CBSE Class 10 Mathematics Board Paper 2026 — Set 4

Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner.

Ansh strikes a disc, kept at position P with a striker. The disc hits the boundary of the board at R and goes straight to pocket at corner C. It is given that P S=9 cm ,PQ=35 cm ,BR=x, ∠PRQ=α and ∠CRB=θ.

Based on the above information, answer the following questions :

Kolam’ is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below. Observe the given figure carefully. There are 4 dots in first square, 8 dots in second square, 12 dots in third square and so on.

Based on the above, answer the following questions :

Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below :

Point A : (-4, 2) Rajasthan High Court

Point B : (4, —4) Birla Mandir

Point C : (4, 3) Heera Bagh

Point D : (-5, —2) Amar Jawan Jyoti

Based on the above, answer the following questions :

If the quadratic equation 9x²+ 8kx + 16 = 0 has real and equal roots, then the value of k is

It is given that △ABC∼△EDF. Which of the following is not true ?

The nᵗʰ term of an A.P. is √2n+1 its common difference is

If PQ and PR are tangents to the circle with centre O and radius 4 cm such that ∠QPR=90° then the length OP is

In the given figure, a circle is centred at (1, 2). The diameter of the circle is

The value of k for which the system of linear equations x/2+ y/3=5 and 2x + ky = 7 is inconsistent, is

A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is

Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is

When sin A=1/3 ,the value of cot A is.

PQ is tangent to a circle with centre O. If ∠ POR = 65°, then m ∠ PTR is

An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is r/2 then h:2r equals

Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If PQ arc=11 cm, then the value of θ is

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

Assertion (A) : If probability of happening of an event is 0.2p, p > 0, then p can’t be more than 5.

Reason (R) : P( E̅ )=1-P(E) for an event E.

Assertion (A) (√3+√5 ) is an irrational number.

Reason (R) : Sum of the any two irrational numbers is always irrational

Verify that roots of the quadratic equation (p — q)x²+ (q—r)x +( r—p) =0 are equal when q +r = 2p.

D is a point on the side BC of Δ ABC such that ∠CAB = ∠CDA. Show tha CA ² = CB x CD.

Prove that 2 + 3 √5 is an irrational number given that √5 is irrational number.

If the HCF of 210 and 55 is expressed as 210 x 5 + 55m, then find the value of m.

Prove that:√ 1+sin A/ 1- sin A =sec A+ tan A

Evaluate : 3 cos² 30° - 6cosec² 30°/tan² 60°

α and βare the zeroes of the polynomial 5x²— 16x — 10. Find the value of α/β + β/α

In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.

Solve the linear equations 3x +y = 14 and y = 2 graphically.

Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120° at the centre. Find the perimeters of the shaded region. (Use√ 3 = 1.73)

Prove that : sinθ - cosθ +1/ sinθ +cos θ- 1= 1/ secθ -tan θ

To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14m x 25m x 16 m

The internal and external radii of a hollow hemisphere are 5√2 cm and 10 cm respectively. A cone of height 5√7 cm and radius 5√2 cm is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of Π. (Use √2 = 1.4)

A bag contains 30 balls out of which ‘m’ number of balls are blue in colour.

(i) Find the probability that a ball drawn at random from the bag is not blue.

(ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 5/4 times the probability of drawing a blue ball in the first case. Find the value of m.

Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.

The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered 2 m extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length?

In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.

i) Name the quadrilateral MQBN.

(ii) Is MN parallel to PA? Justify your answer.

(iii) Find the length TB.

(iv) Find MN.

A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30°. From the bottom of the same building, the angle of elevation of kite is 45°. Find the length of the string and height of roof from the ground. (Use √ 3 = 1.73)

The median of the following data is 50 and sum of all frequencies is 90 :

Find the values of p and q.

Find mean and mode of the following distribution :