List of top Questions asked in CBSE Class X- 2026

How many zeroes does \(p(x) = (x - 2)(x + 3)\) have ?

Given \(\cot \theta = 3\), the value of \(\cos \theta\) is :

Find the coordinates of the points of trisection of the line segment joining the points A\(-1, 4\) and B\(-3, -2\).

If the median of the following distribution is 32.5, then find the values of x and y.
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70
Frequency: x, 5, 9, 12, y, 3, 2 [Total = 40]

Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and \(\angle AOB = 120^\circ\). [Use \(\pi = \frac{22}{7}\)]

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.

Find the value of p, for which one zero of the quadratic polynomial \(px^2 - 14x + 8\) is 6 times the other.

The pair of linear equations \(\frac{3x}{2} + \frac{5y}{3} = 7\) and \(9x + 10y = 14\), is :

In the given figure, PA and PB are tangents to a circle centred at O. If \(\angle OAB = 15^\circ\), then \(\angle APB\) equals :

The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P. is :

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to :

In the given figure, PA and PB are tangents to a circle centred at O. If \(\angle AOB = 130^\circ\), then \(\angle APB\) is equal to :

There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?

The graph of y = f(x) is given. The number of distinct zeroes of y = f(x) is :

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. Find the modal age and median age of the policy holders.
Age (in yrs): 15-20, 20-25, 25-30, 30-35, 35-40, 40-45, 45-50, 50-55, 55-60
Number of policy holders: 2, 4, 18, 21, 33, 11, 3, 6, 2

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

Two dice are thrown at the same time. Determine the probability that (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.

Find the area of the sector of a circle of radius 42 cm and of central angle \(30^\circ\). Also, find the area of the corresponding major sector. [Use \(\pi = \frac{22}{7}\)]

Find the coordinates of the points of trisection of the line segment joining the points A\(-1, 4\) and B\(-3, -2\).

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Prove that \(\sqrt{5}\) is an irrational number.

If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.

If \(\alpha\), \(\beta\) are the zeroes of the quadratic polynomial \(px^2 + qx + r\), then find the value of \(\alpha^3\beta + \beta^3\alpha\).

The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is :