List of top Mathematics Questions asked in UP Board

Which of the following cannot be the probability of any event?
By taking out a hemisphere from both the ends of a wooden solid cylinder, an item is formed. If the height of the cylinder is 10 cm and radius of the base is 3.5 cm, find the total surface area of the item.
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pillar are $45^\circ$ and $60^\circ$ respectively. Find the height of the pillar.
A flagstaff stands on a tower. At a distance 10 m from the tower, the angles of elevation of the top of the tower and flagstaff are $45^\circ$ and $60^\circ$ respectively. Find the length of the flagstaff.
Find the sum of 51 terms of an A.P. whose second and third terms are 14 and 18 respectively.
Solve the following equations: \[ \dfrac{3}{2}x - \dfrac{5}{3}y = -2, \quad \dfrac{x}{3} + \dfrac{y}{2} = \dfrac{13}{6} \]
If the perimeter of a garden of area 800 m$^2$ is 120 m and its length is twice the breadth, then find its length and breadth.
Solve the quadratic equation \(2x^2 - 5x + 3 = 0\).
The sum of the digits of a two-digit number is 9. 9 times of this number is equal to 2 times the number formed by reversing the digits. Find the number.
$D$ is a point on the side $BC$ of a triangle $ABC$ such that $\angle ADC = \angle BAC$. Prove that $CA^2 = CB \cdot CD$.

Find the mode from the following table: 

Prove that $\sqrt{3}$ is an irrational number.

Find the median from the following frequency distribution: 

Prove that $\dfrac{1 + \sin \theta}{\cos \theta} + \dfrac{\cos \theta}{1 + \sin \theta} = 2 \sec \theta$.

The median class of the following table will be: 

The mean from the following table will be: 

The HCF of the numbers 182 and 78 will be
The tangent PQ of a circle of radius 5 cm meets at a point Q on the line passing through the centre O. If OQ = 12 cm, then the measure of PQ will be
An arc of a circle of radius 6 cm subtends an angle of $30^\circ$ at the centre. The measure of the corresponding arc will be

In the figure, in $\triangle MNL$ and $\triangle PQR$, $\angle M = \angle Q = 70^\circ$, $MN = 3$ cm, $ML = 4.5$ cm, $PQ = 2$ cm, and $QR = 3$ cm. Then, the following correct relation will be: 

The surface area of a sphere of diameter $\dfrac{1}{2}$ cm will be

In the figure, if \(DE \parallel BC\), then the measure of \(CE\) will be: 

Find the total surface area of the given figure where $AB = 3.5 \text{ cm}$ and height of the toy $CD = 5 \text{ cm.}$ 

On seeing from the top of a multi-storeyed building, the angles of depression of the top and the ground of an 8 metre high house are found to be 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between both the buildings.
A person takes a loan of Rs. 3,250. He paid Rs. 20 in the first month and then increased Rs. 15 in the payment of every month. Find in how many months he paid the loan.