List of top Mathematics Questions asked in CBSE Class X

In the given graph, the polynomial \(p(x)\) is shown. Number of zeroes of \(p(x)\) is
polynomial p(x)
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
The point \((3, -5)\) lies on the line \(mx - y = 11\). The value of \(m\) is
If \(\sqrt{3} \sin \theta = \cos \theta\), then value of \(\theta\) is
Two dice are rolled together. The probability of getting a sum more than 9 is
Solve the quadratic equation \(\sqrt{3}x^2 + 10x + 7\sqrt{3} = 0\) using the quadratic formula.
Find the nature of roots of the equation \(4x^2 - 4a^2x + a^4 - b^4 = 0\), where \(b \ne 0\).
Using prime factorisation, find the HCF of 180, 140 and 210.
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.
Given that \(\sqrt{5}\) is an irrational number, prove that \(2 + 3\sqrt{5}\) is an irrational number.
Find the ‘mean’ and ‘mode’ marks of the following data:
Numberofstudents
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 \(\sqrt{3} = 1.73\))
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
The system of equations \(y + a = 0\) and \(2x = b\) has
Which of the following equations does not have a real root?
The distance of point \(P(3a, 4a)\) from y-axis is

In the adjoining figure, \( AP = 1 \, \text{cm}, \ BP = 2 \, \text{cm}, \ AQ = 1.5 \, \text{cm}, \ AC = 4.5 \, \text{cm} \) Prove that \( \triangle APQ \sim \triangle ABC \).
Hence, find the length of \( PQ \), if \( BC = 3.6 \, \text{cm} \).

A bag contains balls numbered 2 to 91 such that each ball bears a different number. A ball is drawn at random from the bag. Find the probability that:
  • [(i)] it bears a 2-digit number
  • [(ii)] it bears a multiple of 1

Solve the following pair of equations algebraically: \[ \begin{aligned} 101x + 102y &= 304 \\ 102x + 101y &= 305 \end{aligned} \]

If the points A(6, 1), B(p, 2), C(9, 4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p and q. Hence, check whether ABCD is a rectangle or not.
Find the zeroes of the polynomial \(r(x) = 4x^2 + 3x - 1\). Hence, write a polynomial whose zeroes are reciprocal of the zeroes of \(r(x)\).

If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.

In the adjoining figure, \( \triangle CAB \) is a right triangle, right angled at A and \( AD \perp BC \). Prove that \( \triangle ADB \sim \triangle CDA \). Further, if  \( BC = 10 \text{ cm} \) and \( CD = 2 \text{ cm} \), find the length of } \( AD \).

Fermentation tanks are designed in the form of a cylinder mounted on a cone as shown below:

The total height of the tank is 3.3 m and the height of the conical part is 1.2 m. The diameter of the cylindrical as well as the conical part is 1 m. Find the capacity of the tank. If the level of liquid in the tank is 0.7 m from the top, find the surface area of the tank in contact with liquid.

The population of lions was noted in different regions across the world in the following table:

Number of lionsNumber of regions
0–1002
100–2005
200–3009
300–40012
400–500x
500–60020
600–70015
700–80010
800–900y
900–10002
Total100

If the median of the given data is 525, find the values of x and y.