List of top Mathematics Questions asked in CBSE Class X

In the adjoining figure, if \(\dfrac{AD}{BD} = \dfrac{AE}{EC}\) and \(\angle BDE = \angle CED\), prove that \(\triangle ABC\) is an isosceles triangle.

Assertion (A) : For two prime numbers \(x\) and \(y\) (\(x<y\)), HCF\((x, y) = x\) and LCM\((x, y) = y\). Reason (R): HCF\((x, y) \leq \) LCM\((x, y)\), where \(x, y\) are any two natural numbers.

The system of equations \(x+5=0\) and \(2x-1=0\) has

PA and PB are tangents drawn to a circle with centre O. If \(\angle AOB = 120^\circ\) and OA = 10 cm, then

(i) Find \(\angle OPA\).
(ii) Find the perimeter of \(\triangle OAP\).
(iii) Find the length of chord AB.

The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.

Find 'mean' and 'mode' of the following data : Frequency Distribution Table

Class	0 – 15	15 – 30	30 – 45	45 – 60	60 – 75	75 – 90
Frequency	11	8	15	7	10	9

Solve the following pair of linear equations by graphical method : \(2x + y = 9\) and \(x - 2y = 2\).

Two poles of equal heights are standing opposite each other on either side of the road which is 85 m wide. From a point between them on the road, the angles of elevation of the top of the poles are \(60^\circ\) and \(30^\circ\) respectively. Find the height of the poles and the distances of the point from the poles. (Use \(\sqrt{3} = 1.73\))

The sum of a number and its reciprocal is \(\frac{13}{6}\). Find the number.

Find the zeroes of the polynomial \(p(x) = 3x^2 + x - 10\) and verify the relationship between zeroes and its coefficients.

Find the sum of first 20 terms of an A.P. whose n\(^{th}\) term is given by \(a_n = 5 + 2n\). Can 52 be a term of this A.P. ?

Three friends plan to go for a morning walk. They step off together and their steps measures 48 cm, 52 cm and 56 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ten times?

In the given figure, AB \(||\) DE and BD \(||\) EF. Prove that \(DC^2 = CF \times AC\).

AB || DE and BD || EF. Prove that DC2 = CF ×AC

Find the nature of roots of the equation \(3x^2 - 4\sqrt{3}x + 4 = 0\).

Using prime factorisation, find the HCF of 144, 180 and 192.

Verify that \(\sin 2A = \frac{2 \tan A}{1 + \tan^2 A}\) for \(A = 30^\circ\).

Evaluate : \(\frac{\cos 45^\circ}{\tan 30^\circ + \sin 60^\circ}\)

The line \(2x - 3y = 6\) intersects x-axis at

In \(\triangle ABC, DE || BC\). If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is

Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

To calculate mean of a grouped data, Rahul used assumed mean method. He used \( d = (x - A) \), where A is assumed mean. Then \( \bar{x} \) is equal to

A quadratic polynomial having zeroes 0 and -2, is

15th term of the A.P. \( \frac{13}{3}, \frac{9}{3}, \frac{5}{3}, \dots \) is

In \(\triangle ABC, \angle B = 90^\circ\). If \( \frac{AB}{AC} = \frac{1}{2} \), then cos C is equal to

Gurveer and Arushi built a robot that can paint a path as it moves on a graph paper. Some co-ordinate of points are marked on it. It starts from graph paper. Some co-ordinate of points are marked on it. It starts from (0, 0), moves to the points listed in order (in straight lines) and ends at (0, 0).