List of top Mathematics Questions asked in UP Board

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 two consecutive positive integers, sum of whose squares is $365$.
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:
The value of $(\sec A + \tan A)(1 - \sin A)$ will be:
The value of $\cos 0^\circ$ will be:
If $\tan 2A = 1$, where $2A$ is an acute angle, the value of $A$ will be:
Area of sector of angle $\theta$ of a circle with radius $r$ will be:
Distance between two points $(2,3)$ and $(4,1)$ will be:
If one root of the quadratic equation $x^2 + 2x - p = 0$ is $-2$, then the value of $p$ will be:
25th term of an A.P. 6, 10, 14, ... 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:
Prime factorisation of 156 will be:

$PQ$ is a chord of length $4\ \text{cm}$ of a circle of radius $2.5\ \text{cm}$. The tangents at $P$ and $Q$ intersect at a point $T$. Find the length of $TP$.
 

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

The common difference of the A.P.: $3,\,3+\sqrt{2},\,3+2\sqrt{2},\,3+3\sqrt{2},\,\ldots$ will be:
 

The discriminant of the quadratic equation $3x^2 - 4\sqrt{3}\,x + 4 = 0$ will be:
 

The number of solutions of the pair of linear equations $\tfrac{4}{3}x + 2y = 8$, $2x + 3y = 12$ will be:
 

In the figure $DE \parallel BC$. If $AD = 3\,\text{cm}$, $DE = 4\,\text{cm}$ and $DB = 1.5\,\text{cm}$, then the measure of $BC$ will be: