QUESTION PAPER
2026 BOARD EXAM
CBSE Class 10 Mathematics Board Paper 2026 — Set 6
2026
Mathematics
Class 10
CBSE EXAMINATION PAPER-2026
MATHEMATICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 44 questions. All questions are compulsory.
- This question paper is divided into 5 sections.
- Section A – questions number 1 to 3 are case based questions
- Section B – questions number 4 to 23 are multiple choice questions
- Section C – questions number 24 to 30 are very short answer
- Section D – questions number 31 to 38 are short answer
- Section E – questions number 39 to 44 are long answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
While playing badminton Ravi has set the barrier chain hung between two posts at the edge of the walkway of a street. It is hung in the shape of a parabola.
Based on the above information answer the following questions :
(1) Which type of the polynomial (linear, quadratic, cubic etc.) is graphically represented by a parabola ?
[1 Mark](2) If the polynomial represented by a parabola, intersects the x-axis at –2 and 3 and y-axis at –3, then write the zeroes of the parabola.
[1 Mark](3) Find the expression for the above polynomial.
[1 Mark](4) If the zeroes of the polynomial are –5 and 3, find its expression.
[1 Mark]A friend of you wants to buy an electric car for which he plans to take a loan from a bank and plans to pay the total loan and the interest = ₹ 5,90,000, by paying every month starting with the first instalment of ₹ 5,000. He increases the instalment by ₹ 500 every month.
Based on the above, answer the following questions :
(1) What are the first three instalments paid by him ?
[1 Mark](2) Find the amount to be paid by him in 11th instalment.
[1 Mark](3) After paying the 31st instalment, find how much money he still has to pay.
[1 Mark](4) Find the number of instalments in which he would clear his total loan.
[1 Mark]Raghav has a collection of balls of different colours. He has a total of 35 balls in his basket out of which seven are black in colour and eight are yellow in colour. Out of remaining balls, some are white and the rest are red.
Based on the above, answer the following questions :
(1) If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket.
[2 Marks](2) Find the probability of drawing a ball at random from the basket which is either a black or a white ball.
[2 Marks]Section B
At which of the following points, the quadratic polynomial p(x) = – 3x + 18x² – 1 intersects the positive x-axis ?
If pair of linear equations given by a₁ x + b₁ y + c₁ = 0 and a₂ x + b₂ y + c₂ = 0 has infinitely many solutions, then which of the following is definitely true ?
The 31st term of the A.P. : –5/6.-3/4,-2/3,-7/12,....
Four tangents drawn to a circle are extended from both the sides to form a quadrilateral. Which of these quadrilateral is not possible ?
ABCD is a trapezium in which AB||DC and E, F are points on AD and BC respectively such that EF||DC. If ED = 36 cm, BF = 70 cm and FC = 30 cm, then the length of AD is :
If x⋅tan 45°⋅sin 30° = cos 30°⋅cot 60° then x is equal to
If △DEF∼△PQR such that 3 DE = PQ and EF = 6 cm, then the length of QR is
If a, b, c and d are consecutive terms of an A.P., then c – b is equal to :
If in a △ABC, AB = 6 cm and DE||BC such that AE = 1 /3 AC then the length of BD is
The perimeter of sector of a circle of radius 21 cm and central angle 60°, is
The number of conical bottles of radius 2 cm and height 1.2 cm that can be filled from a cylindrical bottle of radius 6 cm and height 8 cm, full of liquid, is
One ticket is drawn at random from a bag containing 50 tickets numbered 1 to 50. The probability that the drawn ticket has a number which is a multiple of 7 is :
Two dice are thrown simultaneously. The probability of getting a sum of 7 is :
If HCF of 66 and 99 is expressible in the form of 55m – 132, then the value of m is :
sin 2 θ= 2 sin θ is true, when θ is equal to
Assertion (A) : If the Mode and Mean of a data are 12 k and 15 k, then Median of the data is 14 k. Reason (R) : The relation between the Mean, Mode and Median of a data is : Mean = 3 Median – 2 Mode.
Section C
Two numbers are in the ratio 3 : 5 and their LCM is 180. Find the HCF of these two numbers.
Find the quadratic polynomial the sum of whose zeroes is 1 and their product is −12. Hence find the zeroes of the polynomial.
A circle is inscribed in a right triangle ABC, right angled at B. If the lengths of the two sides containing the right angle are 8 cm and 15 cm, find the radius of the circle.
If 4 tan A= 3, then find the value of cosec²A+1./cosec²A-1.
If 7sin²A+3 cos²A=4, then find the value of tan A
A chord AB of a circle of radius 14 cm makes a right angle at the centre of the circle. Find the area of the minor segment.
An arc of length 22 cm subtends an angle of 60° at the centre of the circle. Find the area of the sector of the circle made by the arc.
Section D
Prove that ( 2+3√5)/7 is an irrational number, given that √5 is an irrational number.
Find the coordinates of the points of trisection of the line segment joining the points P(5, –4) and Q(–4, 2).
Find the ratio in which the point P (6, k) divides the line segment joining the points M (4, 2) and N (8, –4). Hence find the value of k.
Find the ratio in which the point P (6, k) divides the line segment joining the points M (4, 2) and N (8, –4). Hence find the value of k.
Prove that the parallelogram circumscribing a circle is a rhombus.
AB is a chord of length 24 cm of a circle of radius 15 cm. The tangents at A and B intersect at a point P. Find the length PA.
If cos A + sin A =√2 cos A, prove that cos A – sin A =√2 sin A.
Find the mean of the following distribution :
Class | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 |
|---|
Frequency | 6 | 13 | 8 | 12 | 11 |
Section E
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
The sum of numerator and denominator of a fraction is 4 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 1/ 3 Find the fraction.
Three consecutive positive integers are such that sum of square of the first and the product of the other two is 67, find the integers.
CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively.
If ΔABC ∼ ΔFEG, then show that
(i) CD/GH = AC/FG and
(ii) ΔDCB ∼ ΔHGE.
Two poles of equal heights are standing opposite to each other on either side of the road which is 90 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 60° respectively. Find the height of the poles and the distances of the point from the poles (use √3 = 1.732.)
From a solid cylinder whose height is 2.8 cm and radius 2.1 cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total surface area of the remaining solid.
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