List of top Questions asked in CBSE Class X- 2026

Equation of a line coincident with 2.5x - 2y = 3 is :
In the given figure, \(\Delta ABC\) is an equilateral triangle. AD is a median of the triangle joining the points \(A\left(0, \frac{5\sqrt{3}}{2}\right)\), \(D(0, 0)\). Points B and C are (in same order) :
In the given figure, \(OA \times OB = OC \times OD\). Which of the following option is correct ?
In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If \(\angle QPR = 60^{\circ}\), then the length of each tangent is :
A cone of maximum size is carved out from a solid cube of edge length \(l\). The volume of the cone is :
A polynomial \(p(x)\), which has sum of its zeroes equal to their product, is :
The number of multiples of 6 lying between 25 and 363 is :
A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :
(i) Find the probability that the drawn card is a face card.
(ii) Find the probability that the drawn card is either a king or a queen.
(iii)(a) Do you think that the probability of getting a queen was higher if none of the cards were dropped? Justify your answer.
OR
(iii)(b) Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher?

In \(\Delta ABC\), AD is a median. X is a point on AD such that AX : XD = 2 : 3. BX is extended so that it intersects AC at Y. Prove that BX = 4 XY.
A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative cylindrical pool where it is recycled.
The diameter of spherical ball is 21 cm.
Cylindrical pool - Outer diameter is 50 cm and inner diameter is 40 cm.
Height of solid base is 14 cm.
Height of water filled is 7 cm.
Observe the figure and answer the following questions :
(i) Determine the total height of the fountain.
(ii) Find the volume of the ball.
(iii)(a) If one-third of the ball is submerged in the water, find the volume of the water filled in the pool.
OR
(iii)(b) Find the sum of the outer curved surface area of the cylindrical part and surface area of the ball.
During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial \(p(x) = -x^2 + 2x + 8\), where x is the length (in feet) on stage level.
Observe the figure and answer the following questions :
(i) Determine the height of the arch.
(ii)(a) Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes?
OR
(ii)(b) Find the span of the arch on the stage floor.
(iii) Write the coordinates of the point of intersection of the above curve with the y-axis.
Two right triangles PRQ and PSQ are drawn on the same hypotenuse PQ. If PR and QS intersect at T, prove that ST \(\times\) TQ = PT \(\times\) TR.

1000 small thermocol balls of radius 0.5 cm are kept in a spherical balloon of radius 20 cm. Find the volume of air in the balloon.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff. From a point on the ground 30 m away from the tower, wires are attached to the top and bottom of the flagstaff making angles of elevation \(60^\circ\) and \(30^\circ\) respectively. Find the height of the tower and lengths of the wires attached. (Take \(\sqrt{3} = 1.73\))
A point P divides the line segment joining the points A(-3, 5) and B(7, -4) in a certain ratio. If the point P lies on the line y = 2x, then find the ratio AP : PB and coordinates of point P.
In the given figure, chord AB subtends an angle of \(120^\circ\) at the centre of the circle with radius 7 cm. Find (i) perimeter of major sector OACB, and (ii) area of the shaded segment, if area of \(\Delta OAB = 21.2\text{ cm}^2\).
PA and PB are tangents to a circle centred at O. If \(\angle PBA = 65^\circ\), then \(\angle APB\) equals :
In the given figure, \(\Delta ABC\) is an equilateral triangle. \(AD\) is a median of the triangle joining the points \(A\left(0, \frac{5\sqrt{3}}{2}\right)\), \(D(0, 0)\). Points \(B\) and \(C\) are (in same order) :
A cone of maximum size is carved out from a solid cube of edge length \(l\). The volume of the cone is :
In \(\Delta DEF\), \(AB \parallel EF\). The value of \(x\) is :
Three coins are tossed together. The probability of getting exactly one head, is :
In the given figure, PT is a tangent to the circle with centre O and radius r. If \(\angle POT = 45^\circ\), then the length of OP is :
The value of \(\left( \frac{1}{3}\cot^2 30^\circ - \frac{1}{2}\sec^2 60^\circ \right)\) is :
The roots of the quadratic equation \(4x^2 - (a - 1)^2 = 0\) are :
It is given that \(\Delta ABC \sim \Delta QRP\) such that \(AB = 9\text{ cm}\), \(BC = 5\text{ cm}\) and \(PR = 2\text{ cm}\). Length of side \(QR\) is :