List of top Mathematics Questions asked in CBSE Class X

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
Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]

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.

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.

Three coins are tossed together. The probability that at least one head comes up 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
22nd term of the A.P.: \(\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\) 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
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.
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
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
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 } \( AD \).