List of top Mathematics Questions asked in UP Board

The length of the minute hand of a clock is \( r \) cm. The area of the sector swept by the minute hand in one minute will be:

The whole surface area of a solid hemisphere of diameter \( \dfrac{1}{2} \, \text{cm} \) will be:

The value of \( (\sec A + \tan A)(1 - \sin A) \) will be:

The value of \( \dfrac{\sin 15^\circ}{\cos 75^\circ} \) will be:

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

The nature of the roots of the equation \( 2x^2 - 5x + 4 = 0 \) will be:

If \( \sin \theta - \cos \theta = 0 \), then the value of \( \sin^4 \theta + \cos^4 \theta \) will be:

Two triangles are said to be similar to each other:

The distance between the points (5, 0) and (-12, 0) will be:

The coordinates of the point on the x-axis and equidistant from the points (5, -2) and (-3, 2) will be:

The sum of first 15 multiples of 8 will be:

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

The least number which when divided by 35, 56 and 91 leaves the same remainder 7 in each case will be:

Which one of the following is a pair of co-prime numbers?

If LCM of 26, 156 is 156, then the value of HCF will be:

The angles of depression of the top and bottom of a 10 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building.

If the sum of the first 8 terms of an A.P. is 64 and the sum of its first 17 terms is 289, then find the first term and the common difference of the progression.

A spherical glass vessel has a cylindrical neck 7 cm long and diameter 2 cm, while the diameter of the spherical part is 8.4 cm. Find how much water can be filled in the vessel.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

A die is thrown once. Find the probability of getting: (i) A prime number. (ii) A number lying between 2 and 6.

Find the values of \( y \) for which the distance between the points (5, -3) and (13, y) is 10 units.

Solve the following pair of linear equations:
\( 0.2x + 0.3y = 1.3 \) and \( 0.4x - 0.5y = -0.7 \).

Find the zeroes of the quadratic polynomial \( 3x^2 - x - 4 \) and verify the relationship between the zeroes and the coefficients.

Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3 : 1 internally.

D is a point on the side BC of a triangle ABC such that \( \angle ADC = \angle BAC \). Prove that \( CA^2 = CB \times CD \).