List of top Questions asked in UP Board X

Irrational number in the following will be

If the difference of two numbers is 26 and one number be three times the other, then find the numbers.

If \(\cot 2A = \tan (A - 22^\circ)\), where \(2A\) is an acute angle, find the value of \(A\).

Prove that \(\sqrt{2}\) is an irrational number.

Find the roots of the quadratic equation \(4x^2 + 9x + 5 = 0.\)

Find the volume of a copper rod of length 8 cm whose diameter is 1 cm.

Total surface area of a solid hemisphere with radius \(r\) will be

The mean and median of a frequency table are 27 and 29 respectively. Then its mode will be

The probability of 53 Mondays in a leap year will be

Two friends were born in 2020. Find the probability that the date of birth of both will be same.

The distance of the point \((-3, -4)\) from the origin will be

If \(\cot A = \dfrac{3}{4}\), then the value of \(\sec A\) will be

If \(\tan \alpha = \sin \alpha\), then the value of \(\alpha\) will be

If the ratio of the length of a rod and its shadow is \(1 : \sqrt{3}\), the elevation angle of the sun will be

Number of parallel tangent lines drawn to the end points of the diameter of a circle will be

The area of the sector of a circle whose angle is \(60^\circ\) and radius \(12 \, \text{cm}\) will be

If the diameter of a sphere is \(d\), then its volume will be

A solid is in the shape of a cone which is surmounted on a hemisphere of same base radius. If the curved surfaces of the hemisphere and the cone are equal, find the ratio of radius and height of the cone.

An arc of a circle of radius 21 cm subtends an angle of \( 60^\circ \) at the centre. Find the area of the sector formed by the arc.

The sum of zeroes of the polynomial \(3x^2 + 5x + 2\) will be

There will be no solution of the equations \(2x + ay = 1\) and \(3x - 5y = 7\) if the value of \(a\) is

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

10th term from the end of the A.P. \(4, 9, 14, \ldots, 254\) will be

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.

In the figure, \( OA, OB, OC, OD \) are drawn such that \( OB = OC \) and \( OA = OD \). Show that \( \angle A = \angle C \) and \( \angle B = \angle D \).