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CBSE Class 10 Maths Important Questions and Answers 2023
The Central Board of Secondary Education (CBSE) conducted the CBSE Class 10 Mathematics exam. Students who will attend the CBSE 10th exam in Maths are advised to review the previous year's Maths question papers. The CBSE 10th Mathematics exam paper consisted of 38 questions, divided into five sections.
This Story also Contains
- Previous Year's CBSE Class 10 Mathematics Paper- MCQs (1 mark each)
- CBSE Class 10 Mathematics Paper - 2 Marks Questions
- CBSE Class 10 Mathematics Question Paper - 3 Marks Questions
- CBSE Class 10 Mathematics question - 5 Marks Questions
- CBSE Class 10 Mathematics questions - 4 Marks Questions
- Benefits of Solving Last Year’s CBSE 10th Maths Question Paper
Students were required to attempt all 5 sections, which consist of MCQs, short answer type questions, and long answer type questions consisting of 1, 2, 3, 4, and 5 marks. We have listed a few questions that were asked in the previous year's CBSE Maths board exam. Students can go through these questions to get an insight into the types of questions that hold importance and are asked in the final board exams.
Previous Year's CBSE Class 10 Mathematics Paper- MCQs (1 mark each)
Section A of the CBSE Mathematics paper Class 10 had 18 multiple-choice questions, which carried a weightage of 1 mark each. 2 assertion-reason based questions were also asked of 1 mark. Below, we have listed questions for students' reference:
Q1. The prime factorisation of the natural number 288 is:
24 x 33
24 x 32
25 x 32
25 x 31
Q2. If $2\cos\theta$= 1, then the value of $\theta$ is
$45^{\circ}$
$60^{\circ}$
$30^{\circ}$
$90^{\circ}$
CBSE Class 10th Syllabus 2025-26
Students can access the subject-wise CBSE Class 10 syllabus for the 2025–26 academic session.
Check NowQ3. A card is drawn at random from a well-shuffled deck of 52 cards. The probability of getting a red card is:
1/26
1/13
1/ 4
1/2
Q4. The discriminant of the quadratic equation $2x^{2} - 5x - 3 = 0$ is
1
49
7
19
Q5. The distance between the points (3, 0) and (0, -3) is
$2 \sqrt{3}$ units
6 units
3 units
$3 \sqrt{2}$ units
Q6. The seventh term of an A.P. whose first term is 28 and common difference
- 4, is
0
4
52
56
Q8. The sides of two similar triangles are in the ratio 4: 7. The ratio of their
perimeters are:
4: 7
12: 21
16: 49
7: 4
Q10. The sum and the product of zeroes of the polynomial p(x) =$ x^2$$ + 5x + 6$ are
respectively
5, -6
-5, 6
2, 3
-2, -3
Q11. A die is thrown once. Find the probability of getting a number less than 7.
5/6
1
1/6
0
Q13. The volume of a cone of radius ‘r' and height '3r' is :
$1/ 3$$\pi r^2$
$3\pi r^3$
$9\pi r^3$
$\pi r^3$
Q14. The distance between two parallel tangents of a circle of diameter 7 cm is:
7 cm
14 cm
7/2 cm
28 cm
Q16. The larger of the two supplementary angles exceeds the smaller by 18 degrees. What is the measure of the larger angle?
$81^{\circ}$
$99^{\circ}$
$36^{\circ}$
$54^{\circ}$
Directions for Q.19 & Q.20 - In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:
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, but Reason (R) is not the
correct explanation of Assertion (A).
c) Assertion (A) is true, but Reason (R) is false.
d) Assertion (A) is false, but Reason (R) is true.
Q19. Assertion (A): A tangent to a circle is perpendicular to the radius
through the point of contact.
Reason (R): The lengths of tangents drawn from the external point to a
circles are equal.
CBSE Class 10 Mathematics Paper - 2 Marks Questions
Section B of the Mathematics paper CBSE 10th Class consists of short answer questions carrying a weightage of 2 marks each. Students are required to attempt 5 questions from this section. Below, we have listed questions that were given in the CBSE 10th Maths previous year PDF:
Q21. a) Find the coordinates of the point which divides the line segment
joining the points (7, -1) and (-3, 4) internally in the ratio 2: 3.
