List of practice Questions

The measure of central tendency is :
The distance between the points \( (2, y) \) and \( (10, 3) \) is 10 units. Find the value of \( y \).
The mean of \( x \) and \( \frac{1}{x} \) is \( M \). Find the mean of \( x^3 \) and \( \frac{1}{x^3} \).
If \( \tan(2A) = \cot(A - 18^\circ) \), where \( 2A \) is an acute angle, then find the value of \( A \).
A perpendicular is drawn from the vertex to the base of an equilateral triangle of side a. The measure of the perpendicular will be:
The whole surface area of a solid hemisphere of diameter \( \frac{1}{2} \) cm will be :
An arc of a circle of radius 6 cm subtends an angle of \( 60^\circ \) at the centre. The area of the sector will be:
The hypotenuse and base of a right triangle are 7.5 cm and 4.5 cm respectively. The measure of the perpendicular side will be:
The median of side AB of an equilateral triangle ABC is CD. The value of \( CD^2 \) will be:
The arithmetic mean of the weight of 12 persons is 45.6 kg. The sum of their weights will be :
The arithmetic mean of 3, 4, 6 and \( x \) is 5. Then the value of \( x \) will be :
From the given numbers the prime number will be:
For any positive integer \( q \), every positive integer will be in the form of:

If\( \sin (A + B) = \frac{\sqrt{3}}{2}\) and \( \cos (A - B) = \frac{\sqrt{3}}{2}\), then the values of A and B respectively will be:
 

The value of \[ \frac{1 - \tan^2 30^\circ}{1 + \tan^2 30^\circ} will be: \]
If one root of the equation \( x^2 - 4x + k = 0 \) is 6, then the value of \( k \) will be:
The sum of two numbers is 24 and one of them is twice the other. The numbers respectively will be:
The areas of two similar triangles are in the ratio 81:121. The ratio of their sides will be:
Solve the following equation: \[ 2\left( \frac{2x - 1}{x + 3} \right) - 3\left( \frac{x + 3}{2x - 1} \right) = 5, \quad x \neq 3, \frac{1}{2}. \]
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.
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 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 \( \sqrt{3} = 1.732 \))
A metallic solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm. Thus, how many such cones will be made?
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.

In the decimal expansion of \(\frac{731}{625}\),  the number of digits will be: