List of top Mathematics Questions asked in CBSE Class X

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.

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.

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 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.

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

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

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 \( BC = 3.6 \, \text{cm} \).

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 \(b \ne 0\).

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.

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.
Check whether the following system of equations is consistent or not. If consistent, solve graphically: \[ x - 2y + 4 = 0, \quad 2x - y - 4 = 0 \]
A bag contains cards numbered from 5 to 100 such that each card bears a different number. A card is drawn at random. Find the probability that the number on the card is:
  • [(i)] a perfect square
  • [(ii)] a 2-digit number