List of top Questions asked in CBSE Class X- 2026

The diagonals of a quadrilateral ABCD intersect each other at the point O such that $\frac{AO}{OC} = \frac{BO}{OD}$. Show that quadrilateral ABCD is a trapezium.

A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.

Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1, 6) respectively.
23(a)(i) Find the co-ordinates of point P.

Solve any one of the following internal choices (a) or (b):
22(a) In an A.P., the first term is 32 and the last term is -10. If the common difference is -2, then find the number of terms and their sum.

Two different dice are thrown together. Find the probability that the numbers obtained have : (i) even sum, (ii) even product.

Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : \(x - 5y = 6; 2x - 10y = 12\)

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons of age 15 years and onwards, but less than 60 years. Find the modal age and median age of the policy holders.

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

In the given figure \(\Delta ABC\) is shown, in which \(DE \parallel BC\). If \(AD = 5\text{ cm}\), \(DB = 2\cdot5\text{ cm}\) and \(DE = 8\text{ cm}\), then the length of \(BC\) is :

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 \(cm^2\).
Reason (R) : The surface area of a cuboid of dimensions \(l \times b \times h\) is \((lb + bh + hl)\).

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 distance between the points (4, p) and (1, 0) is 5, what is the value of p ?

The three vertices of a rhombus PQRS are P(2, – 3), Q(6, 5) and R(– 2, 1). Find the coordinates of the fourth vertex S and coordinates of the point where both the diagonals PR and QS intersect.

A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in \(cm^3\)) 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 :

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 :

The area of a semicircle of diameter 'd' is :

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.