List of top Questions asked in CBSE Class X- 2026

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.

In the given figure, \(AB \parallel DE\) and \(AC \parallel DF\). Show that \(\triangle ABC \sim \triangle DEF\). If \(BC = 10\) cm, \(EB = CF = 5\) cm and \(AB = 7\) cm, then find the length DE.

Prove that \(14 - 2\sqrt{3}\) is an irrational number, given that \(\sqrt{3}\) is irrational.

A circle centered at (2, 1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.

Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line \(x - 3y = -1\). Also find length of PA and PB.

Use graphical method to solve the system of linear equations : \(x = -3\) and \(5x - 2y = -5\).

In an A.P., \(15^{th}\) term exceeds the \(8^{th}\) term by 21. If sum of first 10 terms is 55, then form the A.P.

The sum of first n terms of an A.P. is \(2n^{2} + 13n\). Find its \(n^{th}\) term and hence \(10^{th}\) term.

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).

A chord of a circle, of radius 14 cm, subtends an angle of \(60^{\circ}\) at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that OBGC is a parallelogram.

In the same figure as 32(a), prove that \(EF \parallel BC\).

In the same figure as 32(a), prove that \(\triangle AEF \sim \triangle ABC\).

Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that \(AQ = QR\).

Using the conditions from 32(b), prove that \(AP = 2PQ\).

Using the conditions from 32(b), prove that \(PR = 2AP\).

The mean of the following distribution is 53. Find the missing frequency p.

Hence, find mode of the distribution.}

Compute median of the following data :

Two water taps together can fill a tank in \(8\frac{8}{9}\) hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

The natural number 1 is :

For any natural number n, \( 5^n \) ends with the digit :

If \( \alpha \) and \( \beta \) are two zeroes of a polynomial \( f(x) = px^2 - 2x + 3p \) and \( \alpha + \beta = \alpha\beta \), then value of p is :

If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then