List of top Mathematics Questions

The distance between the points (x, y) and (-x, -y) will be:

From the top of a building 60 metres high, the angles of depression of the top and bottom of a tower are observed to be \( 30^\circ \) and \( 60^\circ \) respectively. Find the height of the tower.

A copper rod of diameter 1 cm and 8 cm length is stretched to form a wire of uniform thickness with length 18 m. Find the thickness of the wire.

A bird is sitting on an 80 m high tree. The angle of elevation of the bird is \( 45^\circ \) from a point on the ground. The bird now flies horizontally such that its height from the ground remains same. After 2 seconds the angle of elevation of the bird from the same point becomes \( 30^\circ \). Find the speed of the flying bird. (Use \( \sqrt{3} = 1.732 \))

The sum of a two-digit number and the number obtained by reversing the order of its digits is 66. If the difference of the two digits is 2, find the number.

Solve the following equation: \[ 2\left( \frac{2x - 1}{x + 3} \right) - 3\left( \frac{x + 3}{2x - 1} \right) = 5, \quad x \neq 3, \frac{1}{2}. \]

Find the median from the following frequency distribution: \[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency}
\hline 10 - 25 & 3
25 - 40 & 10
40 - 55 & 20
55 - 70 & 13
70 - 85 & 4
\hline \end{array} \]

Find the discriminant of the quadratic equation \( 2x^2 - 4x + 3 = 0 \) and then find the nature of the roots.

The angle of depression of the two ships from the top of a lighthouse are \( 30^\circ \) and \( 45^\circ \). If one ship is exactly behind the other on the same side of the lighthouse and are 50 metres apart from each other, find the height of the lighthouse from the sea level.

If the arithmetic mean of the following frequency distribution is 21.5, find the value of \( p \).

Find the relation between \( x \) and \( y \) if the point \( (x, y) \) is equidistant from the points \( (3, 6) \) and \( (-3, 4) \).

Construct \( \triangle ABC \), in which \( BC = 6 \, \text{cm} \), \( AB = 4.5 \, \text{cm} \) and \( \angle ABC = 60^\circ \). Then construct another triangle whose sides are \( \frac{3}{4} \) times the corresponding sides of \( \triangle ABC \).

The sum of the square of two consecutive positive even numbers (integers) is 340. Find the numbers.

Find the arithmetic mean from the following table:

Find the ratio in which the point \( (-1, 6) \) divides the line segment joining the points \( (-3, 10) \) and \( (6, -8) \).

If the circumference of a circle is equal to the perimeter of a square, the ratio of their areas will be:

If \( \sin 3A = \cos (A - 26^\circ) \), where \( 3A \) is an acute angle, find the value of \( A \).

A rectangular sheet of paper 40 cm \( \times \) 22 cm is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder will be:

The radius of the base of a cone is 3.5 cm and the height is 12 cm. Find the slant height of the cone.

Without doing the actual long division process, find if the expansion of the rational number \( \frac{637}{7280} \) is a terminating or non-terminating repeating decimal. Give reasons for your answer.

If mean and median of a distribution are 24.5 and 26 respectively, then its mode will be:

The mean of the following table will be:

The median class of the following table will be:

The discriminant of the equation $3x^2 - 2x + \frac{1}{3} = 0$, will be:

In a triangle ABC, $\angle C = 90^\circ$ and $\tan A = \frac{1}{\sqrt{3}}$. The value of the following will be: \[ \sin A \cos B + \cos A \sin B \]