List of top Questions asked in CBSE Class X- 2026

If \(\cos A + \sin A = \sqrt{2} \cos A\), prove that \(\cos A - \sin A = \sqrt{2} \sin A\).
From a solid cylinder whose height is 2.8 cm and radius 2.1 cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total surface area of the remaining solid.
Two poles of equal heights are standing opposite to each other on either side of the road which is 90 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30\(^\circ\) and 60\(^\circ\) respectively. Find the height of the poles and the distances of the point from the poles. [Use \(\sqrt{3}\) = 1.732]
Find the mean of the following distribution :
Prove that \(\frac{2 + 3\sqrt{5}}{7}\) is an irrational number, given that \(\sqrt{5}\) is an irrational number.
Find the quadratic polynomial the sum of whose zeroes is 1 and their product is –12. Hence find the zeroes of the polynomial.
Find a relation between x and y such that the point P(x, y) is equidistant from the points A(5, 3) and B(1, 7).
Assertion (A) : If the Mode and Mean of a data are 12 k and 15 k, then Median of the data is 14 k.
Reason (R) : The relation between the Mean, Mode and Median of a data is : Mean = 3 Median – 2 Mode.
Two numbers are in the ratio 3 : 5 and their LCM is 180. Find the HCF of these two numbers.
A circle is inscribed in a right triangle ABC, right angled at B. If the lengths of the two sides containing the right angle are 8 cm and 15 cm, find the radius of the incircle.
\(\sin 2 \theta = 2 \sin \theta\) is true, when \(\theta\) is equal to
The number of conical bottles of radius 2 cm and height 1.2 cm that can be filled from a cylindrical bottle of radius 6 cm and height 8 cm, full of liquid, is
Assertion (A) : In a circle of radius 21 cm, an arc of length 22 cm subtends an angle of 60\(^\circ\) at the centre.
Reason (R) : The length of arc of a sector of a circle of radius r and central angle \(\theta\) is \(\frac{2\pi r\theta}{360}\).
Two dice are thrown simultaneously. The probability of getting a sum of 7 is :
If HCF of 66 and 99 is expressible in the form of \(55m - 132\), then the value of m is :
One ticket is drawn at random from a bag containing 50 tickets numbered 1 to 50. The probability that the drawn ticket has a number which is a multiple of 7 is :
If in a \(\Delta ABC\), \(AB = 6\) cm and \(DE \parallel BC\) such that \(AE = \frac{1}{3} AC\), then the length of BD is
If the mean of first n natural numbers is \(\frac{6n}{11}\), then n is
From a point P, tangents PQ and PR are drawn to a circle with centre O and radius 6 cm. If OP = 10 cm, then area of quadrilateral PQOR is :
If \(\Delta DEF \sim \Delta PQR\) such that \(3 DE = PQ\) and \(EF = 6\) cm, then the length of QR is :
The perimeter of sector of a circle of radius 21 cm and central angle 60\(^\circ\), is
If a, b, c and d are consecutive terms of an A.P., then c – b is equal to :
If pair of linear equations given by \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) has infinitely many solutions, then which of the following is definitely true ?
ABCD is a trapezium in which AB || DC and E, F are points on AD and BC respectively such that EF || DC. If ED = 36 cm, BF = 70 cm and FC = 30 cm, then the length of AD is :
Four tangents drawn to a circle are extended from both the sides to form a quadrilateral. Which of these quadrilateral is not possible ?