CBSE Class 10 Maths Sample Paper 2026

If a = 2^2 x 3^x ,b = 2^2 x 3 x 5,c = 2^2 x 3 x 7 and LCM (a, b, c) = 3780, then x is equal to

• (A) 1
• (B) 2
• (C) 3 ✓
• (D) 0

Answer (the board’s key): (C)

The shortest distance (in units) of the point (2,3) from y-axis is

• (A) 2 ✓
• (B) 3
• (C) 5
• (D) 1

Answer (the board’s key): (A)

If the lines given by 3x +2y =2 and 2x+5y +1=0 are not parallel, then k has to be

• (A) 15/4
• (B) != 15/4 ✓
• (C) any rational number
• (D) any rational number having 4 as denominator

Answer (the board’s key): (B)

A quadrilateral ABCD is drawn to circumscribe a circle. If BC=7cm, CD=4cm and AD=3cm, then the length of AB is

• (A) 3cm
• (B) 4cm
• (C) 6cm ✓
• (D) 7cm

Answer (the board’s key): (C)

If sec(theta) + tan(theta) = x ,then sec(theta) - tan(theta) will be

• (A) x
• (B) x^2
• (C) 2/x
• (D) 1/x ✓

Answer (the board’s key): (D)

Which one of the following is not a quadratic equation?

• (A) (x +2)^2 =2(x +3)
• (B) x^2 +3x =(- 1)(1- 3x)^2
• (C) x^3 - x^2 +2 x +1 =(x +1)^3
• (D) (x +2)(x +1) =x^2+ 2x +3 ✓

Answer (the board’s key): (D)

Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm.Total area of all the dotted regions (assuming the thickness of the rings to be negligible) is

• (A) 4[pi/12 - sqrt(3)/4] cm^2
• (B) [pi/6 - sqrt(3)/4] cm^2
• (C) 4[pi/6 - sqrt(3)/4] cm^2
• (D) 8[pi/6 - sqrt(3)/4] cm^2 ✓

Answer (the board’s key): (D)

A pair of dice is tossed. The probability of not getting the sum eight is

• (A) 5/36
• (B) 31/36 ✓
• (C) 5/18
• (D) 5/9

Answer (the board’s key): (B)

If 2sin5x = sqrt(3) ,0^o <= x <= 90^o, then x is equal to

• (A) 10^o
• (B) 12^o ✓
• (C) 20^o
• (D) 50^o

Answer (the board’s key): (B)

The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such numbers are

• (A) 2
• (B) 3
• (C) 4 ✓
• (D) 5

Answer (the board’s key): (C)

If the area of the base of a right circular cone is 51cm^2 and it's volume is 85cm^2, then the height of the cone is given as

• (A) 5/6 cm
• (B) 5/3 cm
• (C) 5/2 cm
• (D) 5cm ✓

Answer (the board’s key): (D)

If zeroes of the quadratic polynomial ax^2 + bx +c (a, c != 0) are equal, then

• (A) c and b must have opposite signs
• (B) c and a must have opposite signs
• (C) c and b must have same signs
• (D) c and a must have same signs ✓

Answer (the board’s key): (D)

The area (in cm^2) of a sector of a circle of radius 21cm cut off by an arc of length 22cm is

• (A) 441
• (B) 321
• (C) 231 ✓
• (D) 221

Answer (the board’s key): (C)

If triangle ABC ~ triangle DEF, AB=6cm, DE=9cm, EF=6cm and FD=12cm, then the perimeter of triangle ABC is

• (A) 28cm
• (B) 28.5cm
• (C) 18cm ✓
• (D) 23cm

Answer (the board’s key): (C)

If the probability of the letter chosen at random from the letters of the word "Mathematics" to be a vowel is 2/(2x+1), then x is equal to

• (A) 4/11
• (B) 9/4 ✓
• (C) 11/4
• (D) 4/9

Answer (the board’s key): (B)

The points A(9,0), B(9, -6) ,C(-9,0) and D(-9,6) are the vertices of a

• (A) Square
• (B) Rectangle
• (C) Parallelogram ✓
• (D) Trapezium

Answer (the board’s key): (C)

The median of a set of 9 distinct observation is 20.5. If each of the observations of a set is increased by 2,then the median of a new set

• (A) is increased by 2 ✓
• (B) is decreased by 2
• (C) is two times the original number
• (D) Remains same as that of original observations

Answer (the board’s key): (A)

The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 41cm from the centre of the circle is

• (A) 40cm ✓
• (B) 9cm
• (C) 41cm
• (D) 50cm

Answer (the board’s key): (A)

Assertion (A): The number 5^n cannot end with the digit 0, where n is a natural number Reason (R): A number ends with 0, if its prime factorization contains both 2 and 5

• (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) ✓
• (B) Both assertion (A) and reason (R) are true and reason (R) is not the explanation of assertion (A)
• (C) Assertion (A) is true but reason (R) is false.
• (D) Assertion (A) is false but reason (R) is true.

Answer (the board’s key): (A)

Assertion (A): If cosA + cos^2A=1, then sin^2A + sin^4A =1 Reason (R): sin^2A + cos^2A =1

• (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) ✓
• (B) Both assertion (A) and reason (R) are true and reason (R) is not the explanation of assertion (A)
• (C) Assertion (A) is true but reason (R) is false.
• (D) Assertion (A) is false but reason (R) is true.

Answer (the board’s key): (A)

(A) The A.P 8, 10, 12,........ has 60 terms. Find the sum of last 10 terms. OR (B) Find the middle term of A.P 6,13, 20, ........, 230

If sin(A + B) = 1 and cos(A - B) = sqrt(3)/2 ,0^o < A, B < 90^o, find the measure of angles A and B.

