- Find the probability that the drawn card is a face card. [1]
- Find the probability that the drawn card is either a king or a queen. [1]
-
- Do you think that the probability of getting a queen was higher if none of the cards were dropped? Justify your answer. [2]
OR - 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? [2]
- Do you think that the probability of getting a queen was higher if none of the cards were dropped? Justify your answer. [2]
Mathematics [Board Official Paper - Standard]
Marks: 80 CBSE
English Medium
Academic Year: 2025-2026
Date & Time: 17th February 2026, 10:30 am
Duration: 3h
English Medium
Academic Year: 2025-2026
Date & Time: 17th February 2026, 10:30 am
Duration: 3h
Advertisements
NOTE:
- Please check that this question paper contains 27 printed pages.
- Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate.
- Please check that this question paper contains 38 questions.
- Please write down the Serial Number of the question in the answer-book at the given place before attempting it.
- 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the candidates will read the question paper only and will not write any answer on the answer-book during this period.
General Instructions:
Read the following instructions very carefully and strictly follow them:
- This question paper contains 38 questions. All questions are compulsory.
- This question paper is divided into five Sections − A, B, C, D, and E.
- In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs), and questions number 19 and 20 are Assertion-Reason based questions of 1 mark each.
- In Section B, Questions no. 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each.
- In Section C, Questions no. 26 to 31 are short answer (SA) type questions, carrying 3 marks each.
- In Section D, Questions no. 32 to 35 are long answer (LA) type questions, carrying 5 marks each.
- In Section E, Questions no. 36 to 38 are case study based questions, carrying 4 marks each. Internal choice is provided in 2 marks questions in each case study.
- There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D, and 3 questions in Section E.
- Draw neat diagrams wherever required. Take π = `22/7` wherever required, if not stated.
- Use of a calculator is not allowed.
SECTION - A (20 Marks)
This section has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
[1]1.The roots of the quadratic equation (x − 1)2 = 16 are ______.
5, 3
4, −4
5, −3
−5, 3
Concept: undefined - undefined
Chapter:
Chapter:
[1]2.
In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If ∠QPR = 60°, then the length of each tangent is:
`3sqrt3` cm
3 cm
6 cm
`sqrt3` cm
Concept: undefined - undefined
Chapter:
Chapter:
[1]3.
In Δ DEF, AB || EF. The value of x is ______.
0, 2
2 only
−2
1
Concept: undefined - undefined
Chapter:
Chapter:
[1]4.
(3 × 11 × 13 + 3) is ______.
a prime number
divisible by 13
a composite number
an odd number
Concept: undefined - undefined
Chapter:
Chapter:
[1]5.
Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is ______.
`1/6`
`11/36`
`1/12`
`1/4`
Concept: undefined - undefined
Chapter:
Chapter:
[1]6.
The number of multiples of 4 lying between 12 and 250 is ______.
59
59.5
60
61
Concept: undefined - undefined
Chapter:
Chapter:
[1]7.
A cone of maximum size is carved out from a solid cube of edge length l. The volume of the cone is ______.
`(pil^3)/(12)`
`(pil^3)/(3)`
`l^3(1 - pi/3)`
`(pil^3)/(8)`
Concept: undefined - undefined
Chapter:
Chapter:
[1]8.
Equation of another line parallel to the line represented by 2x − 6y = 7 is ______.
y = 3x − 7
2x = 9 − 6y
x − 3y = 7
`x = 7/2 - 3y`
Concept: undefined - undefined
Chapter:
Chapter:
[1]9.
If the length of the shadow of a tower is `sqrt(3)` times that of its height, then altitude of the sun is ______.
45°
30°
60°
15°
Concept: undefined - undefined
Chapter:
Chapter:
[1]10.
If the roots of the quadratic equation `sqrt3x^2 - kx + 2sqrt3 = 0` are real and equal, then the value (s) of k is/are ______.
`±sqrt24`
0
4
−5
Concept: undefined - undefined
Chapter:
Chapter:
[1]11.
