List of practice Questions

Prove that the angle between the tangents drawn from an external point to a circle is supplementary to the angle formed by the line segment joining the points of contact at the centre of the circle.
In what ratio does the point \((-4, 6)\) divide the line segment joining the points \(A(-6, 10)\) and \(B(3, -8)\)?
Find the roots of the quadratic equation \(3x^2 - 2\sqrt{6}x + 2 = 0\).
The distance between the two points (2, 3) and (4, 1) will be
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