List of practice Questions

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

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

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

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

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

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

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 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.

Find the arithmetic mean from the following table:

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

The mean of the following table will be:

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

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 median class of the following table will be:

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

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

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.

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

In the given figure, \( DE \) is drawn parallel to base \( BC \) of triangle \( ABC \). If \( DB = 7.2 \) cm, \( AE = 1.8 \) cm, and \( EC = 5.4 \) cm, then the value of \( AD \) will be:

Heights of two similar triangles are 3 cm and 4 cm respectively. Ratio of the areas of the triangles will be:

In the figure, the area of sector OAB will be:

The value of \( 2 \tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ \) will be:

The value of \( \cos^2 67^\circ - \sin^2 23^\circ \) will be:

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