The nth term of the A.P. `(-1)/3, 2/3, 5/3, 8/3,` ......, is ______.
3n − 4
`n - 4/3`
`(n - 2)/3`
`(n - 4)/3`
Concept: undefined - undefined
Chapter:
Chapter:
[1]12.
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:
`rsqrt2`
`sqrt2r`
2r
r2
Concept: undefined - undefined
Chapter:
Chapter:
[1]13.
It is given that ΔABC ~ ΔQRP such that AB = 9 cm, BC = 5 cm and PR = 2 cm. Length of side QR is ______.
0.9 cm
`5/18` cm
`10/9` cm
3.6 cm
Concept: undefined - undefined
Chapter:
Chapter:
[1]14.
The sum and product of zeroes of a quadratic polynomial p(x) are `(-1)/3 and 2` respectively. The polynomial p(x) is ______.
3x2 − x + 6
`x^2 + 1/3 x - 2`
3x2 − x + 2
−3x2 − x − 6
Concept: undefined - undefined
Chapter:
Chapter:
Advertisements
[1]15.
Given that sin 2α = `sqrt3/2`, the value of sin 3α is ______.
`(3sqrt3)/4`
`1/2`
1
`sqrt3/4`
Concept: undefined - undefined
Chapter:
Chapter:
[1]16.
The median and mode of a distribution are 25.2 and 26.1 respectively. The mean of the distribution is ______.
24.75
24.25
24.3
25.5
Concept: undefined - undefined
Chapter:
Chapter:
[1]17.
In the given figure, Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points `A(0, (5sqrt3)/2), D(0, 0)`. Points B and C are (in same order):
(−5, 0), (5, 0)
`((−5)/2, 0), (5/2, 0)`
(−10, 0), (10, 0)
`(−5sqrt3, 0), (5sqrt3, 0)`
Concept: undefined - undefined
Chapter:
Chapter:
[1]18.
The value of `(1/2 tan^2 45° - cos^2 60°)` is ______.
0
`-1/2`
`1/4`
`-1/4`
Concept: undefined - undefined
Chapter:
Chapter:
Questions numbers 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:
[1]19.Assertion (A): Radius is the smallest distance of a tangent from the centre of the circle.
Reason (R): Radius is perpendicular to the tangent.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Concept: undefined - undefined
Chapter:
Chapter:
[1]20.
Assertion (A): tan 2θ is not defined at θ = 45°.
Reason (R): sin90° = cos 90°.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Concept: undefined - undefined
Chapter:
Chapter:
SECTION - B (10 Marks)
This section has 5 Very Short Answer (VSA) type questions carrying 2 marks each.
[2]21.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.
Concept: undefined - undefined
Chapter:
Chapter:
[2]22. (a)
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.
Concept: undefined - undefined
Chapter:
Chapter:
OR
[2]22. (b)Find the sum of the first 28 terms of an AP. whose nth term is given by an = 3n − 2.
Concept: undefined - undefined
Chapter:
Chapter:
[2]23. (a)
Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, −2) and (1, 6) respectively.
- Find the co-ordinates of point P.
- Find the length of the side of the square.
Concept: undefined - undefined
Chapter:
Chapter:
OR
[2]23. (b)Find the coordinates of a point on the line x + y = 5 which is equidistant from (6, 4) and (5, 2).
Concept: undefined - undefined
Chapter:
Chapter:
[2]24.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that `(AO)/(BO) = (CO)/(DO)`. Show that ABCD is a trapezium.
Concept: undefined - undefined
Chapter:
Chapter:
[2]25.
A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.
Concept: undefined - undefined
Chapter:
Chapter:
SECTION - C (18 Marks)
This section has 6 Short Answer (SA) type questions carrying 3 marks each.
[3]26. (a)If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Concept: undefined - undefined
Chapter: [9] Introduction to Trigonometry
Chapter: [9] Introduction to Trigonometry
Advertisements
OR
[3]26. (b)Prove that:
(sin A + sec A)2 + (cos A + cosec A)2 = (1 + sec A cosec A)2
Concept: undefined - undefined
Chapter:
Chapter:
[3]27.
