List of top Questions asked in UP Board

The angle of depression of the two ships from the top of a lighthouse are \( 30^\circ \) and \( 45^\circ \). If one ship is exactly behind the other on the same side of the lighthouse and are 50 metres apart from each other, find the height of the lighthouse from the sea level.
Find the arithmetic mean from the following table:
Find the median from the following frequency distribution: \[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency}
\hline 10 - 25 & 3
25 - 40 & 10
40 - 55 & 20
55 - 70 & 13
70 - 85 & 4
\hline \end{array} \]
The mean of the following table will be:
If the circumference of a circle is equal to the perimeter of a square, the ratio of their areas will be:
A rectangular sheet of paper 40 cm \( \times \) 22 cm is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder will be:
The median class of the following table will be:
If mean and median of a distribution are 24.5 and 26 respectively, then its mode will be:
Without doing the actual long division process, find if the expansion of the rational number \( \frac{637}{7280} \) is a terminating or non-terminating repeating decimal. Give reasons for your answer.
If \( \sin 3A = \cos (A - 26^\circ) \), where \( 3A \) is an acute angle, find the value of \( A \).
The radius of the base of a cone is 3.5 cm and the height is 12 cm. Find the slant height of the cone.
The discriminant of the equation $3x^2 - 2x + \frac{1}{3} = 0$, will be:
In the given figure, \( DE \) is drawn parallel to base \( BC \) of triangle \( ABC \). If \( DB = 7.2 \) cm, \( AE = 1.8 \) cm, and \( EC = 5.4 \) cm, then the value of \( AD \) will be:
Heights of two similar triangles are 3 cm and 4 cm respectively. Ratio of the areas of the triangles will be:
In the figure, the area of sector OAB will be:
The value of \( 2 \tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ \) will be:
The value of \( \cos^2 67^\circ - \sin^2 23^\circ \) will be:
In a triangle ABC, $\angle C = 90^\circ$ and $\tan A = \frac{1}{\sqrt{3}}$. The value of the following will be: \[ \sin A \cos B + \cos A \sin B \]
In the decimal expansion of the number $\frac{129}{125}$, the number of digits will be:
If LCM of 26, 156 is 156, then the value of HCF will be:
The largest number which divides 245 and 1037, leaving remainder 5 in each case, will be:
If one root of the equation $2x^2 + ax + 6 = 0$ is 2, then the value of $a$ will be:
If the sum and difference of two numbers are 8 and 2 respectively, the numbers will be:
The roots of equation \( 4x^2 - 12x + 9 = 0 \) will be:
Distance between two points \( (2, 3) \) and \( (4, 1) \) will be: