List of top Questions asked in CBSE Class X- 2026

Case Study - 2: 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 :

37(i) Find the probability that the drawn card is a face card.
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 boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of $30^\circ$. Another boy standing on the roof of a 20 m high building, finds the angle of elevation of same kite to be $45^\circ$. If both the boys are on opposite sides of the kite, find the distance of the first boy from the base of the building. Also, find the height of the kite from the ground. (Use $\sqrt{3} = 1.73$)
Solve any one of the following internal choices (a) or (b):
34(a) Solve the following system of equations graphically : $x - 2y = 3, 3x - 8y = 7$
Case Study - 3: 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 :

38(i) Determine the total height of the fountain.
Case Study - 1: 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. Based on the figure given, answer the following questions :

(i) Determine the height of the arch.
Solve any one of the following internal choices (a) or (b):
26(a) If $\sin \theta + \cos \theta = \sqrt{3}$, then prove that $\tan \theta + \cot \theta = 1$.
A point P(x, 7) divides a line segment joining the points A(-5, 4) and B(7, 9) in a certain ratio. Find the ratio and hence find the value of x.
Find two consecutive negative integers, sum of whose squares is 481.
Solve any one of the following internal choices (a) or (b):
32(a) The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68.

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 $\Delta OAB = 21.2\text{ cm}^2$.
Solve any one of the following internal choices (a) or (b):
31(a) Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that $\angle APB = 2 \angle OAB$.
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.
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.
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.
Assertion (A) : $\tan 2\theta$ is not defined at $\theta = 45^\circ$.
Reason (R) : $\sin 90^\circ \neq \cos 90^\circ$.
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.
Given that $\sin 2\alpha = \frac{\sqrt{3}}{2}$, the value of $\sin 3\alpha$ is :
The value of $\left(\frac{1}{2} \tan^2 45^\circ - \cos^2 60^\circ\right)$ 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) :
The median and mode of a distribution are $25.2$ and $26.1$ respectively. The mean of the distribution is :
Assertion (A) : Radius is the smallest distance of a tangent from the centre of the circle.
Reason (R) : Radius is perpendicular to the tangent.
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 $n^{\text{th}}$ term of the A.P. $\frac{-1}{3}, \frac{2}{3}, \frac{5}{3}, \frac{8}{3}, \dots$ is :