List of top Mathematics Questions asked in UP Board

If a tangent $PQ$ at a point $P$ of a circle of radius $5 \,\text{cm}$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \,\text{cm}$, then length of $PQ$ will be:
 

The product of $\sqrt{2}$ and $(2-\sqrt{2})$ will be:
 

The value of $\dfrac{1+\cot^2 \theta}{1+\tan^2 \theta}$ will be:
 

If $3 \cot A = 4$, then the value of $\dfrac{1 - \tan^2 A}{1 + \tan^2 A}$ will be:
 

The modal class of the following table will be: 
\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class Interval} & 0\text{--}5 & 5\text{--}10 & 10\text{--}15 & 15\text{--}20 & 20\text{--}25 \\ \hline \text{Frequency} & 2 & 7 & 11 & 8 & 6 \\ \hline \end{array} \]

The median class of the following frequency distribution will be: 
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-Interval} & \text{$0$--$10$} & \text{$10$--$20$} & \text{$20$--$30$} & \text{$30$--$40$} & \text{$40$--$50$} \\ \hline \text{Frequency} & \text{$7$} & \text{$8$} & \text{$15$} & \text{$10$} & \text{$5$} \\ \hline \end{array}\]

A die is thrown once, the probability of getting an even number will be:

If $\tan \theta = \tfrac{3}{4}$, then the value of $\cos \theta$ will be:
 

A cubical block of side $14\,$cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. (Use $\pi=3.14$)
Prove that \(\displaystyle \frac{\sin\theta-\cos\theta+1}{\sin\theta+\cos\theta-1}=\sec\theta+\tan\theta\).
The length of a rectangular field is 9 m more than the twice of its width. If the area of the field is $810 \, m^2$, find the length and width of the field.
Find the ratio in which Y-axis divides the line segment joining the points $(5,-6)$ and $(-1,-4)$.
A chord of a circle of radius 14 cm subtends an angle of $120^\circ$ at the centre. Find the area of the corresponding segment of the circle.
Prove that \[ \sqrt{\frac{1-\cos\theta}{1+\cos\theta}} = \csc\theta - \cot\theta \]
If sum of first 9 terms of an $A.P.$ is $81$ and the sum of first $17$ terms is $289$, find its first term and the common difference.
Find the zeroes of the quadratic polynomial $x^2-5$ and verify the relationship between the zeroes and the coefficients.
One card is drawn from a well-shuffled pack of 52 cards, find the probability of getting:
(i) A king of red colour
(ii) A face card
If point $Q(0,1)$ is equidistant from points $P(5,-3)$ and $R(x,6)$, find the values of $x$.
The zeroes of quadratic polynomial $6x^2 - 7x - 3$ will be:
The angle of a sector of a circle with radius of 6 cm is $60^\circ$. The area of the sector will be:
The distance between the points $(2,3)$ and $(4,1)$ will be:
The $LCM$ of the numbers 12, 15 and 21 will be:
A solid is made by joining corresponding faces of two cubes each of side 10 cm. The surface area of the resulting cuboid will be:
If $LCM(35, 63) = 315$, the $HCF(35, 63)$ will be:
The value of $\cos 60^\circ$ is: