List of top Mathematics Questions

The distance of point \(P(3a, 4a)\) from y-axis is
Which of the following equations does not have a real root?
The system of equations \(y + a = 0\) and \(2x = b\) has
If \(x = 2 \sin 60^\circ \cos 60^\circ\) and \(y = \sin 230^\circ - \cos 230^\circ\), and \(x^2 = ky^2\), the value of \(k\) is
A drone is flying at a height of \(h\) metres. At an instant it observes the angle of elevation of the top of an industrial turbine as \(60^\circ\) and the angle of depression of the foot of the turbine as \(30^\circ\). If the height of the turbine is \(200\, \text{metres}\), find the value of \(h\) and the distance of the drone from the turbine.
(Use \(\sqrt{3} = 1.73\))
Find the ‘mean’ and ‘mode’ marks of the following data:
Numberofstudents
Find the zeroes of the polynomial \(2x^2 + 7x + 5\) and verify the relationship between its zeroes and coefficients.
\(\alpha, \beta\) are zeroes of the polynomial \(3x^2 - 8x + k\). Find the value of \(k\), if \(\alpha^2 + \beta^2 = \dfrac{40}{9}\)
Prove that \(\dfrac{\sin \theta}{1 + \cos \theta} + \dfrac{1 + \cos \theta}{\sin \theta} = 2\csc \theta\)
Given that \(\sqrt{5}\) is an irrational number, prove that \(2 + 3\sqrt{5}\) is an irrational number.
The perimeters of two similar triangles are 22 cm and 33 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.
Using prime factorisation, find the HCF of 180, 140 and 210.
Find the nature of roots of the equation \(4x^2 - 4a^2x + a^4 - b^4 = 0\), where \(b \ne 0\).
Two dice are rolled together. The probability of getting a sum more than 9 is
If \(\sqrt{3} \sin \theta = \cos \theta\), then value of \(\theta\) is
The point \((3, -5)\) lies on the line \(mx - y = 11\). The value of \(m\) is
To calculate mean of grouped data, Rahul used assumed mean method. He used \(d = (x - A)\), where \(A\) is the assumed mean. Then \(\bar{x}\) is equal to
In the given graph, the polynomial \(p(x)\) is shown. Number of zeroes of \(p(x)\) is
polynomial p(x)
22nd term of the A.P.: \(\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\) is
If the length of the shadow of a tower is \(\sqrt{3}\) times its height, then the angle of elevation of the sun is
Three coins are tossed together. The probability that at least one head comes up is

On the day of her examination, Riya sharpened her pencil from both ends as shown below.

The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and the length of the entire pencil is 105.6 mm, find the total surface area of the pencil.

The following data shows the number of family members living in different bungalows of a locality:
 

Number of Members0−22−44−66−88−10Total
Number of Bungalows10p60q5120


If the median number of members is found to be 5, find the values of p and q.

A 24 cm line AB is vertically standing on a horizontal plane. The station point is located 18 cm above ground and 15 cm in front of the line AB. The picture plane is located in between the line AB and station point perpendicular to the sight line. The distance between the picture plane and the station point is 9 cm. The height of the perspective view of the line AB is ________cm. (rounded off to one decimal place)

If \[ A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix} \] then find \( A^{-1} \). Hence, solve the system of linear equations: \[ x - 2y = 10, \] \[ 2x - y - z = 8, \] \[ -2y + z = 7. \]