OR
(b) Find the value(s) of y for which the distance between the points
A(3, -1) and B(11, y) is 10 units.
Q22. Evaluate :$\tan^{2}60^{\circ}-2 \operatorname{cosec^{2}} 30^{\circ}-2 \tan ^{2}30^{\circ}$
Q23. Find the LCM and HCF of 92 and 510, using prime factorisation.
Q 24. (a) Solve for x and y : x + y = 6, 2x - 3y = 4.
OR
(b) Find out whether the following pair of linear equations is
consistent or inconsistent:
5x - 3y = 11, 10x + 6y = 22
CBSE Class 10 Mathematics Question Paper - 3 Marks Questions
Section C of the Mathematics paper CBSE 10th Class consisted of short answer questions carrying a weightage of 3 marks each. Students are required to attempt 6 questions from this section. Below are the questions have been mentioned which were a part of the CBSE Maths Class 10 exam.
Q27. Show that the points A(1, 7), B(4, 2) C(-1, -1) and D(- 4, 4) are vertices of the square ABCD.
Q28. Prove that the tangents drawn from an external point to a circle are equal
in length.
Q29. If $\alpha$, $\beta$ are zeroes of the quadratic polynomial $x^2+ 3x + 2$, find a quadratic
polynomial whose zeroes are $\alpha+ 1$, $\beta + 1$.
Q30. Prove that $3 + 7 \sqrt {2}$ is an irrational number, given that $\sqrt{2}$ is an irrational
number.
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CBSE Class 10 Mathematics question - 5 Marks Questions
Section D of the CBSE 10th Maths paper consists of long-answer type questions that each carry 5 marks. Students have to attempt 4 questions from this section. Below, we have listed the questions that were asked in the previous year's CBSE Maths paper:
Q32. (a) The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 80 m more than the shorter side, find the length of the sides of the field.
OR
(b) The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present age.
Q33. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of the same diameter. The diameter of the hemispherical bowl is 14 cm, and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. Also, find the volume of the vessel.
Q34. The table given below shows the daily expenditure on food of 25 households in a locality:
Daily Expenditure | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |
No. of households | 4 | 5 | 12 | 2 | 2 |
Find the mean daily expenditure on food. Also, find the mode of the data.
Q35. (a) A TV tower stands vertically on the bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from the point on the line joining this point to the foot of the tower, the angle
of elevation of the top of the tower is $30^{\circ}$. Find the height of the tower.
OR
(b) An aeroplane, when flying at a height of 4000 m from the ground, passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. Find the vertical distance between the aeroplanes at that instant. (Use $\sqrt{3}$ = 1.73)
CBSE Class 10 Mathematics questions - 4 Marks Questions
Section E of the CBSE 10th Maths exam paper consists of 3 source-based/Case-based/passage-based/integrated units of assessment (4 marks each) with sub-parts of the values of 1, 1, and 2 marks each, respectively. Below, we have mentioned the questions that were asked in the CBSE Class 10 Maths paper:
Q36. Aahan, being a plant lover, decides to convert her balcony into a beautiful garden full of plants. She bought a few plants with pots for her balcony. She placed the pots in such a way that the number of pots in the first row is 2, second row is 5. The third row is 8 and so on.
Based on the above information, answer the following questions :
(i)Find the number of pots placed in the 10th row.
(ii) Find the difference in the number of pots placed in the 5th row and the 2nd row.
(iii) If Aahana wants to place 100 pots in total, then find the total number of rows formed in the arrangement.
OR
(iii) If Aahana has sufficient space for 12 rows, then how many total number of pots are placed by her with the same arrangement?
Q37. The Interschool Rangoli Competition was organized by one of the reputed
schools of Odisha. The theme of the Rangoli Competition was Diwali celebrations, where students were supposed to make mathematical designs. Students from various schools participated and made beautiful Rangoli designs. One such design is given below:
Rangoli is in the shape of a square marked as ABCD, the side of the square being 40 cm. At each corner of a square, a quadrant of a circle of radius 10 cm is drawn (in which diyas are kept). Also, a circle of diameter 20 cm is drawn inside the square.
