List of top Mathematics Questions asked in UP Board

By observing from the top of a multi-storeyed building, the angle of depression of the top and bottom of a 4 m high building are \( 30^\circ \) and \( 45^\circ \) respectively. Find the height of the multi-storeyed building and the distance between both the buildings.

Find the median of the following frequency distribution:

Prove that \( \sqrt{2} \) is an irrational number.

Given that HCF(255, 867) = 51, find the value of LCM(255, 867).

Construct a triangle of sides 4 cm, 5 cm, and 6 cm, and again construct another corresponding triangle whose sides are \( \frac{2}{3} \) of the corresponding sides of the previous triangle.

In a right triangle \( ABC \), angle \( B \) is a right angle and \( BD \) is perpendicular on \( AC \). Prove that: \( AB^2 = AC \cdot AD \).

Find the mode from the following table:

The product of the age of Punita 2 years ago and her age after 4 years from now is 1 year more than twice her present age. Find her present age.

Solve the following equation: \[ \frac{1}{x} - \frac{1}{x-2} = 3, \quad x \neq 0, 2. \]

Find two positive even consecutive numbers, the sum of whose squares is 340.

The mean and median of a frequency distribution are 26.1 and 25.8 respectively. The value of mode for the distribution will be :

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 discriminant of the quadratic equation \( x - \frac{1}{x} = 1 \) will be:

The area of a rectangular field is 30 m². If its length is 1 m greater than its breadth, then the quadratic equation to find them will be:

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 \( A \).

The arithmetic mean of 3, 4, 6 and \( x \) is 5. Then the value of \( x \) will be :

The median of side AB of an equilateral triangle ABC is CD. The value of \( CD^2 \) 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 arithmetic mean of the weight of 12 persons is 45.6 kg. The sum of their weights will be :

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 hypotenuse and base of a right triangle are 7.5 cm and 4.5 cm respectively. The measure of the perpendicular side will be:

For any positive integer \( q \), every positive integer will be in the form of: