List of top Mathematics Questions

Find the mode of the following frequency table : 

If an arc of a circle of radius 10.5 cm, subtends an angle of 60° at the centre, then find the length of the arc.
Prove that : $\frac{2 \cos^3} \theta - \cos \theta{\sin \theta - 2 \sin^3 \theta} = \cot \theta$
In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8)?
Find the distance between the points (-4, 5) and (2, -3).
Prove that $2\sqrt{2}$ is an irrational number.

The modal class of the following frequency table will be : 

The median class of the following frequency distribution will be : 

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 2 cm and the height of the cone is equal to its radius. The volume of the solid will be :
The angle of a sector of a circle with radius 4 cm is 30°. The area of the sector will be :
If the mode of some observations is 20 and mean is 26. The value of their median will be :
Two coins are tossed simultaneously. The probability of getting at least one head is :
The value of $4 \sin 30^\circ \cos 60^\circ$ will be :
In triangle $ABC$ if $\angle B = 90^\circ$, $AB = 5$ cm and $BC = 12$ cm, the value of $\sin A$ will be :

In the above figure, if $AD = 2.0$ cm, $AE = 1.8$ cm, $EC = 3.6$ cm and $DE \parallel BC$ the measure of $BD$ will be : 

 

If the points A (6, 1), B (8, 2), C (9, 4) and D (7, 3) are the vertices of a parallelogram, taken in order, the point of intersection of diagonals will be :
The seventeenth term of the A. P. : 3, 8, 13, ... will be :
In linear equation $\frac{x}{3} + \frac{y}{2} = 6$ if $x = 9$ then the value of $y$ will be :
The sum of zeroes of the quadratic polynomial $x^2 + 2x + 5$ will be :
LCM and HCF of two numbers are 182 and 13 respectively. If one number is 26, then other number will be :
If tan A = √3, then the value of Sec A will be :
The value of Tan A + Cot A will be :
HCF of the numbers 49 and 91 will be :
Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : \( x - 5y = 6; 2x - 10y = 12 \)

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If 
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.