(i) What is the area of square ABCD?
(ii) Find the area of the circle.
(iii) If the circle and the four quadrants are cut off from the square ABCD
and removed, then find the area of the remaining portion of square ABCD.
OR
(iii) Find the combined area of 4 quadrants and the circle, removed.
Q38. Blood group describes the type of blood a person has. It is a classification of blood based on the presence or absence of inherited antigenic substances on the surface of red blood cells. Blood types predict whether a serious reaction will occur in a blood transfusion.
In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B, and the rest had type AB blood group.
Based on the above, answer the following questions:
(i) What is the probability that a person chosen at random has type O blood?
(ii) What is the probability that a person chosen at random has type AB blood group?
(iii) What is the probability that a person chosen at random has neither type A nor type B blood group?
OR
(iii) What is the probability that a person chosen at random has either type A or type B, or type O blood group?
Benefits of Solving Last Year’s CBSE 10th Maths Question Paper
There are numerous benefits of referring to and solving previous years’ Maths question papers of CBSE 10th class. Below, we have listed a few pros of solving the CBSE 10th Maths question paper:
Solving last year's CBSE Class 10 Mathematics board exam question paper helps students understand the exam pattern and question paper format.
By solving past papers, students can identify the topics that are frequently asked and prioritize their study accordingly.
Practising with the previous year's Maths papers CBSE 10th enables students to manage their time effectively during the actual exam, as they get accustomed to the allotted time for answering the paper.
Successfully solving CBSE Class 10 Maths previous year paper boosts students' confidence as they get a sense of accomplishment and readiness for the upcoming 2026 board exam.
Analyzing previous year's papers also helps students understand the marking scheme and allocate time and effort accordingly to high-scoring sections.
By reviewing their answers, students can identify and rectify common mistakes, improving their overall accuracy.
Regular practice with CBSE 10th Maths past year papers enhances students' problem-solving abilities and equips them with strategies to tackle complex problems.
Solving the CBSE 10th Maths exam paper serves as a comprehensive revision tool, allowing students to consolidate their understanding of concepts and formulas.
Also, Check:
Frequently Asked Questions (FAQs)
Q: Are calculators allowed in the CBSE 10th class Maths exam?
A:
No, calculators are generally not allowed in the CBSE 10th class Maths exam. Students are expected to perform calculations manually.
Q: What are the total marks for CBSE 10th Maths theory paper?
A:
The CBSE 10th Maths theory paper carries a weightage of 80 marks, while 20 marks are reserved for internal assessment/project.
Q: How should I manage my time during the CBSE 10th class Maths exam?
A:
Allocate time wisely to each section based on the number of questions and difficulty level. Start with easier questions to build confidence and manage time effectively for the more challenging ones.
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On Question asked by student community
Have a question related to CBSE Class 10th ?
Hello,
Yes, you can give the CBSE board exam in 2027.
If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.
Hope it helps !
Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.
Hello Aspirant,
Here's how you can find it:
-
School ID Card: Your registration number is often printed on your school ID card.
-
Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.
-
School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.
-
Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.
Your school is the best place to get this information.
Hello,
It appears you are asking if you can fill out a form after passing your 10th grade examination in the 2024-2025 academic session.
The answer depends on what form you are referring to. Some forms might be for courses or examinations where passing 10th grade is a prerequisite or an eligibility criteria, such as applying for further education or specific entrance exams. Other forms might be related to other purposes, like applying for a job, which may also have age and educational requirements.
For example, if you are looking to apply for JEE Main 2025 (a competitive exam in India), having passed class 12 or appearing for it in 2025 are mentioned as eligibility criteria.
Let me know if you need imformation about any exam eligibility criteria.
good wishes for your future!!
Hello Aspirant,
"Real papers" for CBSE board exams are the previous year's question papers . You can find these, along with sample papers and their marking schemes , on the official CBSE Academic website (cbseacademic.nic.in).
For notes , refer to NCERT textbooks as they are the primary source for CBSE exams. Many educational websites also provide chapter-wise revision notes and study material that align with the NCERT syllabus. Focus on practicing previous papers and understanding concepts thoroughly.
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