List of top Questions asked in UP Board

If ratio of volumes of two spheres is \( 27 : 64 \), then ratio of their surface areas will be:

If mode and mean of some observations are 45 and 27 respectively, then median will be:

The roots of the equation \( x^2 - 2x + 1 = 0 \) will be:

If \( C \left( \frac{\alpha}{8}, 4 \right) \) is the mid-point of the line joining the points \( A(-4, 2) \) and \( B(5, 6) \), then the value of \( \alpha \) will be:

If \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm and \( BC = 6 \) cm in triangle \( ABC \), then the value of \( \angle B \) will be:

The biggest number which divides 125 and 70, and gives remainder 8 and 5 respectively will be:

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

If the length of diagonals of a rhombus are 12 cm and 16 cm, then the length of the side of the rhombus will be:

If \( \sin \theta = \cos \theta \), \( 0^\circ \leq \theta \leq 90^\circ \), then the value of \( \theta \) is:

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

Solve the following pair of equations by converting these into linear pair of equations: \[ \frac{1}{2x} - \frac{1}{3y} = 2, \quad \frac{1}{3x} + \frac{1}{2y} = \frac{13}{16}. \]

Sum of areas of two squares is 117 m\(^2\). If the difference between their perimeters is 12 m, then find the sides of both the squares.

From the top of a tower 60 meters high, the angles of depression of top and bottom of a building (house) are 45° and 60° respectively. Find the height of the building and its distance from the tower.

Two poles of equal height are placed opposite to each other on either side of a road 80 meters wide. From a point on the road between these two poles, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distance from the point from the poles.

A well of 3 meter in diameter is dug to a depth of 14 meter. An embankment is made by spreading the soil out of it, making a circular ring of 4 meters wide, evenly around the well. Find the height of the embankment.

A hollow sphere whose inner and outer diameters are 4 cm and 8 cm respectively is melted to form a cone whose base is 8 cm in diameter. Find the slant height and curved surface area of the cone.

Discriminant of the quadratic equation \( 3x^2 - 6x + 4 = 0 \) will be:

Solution of equations \( 3x + 2y = 6 \) and \( y = 0 \) will be:

Find the median of the following data:

Find the coordinates of the point which divides the line segment formed by joining the points \( (-1, 7) \) and \( (4, -3) \) in the ratio \( 2 : 3 \).

For what value of \( K \), points \( (K, -1) \), \( (2, 1) \), and \( (4, 5) \) will be on the same line?

Show through graphical method that the linear equation system \( 3x - y = 2 \) and \( 9x - 3y = 6 \) have infinite number of solutions.

The sum of the digits of a two-digit number is 9. If the digits of the number are interchanged, then the new number will exceed the original number by 27. Find the number.

Construct \( \triangle ABC \) in which \( BC = 6 \, \text{cm} \), \( AB = 3 \, \text{cm} \), and \( \angle ABC = 45^\circ \). Construct a similar triangle \( A'B'C' \) whose corresponding sides are \( \frac{3}{4} \) of the sides of \( \triangle ABC \). Write the steps of construction in brief.

In the figure, if \( BD \perp AC \) and \( CE \perp AB \), prove that \( \triangle AEC \sim \triangle ADB \).