by melting a solid metal cylinder of height $45$ cm and diameter $4$ cm is:
If \( \cos(A - B) = \frac{\sqrt{3}}{2} \) and \( \sin(A + B) = \frac{\sqrt{3}}{2} \), where \( 0^\circ<(A + B) \leq 90^\circ \) and \( A>B \), then find the values of \( A \) and \( B \).
Find the median of the following frequency distribution:
If the length of shadow of a tower on the plane ground is \( \sqrt{3} \) times of its height, the angle of elevation of the sun is:
If mean and mode of a grouped data are 24 and 12 respectively, then its median is:
If the radii of two circles are 4 cm and 3 cm respectively, then the radius of the circle having area equal to the sum of the areas of these circles is: