List of top Questions asked in UP Board

A solid sphere is made by melting the three metallic solid spheres of diameters 12 cm, 16 cm and 20 cm. Find the diameter of this solid sphere.

The distance between the points $P(2, -3)$ and $Q(10, v)$ is 10 units. The value of $v$ will be:

Find the median from the following table:

Find the co-ordinates of the point divided by x-axis to the line segment joining the points \( (1, -5) \) and \( (-4, 5) \).

Find the coordinates of the point A, where AB is the diameter of a circle whose center is \( (2, -3) \) and the coordinates of B are \( (1, 4) \).

Find the value of \( k \) for which the equations \( 2x + ky = 1 \) and \( 3x - 5y = 7 \) have a unique solution.

Solve the following pair of equations using the cross-multiplication method: \[ 2x + 3y - 46 = 0 \] \[ 3x + 5y - 74 = 0 \]

Draw a line segment of length 76 cm and divide it in the ratio 3:4. Write the measures of both the two parts.

If \( \cos \theta = \frac{4}{5} \), find the value of \( \sin \theta \cos \theta + \tan^2 \theta \).

Find the value of \( f \) from the following frequency table if 25 is the mean of marks obtained by the students:

The dimensions of a metallic solid cuboid are \( 9 \, \text{m} \times 8 \, \text{m} \times 2 \, \text{m} \). It is melted and recast into cubes of dimension 2 m. Thus the number of cubes so formed will be:

The mean of the following table will be:

If the arithmetic mean and mode of the given data are 28 and 16 respectively, the median will be:

The modal class of the following frequency distribution will be:

The median class of the following frequency distribution will be:

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

Two cubes each of volume 64 cm\(^3\) are joined end to end to form a cuboid. Find the total surface area of the resulting cuboid.

In \( \triangle ABC \) if \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm, and \( BC = 6 \) cm, then measure of \( \angle B \) will be:

Areas of two similar triangles are in the ratio $16 : 25$. The ratio of corresponding sides of the triangles will be:

In the figure, \( AB = 3 \) cm, \( AC = 6 \) cm, \( BD = 2 \) cm and \( CD = 4 \) cm. The ratio of \( \angle BAD \) and \( \angle CAD \) will be:

The value of $\frac{\sin 31^\circ}{\cos 59^\circ}$ will be:

In the figure, the angles of depressions of point O as seen from points A and P are:

If the circumference and the area of a circle are numerically equal, the radius of the circle will be:

The sum of powers of prime factors of the factorization of the number 144 will be:

Given that LCM of \( (132, 288) = 3168 \), then HCF of \( (132, 288) \) will be: