List of top Mathematics Questions asked in UP Board X

In the figure, $DE \parallel AC$ and $DF \parallel AE$. Prove that $\dfrac{BF}{FE} = \dfrac{BE}{EC}$.

A solid is a cone standing on a hemisphere with both radii $2$ cm and the slant height of the cone $=2\sqrt{2}$ cm. Find the volume of the solid. (Use $\pi=3.14$)

The shadow of a tower on level ground is $30\ \text{m}$ longer when the sun's altitude is $30^\circ$ than when it is $60^\circ$. Find the height of the tower. (Use $\sqrt{3}=1.732$.)
 

The following table shows the literacy rate (in percent) of 35 cities. Find the mean literacy rate.
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Literacy rate (in \%)} & 45-55 & 55-65 & 65-75 & 75-85 & 85-95 \\ \hline \text{Number of cities} & 3 & 10 & 11 & 8 & 3 \\ \hline \end{array}\]

A spherical glass vessel has a cylindrical neck $8$ cm long, $2$ cm in diameter, and the diameter of the spherical part is $8.5$ cm. Find the volume of water that can be filled in it.
A toy is in the form of a hemisphere surmounting a cone whose radius is $3.5$ cm. If the total height of the toy is $15.5$ cm, find its total surface area and volume.
The shadow of a tower, when the angle of elevation of the sun is $30^\circ$, is $50$ m longer than when the angle of elevation was $60^\circ$ on the plane ground. Find the height of the tower.
A bag contains 5 black, 7 red and 3 white balls. One ball is drawn at random. Find the probability of drawing the ball is (i) red (ii) black (iii) not black.
Find two consecutive positive integers, sum of whose squares is $365$.
Prove that if a straight line is drawn parallel to one side of a triangle to intersect the other two sides in two distinct points, then the other two sides are divided by those points in the same ratio.
Find the length of an arc of a circle of radius $14$ cm which subtends an angle of $30^\circ$ at the centre.
Find the co-ordinates of the point which divides the line segment joining the points $A(3,4)$ and $B(-2,-1)$ in the ratio $3:2$.
Find the value of $x$ for which the distance between the points $(x,2)$ and $(6,5)$ is 5 units.
The area of a rectangular field is $30 \, m^2$. If its length is $1 \, m$ greater than its breadth $x$, then the quadratic equation to find them will be:
When a die is thrown once, the probability of getting an even number will be:
The mean and median of a frequency distribution are $26.1$ and $25.8$ respectively. The value of mode for the distribution will be:
If $\tan 2A = 1$, where $2A$ is an acute angle, the value of $A$ will be:
The value of $(\sec A + \tan A)(1 - \sin A)$ will be:
Distance between two points $(2,3)$ and $(4,1)$ will be:
25th term of an A.P. 6, 10, 14, ... will be:
If one root of the quadratic equation $x^2 + 2x - p = 0$ is $-2$, then the value of $p$ will be:
The solution of a pair of linear equations $2x + y = 5$ and $3x + 2y = 8$ will be:
Which of the following numbers will be a rational number?
The HCF of the numbers 175 and 91 will be:

Prove that $6\sqrt{3}$ is irrational.