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.
Concept: undefined - undefined
Chapter:
Chapter:
[3]28.
[3]29.
Find two consecutive negative integers, sum of whose squares is 481.
Concept: undefined - undefined
Chapter:
Chapter:
[3]30.
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.
Concept: undefined - undefined
Chapter:
Chapter:
[3]31. (a)
PA and PB are tangents drawn to the circle with centre O as shown in the figure. Prove that ∠APB = 2∠OAB.
Concept: undefined - undefined
Chapter:
Chapter:
OR
[3]31. (b)In the given figure, PA is the tangent to the circle with centre O such that OA = 10 cm, AB = 8 cm and AB ⊥ OP. Find the length of PB.
Concept: undefined - undefined
Chapter:
Chapter:
SECTION - D (20 Marks)
This section has 4 Long Answer (LA) type questions carrying 5 marks each.
[5]32. (a)The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68.
| Class | Frequency |
| 65-85 | 4 |
| 85-105 | 5 |
| 105-125 | x |
| 125-145 | 20 |
| 145-165 | 14 |
| 165-185 | y |
| 185-205 | 4 |
Concept: undefined - undefined
Chapter:
Chapter:
OR
[5]32. (b)Find mean and mode of the following distribution:
| Class | Frequency |
| 0-10 | 3 |
| 10-20 | 6 |
| 20-30 | 11 |
| 30-40 | 10 |
| 40-50 | 13 |
| 50-60 | 3 |
| 60-70 | 4 |
Concept: undefined - undefined
Chapter:
Chapter:
[5]33.
In Δ 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.
Concept: undefined - undefined
Chapter:
Chapter:
[5]34. (a)
Solve the following system of equations graphically:
x − 2y = 3, 3x − 8y = 7
Concept: undefined - undefined
Chapter:
Chapter:
OR
[5]34. (b)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:
- Form the linear equations representing the above information.
- Show that the system of equations is consistent with unique solution.
- Find the present ages of Adil and Bharat.
Concept: undefined - undefined
Chapter:
Chapter:
[5]35.
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 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 `sqrt3 = 1.73`)
Concept: undefined - undefined
Chapter:
Chapter:
SECTION - E (12 Marks)
The section has 3 case study based questions carrying 4 marks each.
[4]36.|
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) = −x2 + 2x + 8, where x is the length (in feet) on stage level.
|
Based on the figure given above, answer the following questions:
- Determine the height of the arch. [1]
-
- Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes? [2]
OR - Find the span of the arch on the stage floor. [2]
- Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes? [2]
- Write the coordinates of the point of intersection of the above curve with the y-axis. [1]
Concept: undefined - undefined
Chapter:
Chapter:
[4]37.
|
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:
|
Concept: undefined - undefined
Chapter:
Chapter:
[4]38.
|
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:
- Determine the total height of the fountain. [1]
- Find the volume of the ball. [1]
-
- If one-third of the ball is submerged in the water, find the volume of the water filled in the pool. [2]
OR - Find the sum of the outer curved surface area of the cylindrical part and surface area of the ball. [2]
- If one-third of the ball is submerged in the water, find the volume of the water filled in the pool. [2]
Concept: undefined - undefined
Chapter:
Chapter:
Other Solutions
Submit Question Paper
Help us maintain new question papers on Shaalaa.com, so we can continue to help studentsonly jpg, png and pdf files
CBSE previous year question papers Class 10 Mathematics with solutions 2025 - 2026
CBSE Class 10 Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our CBSE Class 10 Maths question paper 2026 serve as a catalyst to prepare for your Mathematics board examination.
Previous year Question paper for CBSE Class 10 Maths-2026 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 10.
How CBSE Class 10 Question Paper solutions Help Students ?
• Question paper solutions for Mathematics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
Previous year Question paper for CBSE Class 10 Maths-2026 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 10.
How CBSE Class 10 Question Paper solutions Help Students ?
• Question paper solutions for Mathematics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
