List of top Mathematics Questions

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

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

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

Irrational number in the following will be

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

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

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

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

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

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

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

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

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.

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

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

The sum of a two-digit number and the number obtained by reversing the order of its digits is 66. If the digits differ by 2, find the number.

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.

Solve the following pair of equations:
\[ 3x - 5y - 4 = 0 \] \[ 9x = 2y + 7 \]

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