CBSE Class 10 Mathematics Board Paper 2026 — Set 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

The roots of the quadratic equation (x — 1)² =16 are

In △DEF, AB∥ EF. The value of x is :

(3 ×11 ×13+3) is:

Equation of another line parallel to the line represented by 2 x−6y=7 is:

If the length of the shadow of a tower is √3​ times that of its height, then altitude of the Sun is :

If the roots of the quadratic equation √3​x² −kx+2√ 3​=0 are real and equal, then the value (s) of k is / are :

The nᵗʰ term of the A.P. -1/3,2/3,5/3,8,3,....is

In the given figure, PT is a tangent to the circle with centre O and radius r . If ∠POT= 45° , then the length of OP is :

It is given that △ABC∼△QRP such that AB=9, BC=5 and PR=2 Length of side QR is :

The median and mode of a distribution are 25.2 and 26.1 respectively. The mean of the distribution is :

In the given figure Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points A (0,5√3/2) D(0, 0). Points B and C are (in same order) :

The value of ( 1/2 tan² 45° -cos² 60°) 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.

Assertion (A) : tan 2θ is not defined at θ = 45°. Reason (R) : sin 90° ≠ cos 90°.

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.

In an AP., 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.

Find the sum of the first 28 terms of an A.P. whose nth term is given by aₙ = 3n - 2.

Find the coordinates of a point on the line x + y = 5 which is equidistant from (6, 4) and (5, 2).

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 co-ordinates of point P.

(ii) Find the length of the side of the square.

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/OC= 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.

If sin θ + cos θ = √3, then prove that

tan θ+cot θ=1

Prove that : (sin A + sec A)² + (cos A + cosec A)² = (1 + sec A cosec A)²

In the given figure, chord AB subtends an angle of 120° 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 Δ OAB = 21.2 cm²

Prove that√5 is an irrational number.

Find two consecutive negative integers, sum of whose squares is 481.

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.

Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠ APB =2 ∠ OAB.

In the given figure, PA is the tangent to the circle with centre O such that OA = 10 cm, AB = 8cm and AB⊥ OP. Find the length of PB.

The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68.

Find mean and mode of the following distribution :

In △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=4XY

Solve the following system of equations graphically :

x-2y=3, 3x-8y=7

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.

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°. Another boy standing on the roof of a 20 m high building, finds the angle of elevation of the same kite to be 45°. 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√ 3=1.73) .