If AP and DQ are medians of triangles ABC and DEF respectively, where triangle ABC ~ triangle DEF, then prove that AB/DE = AP/DQ

(A) A horse, a cow and a goat are tied, each by ropes of length 14m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35m, 40m and 50 m. Find the area of grass field that can be grazed by them. OR (B) Find the area of the major segment (in terms of pi) of a circle of radius 5cm, formed by a chord subtending an angle of 90^o at the centre.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that ar(triangle ABC) = 90cm^2 For Visually Impaired candidates: A circle is inscribed in a right-angled triangle ABC, right angled at B. If BC=7cm and AB=24cm, find the radius of the circle

In Figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90° For Visually Impaired candidates: Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠APB= 2(∠OAB)

In a workshop, the number of teachers of English, Hindi and Science are 36, 60 and 84 respectively. Find the minimum number of rooms required, if in each room the same number of teachers are to be seated and all of them being of the same subject.

Find the zeroes of the quadratic polynomial 2x^2 - (1 + 2sqrt(2)) x + sqrt(2) and verify the relationship between the zeroes and coefficents of the polynomial.

If sinθ + cosθ = sqrt(3) ,then prove that tanθ + cotθ = 1 OR Prove that (cosA-sinA+1)/(cosA+sinA-1) =cosec A + cotA

On a particular day, Vidhi and Unnati couldn't decide on who would get to drive the car. They had one coin each and flipped their coin exactly three times. The following was agreed upon: 1. If Vidhi gets two heads in a row, she would drive the car 2. If Unnati gets a head immediately followed by a tail, she would drive the car. Who has greater probability to drive the car that day? Justify your answer.

(A) The monthly income of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in ratio 5:7. If each saves ₹ 15,000 per month, find their monthly incomes. OR (B) Solve the following system of equations graphically: 2x + y =6, 2x - y - 2=0. Find the area of the triangle so formed by two lines and x - axis. For Visually Impaired candidates: Five years hence, fathers age will be three times the age of son. Five years ago, father was seven times as old as his son. Find their present ages.

A train travels at a certain average speed for a distance of 63km and then travels at a distance of 72km at an average speed of 6km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original average speed?

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the sameratio. Hence in ΔPQR, prove that a line ℓ intersects the sides PQ and PR of a ΔPQR at L and M respectively such that LM || QR. If PL = 5.7cm, PQ=15.2cm and MR=5.5cm, then find the length of PM (in cm)

(A) From a solid right circular cone, whose height is 6cm and radius of base is 12cm, a right circular cylindrical cavity of height 3cm and radius 4cm is hollowed out such that bases of cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms of π. OR (B) An empty cone of radius 3cm and height 12cm is filled with ice-cream such that the lower part of the cone which is (1/6)^th of the volume of the cone is unfilled (empty) but a hemisphere is formed on the top. Find the volume of the ice-cream.

(A) If the mode of the following distribution is 55, then find the value of x. Hence, find the mean. Class Interval: 0 - 15, 15 - 30, 30 - 45, 45 - 60, 60 - 75, 75 - 90 Frequency: 10, 7, x, 15, 10, 12 OR (B) A survey regarding heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained: Heights (in cm): less than 140, less than 145, less than 150, less than 155, less than 160, less than 165 Number of girls: 04, 11, 29, 40, 46, 51 Find the median height of girls. If mode of the above distribution is 148.05, find the mean using empirical formula.

In a class, the teacher asks every student to write an example of A.P. Two boys Aryan and Roshan writes the progression as -5, -2,1,4, ...... and 187, 184, 181, .... respectively. Now the teacher asks his various students the following questions on progression. Help the students to find answers for the following: i. Find the sum of the common difference of two progressions. ii. Find the 34th term of progression written by Roshan. iii. (A) Find the sum of first 10 terms of the progression written by Aryan. OR (B) Which term of the progressions will have the same value?

A group of class X students goes to picnic during winter holidays. The position of three friends Aman, Kirti and Chahat are shown by the points P, Q and R (i) Find the distance between P and R. (ii) Is Q, the midpoint of PR? Justify by finding midpoint of PR. (iii) (A) Find the point on x-axis which is equidistant from P and Q. OR (B) Let S be a point which divides the line joining PQ in ratio 2:3. Find the coordinates of S. For Visually Impaired Candidates: A group of class X students goes to picnic during winter holidays. Aman, Kirti and Chahat are three friends. The position of three friends Aman, Kirti and Chahat are shown by the points P, Q and R. The co-ordinates of P (2,5), Q (4,4) and R (8,3) are given. (i) Find the distance between P and R. (ii) Is Q the midpoint of PR? Justify by finding midpoint of PR. (iii) (A) Find the point on x-axis which is equidistant from P and Q. OR (B) Let S be a point which divides the line joining PQ in ratio 2:3. Find the coordinates of S.

India gate (formerly known as All India war memorial) is located near Karthavya path. (formerly Rajpath) at New Delhi. It stands as a memorial to 74187 soldiers of Indian Army, who gave their life in the first world war. This 42m tall structure was designed by Sir Edwin Lutyens in the style of Roman triumphal arches. A student Shreya of height 1 m visited India Gate as a part of her study tour. i. What is the angle of elevation from Shreya's eye to the top of India Gate, if she is standing at a distance of 41m away from the India Gate? ii. If Shreya observes the angle of elevation from her eye to the top of India Gate to be 60 degrees, then how far is the she standing from the base of the India Gate? iii. (A) If the angle of elevation from Shreya's eye changes from 45 degrees to 30 degrees, when she moves some distance back from the original position. Find the distance she moves back. OR (B) If Shreya moves to a point which is at a distance of 41/sqrt(3) m from the India Gate, then find the angle of elevation made by her eye to the top of India Gate.