List of top Questions asked in UP Board X

The areas of two similar triangles are in the ratio 81:121. The ratio of their sides will be:

From the given numbers the prime number will be:

For any positive integer \( q \), every positive integer will be in the form of:

If one root of the equation \( x^2 - 4x + k = 0 \) is 6, then the value of \( k \) will be:

The sum of two numbers is 24 and one of them is twice the other. The numbers respectively will be:

From the top of a building 60 metres high, the angles of depression of the top and bottom of a tower are observed to be \( 30^\circ \) and \( 60^\circ \) respectively. Find the height of the tower.

A bird is sitting on an 80 m high tree. The angle of elevation of the bird is \( 45^\circ \) from a point on the ground. The bird now flies horizontally such that its height from the ground remains same. After 2 seconds the angle of elevation of the bird from the same point becomes \( 30^\circ \). Find the speed of the flying bird. (Use \( \sqrt{3} = 1.732 \))

The distance between the points (x, y) and (-x, -y) will be:

A metallic solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm. Thus, how many such cones will be made?

A copper rod of diameter 1 cm and 8 cm length is stretched to form a wire of uniform thickness with length 18 m. Find the thickness of the wire.

Solve the following equation: \[ 2\left( \frac{2x - 1}{x + 3} \right) - 3\left( \frac{x + 3}{2x - 1} \right) = 5, \quad x \neq 3, \frac{1}{2}. \]

The sum of a two-digit number and the number obtained by reversing the order of its digits is 66. If the difference of the two digits is 2, find the number.

If the arithmetic mean of the following frequency distribution is 21.5, find the value of \( p \).

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 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 ratio in which the point \( (-1, 6) \) divides the line segment joining the points \( (-3, 10) \) and \( (6, -8) \).

Find the relation between \( x \) and \( y \) if the point \( (x, y) \) is equidistant from the points \( (3, 6) \) and \( (-3, 4) \).

Find the discriminant of the quadratic equation \( 2x^2 - 4x + 3 = 0 \) and then find the nature of the roots.

The sum of the square of two consecutive positive even numbers (integers) is 340. Find the numbers.

Construct \( \triangle ABC \), in which \( BC = 6 \, \text{cm} \), \( AB = 4.5 \, \text{cm} \) and \( \angle ABC = 60^\circ \). Then construct another triangle whose sides are \( \frac{3}{4} \) times the corresponding sides of \( \triangle ABC \).

The mean of the following table 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: