List of top Questions asked in CBSE Class X- 2026

Fill in the blank with correct option to complete a message from Yogita to her friend Shobit:
Dear Shobit,
Let’s meet at 5 p.m. for the rehearsal but I need to go home first since morning I _______} anything since morning.
Case Study - 2 : 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, 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.
Case Study - 3 : 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?
Five years ago, Adil was thrice as old as Bharat. Ten years later Adil shall be twice as old as Bharat. To know the present ages of Adil and Bharat: (i) form the linear equations representing the above information. (ii) show that the system of equations is consistent with unique solution. (iii) find the present ages of Adil and Bharat.
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.
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 cm\(^2\).
The angle of elevation of the top of a building from a point A, on the ground, is 30\(^{\circ}\). On moving a distance of 24 m towards its base to the point B, the angle of elevation changes to 60\(^{\circ}\). Find the height of the building and distance of point A from the base of the building. (Take \(\sqrt{3}\) = 1.73)
A tower stands vertically on the ground. A man standing at the top of the tower observes his friend at an angle of depression of 30\(^{\circ}\), who is approaching the foot of the tower with a uniform speed. 30 seconds later, the angle of depression changes to 60\(^{\circ}\). Find the time taken by his friend to reach the foot of the tower from this point.
Find the mean and the mode of the following frequency distribution :
Solve the following system of equations graphically: x - 2y = 3, 3x - 8y = 7.
Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1, 6) respectively. (i) Find the coordinates of point P. (ii) Find the length of the side of the square.
In the given figure, PA is the tangent to the circle with centre O such that OA = 10 cm, AB = 8 cm and AB \(\perp\) OP. Find the length of PB.
If sin \(\theta\) + cos \(\theta\) = \(\sqrt{3}\), then prove that tan \(\theta\) + cot \(\theta\) = 1.
Prove that : (sin A + sec A)\(^2\) + (cos A + cosec A)\(^2\) = (1 + sec A cosec A)\(^2\)
Determine the ratio in which the line 3x + y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 5). Find the point of intersection.
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.
Find the coordinates of a point on the line x + y = 5 which is equidistant from (6, 4) and (5, 2).
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
Assertion (A) : tan 2\(\theta\) is not defined at \(\theta\) = 45\(^{\circ}\).
Reason (R) : sin 90\(^{\circ}\) \(\neq\) cos 90\(^{\circ}\).
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 :
In the given figure, \(\Delta ABE \cong \Delta ACD\). Prove that \(\Delta ADE \sim \Delta ABC\).
The n\(^{th}\) term of the A.P. \(-\frac{1}{3}\), \(\frac{2}{3}\), \(\frac{5}{3}\), \(\frac{8}{3}\), ... is :
In an A.P., the first term is 4 and the last term is 31. If sum of all the terms is 175, find the number of terms and the common difference.
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.
How many terms of the A.P. 21, 18, 15, ... must be added to get the sum zero?
Equation of a line coincident with 2.5x - 2y = 3 is :