List of top Questions asked in UP Board X

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.

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

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

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

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

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

If \( \sin\theta = \dfrac{3}{4} \), then the value of \( \tan\theta \) will be:

The value of \( (\csc A + \cot A)(1 - \cos A) \) will be:

The value of \( \dfrac{1 - \tan^2 A}{1 - \cot^2 A} \) will be:

Prove that \( \dfrac{1 + \sec A}{\sec A} = \dfrac{\sin^2 A}{1 - \cos A} \).

A chord of a circle of radius 21 cm subtends a right angle at the centre. Find the area of the corresponding minor segment.

If one root of the equation \( x^2 - kx - 8 = 0 \) is 2, then the value of \( k \) will be:

Find the 20th term of the Arithmetic Progression (A.P.) 10, 7, 4, …

A tangent PQ at a point P of a circle of radius 10 cm meets a line through the centre O at a point Q so that OQ = 12 cm. The length of PQ will be:

If two cubes each of volume 8 cm\(^3\) are joined end-to-end, then the surface area of the resulting cuboid will be:

If the area of a sector of a circle of radius 14 cm is 154 cm\(^2\), then the angle of the sector will be:

The value of \( 2\sin30^\circ \cos30^\circ \) is:

One card is drawn from a well-shuffled pack of 52 cards. The probability of getting a face card is:

The difference of a rational number and an irrational number is:

Which of the following numbers is a rational number?

The distance between the points (a, b) and (b, -a) will be:

The sum of the zeroes of the quadratic polynomial \( 4x^2 - 4x + 1 \) will be:

The number of solutions of the pair of linear equations \( x - y = 8 \) and \( 3x - 3y = 16 \) will be:

Given that LCM (12, 21) = 84, HCF (12, 21) will be:

A box contains 6 blue, 4 white, and 8 red marbles. If a marble is drawn at random, find the probability that it is blue.