List of top Mathematics Questions asked in UP Board

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45°. Find the height of the tower PQ and the distance PX.
A fraction becomes \( \frac{1}{3} \) when 1 is subtracted from the numerator and it becomes \( \frac{1}{4} \) when 8 is added to its denominator. Find the fraction.
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Two cubes of volume 64 cm\(^3\) each are joined end to end to make a solid. Find the surface area of the resulting cuboid.
A sphere of diameter 12 cm is dropped into a right circular cylindrical vessel partly filled with water. If the sphere is emersed completely in the water, the water level in the cylindrical vessel rises by \( \frac{35}{9} \) cm. Find the diameter of the cylindrical vessel.
Find the roots of the equation \( x + \frac{1}{x} = 3, \, x \neq 0 \).
Solve \( 2x + 3y = 11 \) and \( 2x - 4y = -24 \) and hence find the value of \( m \) for which \( y = mx + 3 \).
If a line intersects sides \( AB \) and \( AC \) of a triangle \( ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), prove that \( \frac{AD}{AB} = \frac{AE}{AC} \).
If the median of the frequency distribution given is 28.5, find the values of \( x \) and \( y \) while the total of frequencies is 60.
Find the relation between \( x \) and \( y \) such that the point \( (x, y) \) is equidistant from the points \( (3, 6) \) and \( (-3, 4) \).
Find the distance between the points \( (a, b) \) and \( (-a, -b) \).
The base radius of a right circular cone is 3.5 cm and height is 12 cm. Find the slant height of the cone.
Find two consecutive positive integers, the sum of whose squares is 365.
If \( 2 \cos^2 45^\circ - 1 = \cos \theta \), then find the value of \( \theta \).
Relation between mean, median, and mode will be:
The ratio between the diameters of two circles is \( 4 : 9 \). The ratio between their circumferences will be:
If the radius of a sphere is doubled, then the increase in percentage of its surface area will be:
If \( A = 30^\circ \), then the value of \( \frac{1 + \tan^2 A}{1 + \cot^2 A} \) will be:
If $\sin A = \cos A$, then the value of $A$ will be:
If \( \triangle ABC \) is an equilateral triangle of side \( 2a \), the length of each of its altitudes will be:
The mean of a frequency distribution is \( 24.1 \) and the mode is \( 28 \). Its median will be:
One third of any number is equal to 21. Then the number will be:
The coordinate of the point on the $x$-axis and equidistant from the points $(2, -5)$ and $(-2, 9)$ will be:
If one root of the quadratic equation $x^2 + 2x - p = 0$ is $-2$, then the value of $p$ will be:
The ratio of the areas of two triangles is equal to the square of the ratio of their corresponding sides. Then these triangles will be: