CBSE Class 10 Maths (Standard) Topper’s Answer Sheet 2024: PDF Download & Analysis

Are you curious about how CBSE toppers write their answers in the Class 10 Maths (Standard) board exam? Understanding the presentation style, stepwise marking, and structure of a topper's answer sheet can significantly boost your own preparation. In this blog post, we will analyze the CBSE Class 10 Maths (Standard) Topper's Answer Sheet for 2024 and provide expert insights to help you ace your board exams!

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Why Analyze the CBSE Class 10 Maths Topper’s Answer Sheet?

1. Understand the Ideal Answer Format: Learn how toppers structure their responses for maximum marks.
2. Stepwise Marking Advantage: Discover how systematic solving helps secure full marks.
3. Effective Time Management: Learn how toppers allocate time for each question.
4. Neat & Organized Presentation: See how clarity, spacing, and diagram usage impact scores.

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Topper’s Answer Sheet – Important Points to Note

1️⃣ Stepwise Answering Approach

• Always write the given data first.
• Clearly state the formula before applying it.
• Show calculations step by step to secure method marks.

2️⃣ Proper Diagram & Graph Usage

• Geometry and coordinate geometry questions require labeled diagrams.
• Graph-based questions should have proper scaling and axes labeling.

3️⃣ Neatness & Presentation

✔ Use a pencil for diagrams & rough work.
✔ Highlight the final answer with a box.
✔ Leave proper spacing between steps.
✔ Avoid overwriting and cutting.

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Solve the CBSE Class 10 Maths 2024 Board Exam Question Paper

To help students prepare effectively, we have provided the typed question paper of the CBSE 2024 board exam. It is highly recommended that students solve this paper before appearing for the 2024-25 board exam. After solving a question, students can compare their solution with the topper’s approach (screenshot provided). This will help in time management and improving paper presentation.

Why is Time Management Crucial?

In the Class 10 Maths exam, time management is a major issue. Many students fail to complete the paper despite knowing the correct answers. This happens when:

• They spend too much time on a single question.
• They waste time by double or triple-checking answers instead of completing the paper first and then reviewing.

Follow this strategy: Solve the whole paper first, then use the remaining time to recheck answers.

Also See	Link
CBSE Class 10 Maths Topper’s Answer Sheet 2023	Click Here
CBSE Class 10 Maths Topper’s Answer Sheet 2022	Click Here
CBSE Class 10 Top Case-Based Questions	Click Here

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MATHEMATICS (Standard)

General Instructions:

1. This question paper contains 38 questions. All questions are compulsory.
2. This question paper is divided into FIVE Sections – A, B, C, D, and E.
3. In Section–A, questions 1 to 18 are Multiple Choice Questions (MCQs) and questions 19 and 20 are Assertion-Reason based questions of 1 mark each.
4. In Section–B, questions 21 to 25 are Very Short Answer (VSA) type questions, carrying 2 marks each.
5. In Section–C, questions 26 to 31 are Short Answer (SA) type questions, carrying 3 marks each.
6. In Section–D, questions 32 to 35 are Long Answer (LA) type questions, carrying 5 marks each.
7. In Section–E, questions 36 to 38 are Case Study based questions carrying 4 marks each. Internal choice is provided in 2-mark questions in each case study.
8. 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.
9. Draw neat diagrams wherever required. Take π = 22/7 wherever required, if not stated.
10. Use of a calculator is NOT allowed.

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SECTION – A

(20 × 1 = 20)
This section consists of 20 questions of 1 mark each.

1. The value of k for which the system of equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 has infinitely many solutions is:
(A) -2
(B) 2
(C) 1/2
(D) -1/2

2. Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5:2. The coordinates of point P are:
(A) (5/2, -3/2)
(B) (11/7, 0)
(C) (13/7, 0)
(D) (0, 13/7)

3. The common difference of an A.P. in which a₁₅ - a₁₁ = 48 is:
(A) 12
(B) 16
(C) -12
(D) -16

4. The quadratic equation x² + x + 1 = 0 has ______ roots.
(A) real and equal
(B) irrational
(C) real and distinct
(D) not-real

5. If the HCF(2520, 6600) = 40 and LCM(2520, 6600) = 252 × k, then the value of k is:
(A) 1650
(B) 1600
(C) 165
(D) 1625

6. In the given figure, △ABC is shown. DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm, and BC = 12 cm, then DE is equal to:

(A) 10 cm
(B) 6 cm
(C) 8 cm
(D) 7.5 cm

7. If sin θ = cos θ, (0° < θ < 90°), then the value of sec θ · sin θ is:
(A) 1/√2
(B) √2
(C) 1
(D) 0

8. Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10 is:
(A) 1/9
(B) 1/6
(C) 7/12
(D) 1/12

9. If α and β are zeroes of the polynomial 5x² + 3x - 7, the value of 1/α + 1/β is:
(A) 3/7
(B) 3/5
(C) -3/7
(D) 5/7

10. The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. The ratio PQ/AB is equal to:
(A) 7/8
(B) 6/7
(C) 7/6
(D) 8/7

11. AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the following:

(A) △ ADP~ △ CBA
(B) △ ADP~ △ BPC
(C) △ ADP~ △ BCP
(D) △ ADP~ △ CBP

12. If the value of each observation in a data set is increased by 2, then the median of the new data:
(A) increases by 2
(B) increases by 2n
(C) remains the same
(D) decreases by 2

13. A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square is:
(A) 7/50
(B) 7/55
(C) 1/10
(D) 5/49

14. In the given figure, tangents PA and PB to the circle centered at O, from point P, are perpendicular to each other. If PA = 5 cm, then the length of AB is equal to:

(A) 5 cm
(B) 5√2 cm
(C) 2√5 cm
(D) 10 cm

15. XOYZ is a rectangle with vertices X(-3, 0), O(0, 0), Y(0, 4), and Z(x, y). The length of each diagonal is:
(A) 5 units
(B) √5 units
(C) x² + y² units
(D) 4 units

16. Which term of the A.P. -29, -26, -23, …, 61 is 16?
(A) 11th
(B) 16th
(C) 10th
(D) 31st

17. In the given figure, AT is a tangent to a circle centered at O. If ∠CAT = 40°, then ∠CBA is equal to:

(A) 70°
(B) 50°
(C) 65°
(D) 40°

18. After an examination, a teacher wants to know the marks obtained by the maximum number of students in her class. She requires calculating the _______ of marks.
(A) median
(B) mode
(C) mean
(D) range

Directions: For Questions 19 and 20, Assertion (A) and Reason (R) are given. Select the correct option from the following:
(A) Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true. Reason (R) does not give the correct explanation of (A).
(C) Assertion (A) is true but Reason (R) is not true.
(D) Assertion (A) is not true but Reason (R) is true.

19. Assertion (A): If sin A = 1/3 (0° < A < 90°), then the value of cos A is 2sqrt(2)/3.
Reason (R): For every angle θ, sin² θ + cos² θ = 1.

20. Assertion (A): Two cubes each of edge length 10 cm are joined together. The total surface area of the newly formed cuboid is 1200 cm².
Reason (R): The area of each surface of a cube of side 10 cm is 100 cm².

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SECTION – B

(5 × 2 = 10)
This section consists of 5 questions of 2 marks each.

21. Can the number (15)ⁿ, where n is a natural number, end with the digit 0? Give reasons.

22. Find the type of triangle ABC formed by the vertices A(1, 0), B(-5, 0), and C(-2, 5).

23. (a) Evaluate: 2 sin² 30° sec 60° + tan² 60°.
OR
(b) If 2 sin (A + B) = sqrt(3) and cos (A - B) = 1, find the measures of angles A and B, where 0° ≤ A, B, (A + B) ≤ 90°.

24. In the given figure, AB and CD are tangents to a circle centered at O. Is ∠BAC = ∠DCA? Justify your answer.

25. (a) In what ratio is the line segment joining the points (3, -5) and (-1, 6) divided by the line y = x?
OR
(b) A(3, 0), B(6, 4), and C(-1, 3) are vertices of triangle ABC. Find the length of its median BE.

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SECTION – C

(6 × 3 = 18)
This section consists of 6 questions of 3 marks each.

26. (a) If the sum of the first m terms of an A.P. is the same as the sum of its first n terms (m ≠ n), then show that the sum of its first (m + n) terms is zero.
OR
(b) In an A.P., the sum of three consecutive terms is 24 and the sum of their squares is 194. Find the numbers.

27. Prove that √5 is an irrational number.

28. (a) In the given figure, PQ is a tangent to a circle centered at O and ∠BAQ = 30°; show that BP = BQ.

OR
(b) In the given figure, AB, BC, CD, and DA are tangents to the circle with center O forming a quadrilateral ABCD.

Show that ∠AOB + ∠COD = 180°.

29. Prove that (1 + sec θ - tan θ)/(1 + sec θ + tan θ) = (1 - sin θ)/(cos θ).

30. In a test, the marks obtained by 100 students (out of 50) are given below:

Marks Obtained	0–10	10–20	20–30	30–40	40–50
Number of Students	12	23	34	25	6

Find the mean marks of the students.

31. In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The product of the digits is 36. Find the number.

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SECTION – D

(4 × 5 = 20)
This section consists of 4 questions of 5 marks each.

32. (a) Using the graphical method, solve the following system of equations:
3x + y + 4 = 0 and 3x - y + 2 = 0.
OR
(b) Tara scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, Tara would have scored 50 marks. Assuming Tara attempted all questions, find the total number of questions in the test.

33. (a) 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.
OR
(b) Sides AB and AC and median AD of △ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that △ABC ~ △PQR.

34. From the top of a 45 m high lighthouse, the angles of depression of two ships, on opposite sides of it, are observed to be 30° and 60°. If the line joining the ships passes through the foot of the lighthouse, find the distance between the ships. (Use √3 = 1.73)

35. The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.

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SECTION – E

(3 × 4 = 12)
This section consists of 3 case-based questions of 4 marks each.

Also See: CBSE Class 10 Top Case-Based Questions

36. A ball is thrown in the air so that t seconds after it is thrown, its height h meters above its starting point is given by the polynomial h = 25t - 5t².

Observe the graph of the polynomial and answer the following questions:
(i) Write the zeroes of the given polynomial. (1 mark)
(ii) Find the maximum height achieved by the ball. (1 mark)
(iii) (a) After throwing upward, how much time did the ball take to reach the height of 30 m? (2 marks)
OR
(iii) (b) Find the two different values of t when the height of the ball was 20 m. (2 marks)

37. The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.
A circus tent is cylindrical up to a height of 8 m and conical above it. The diameter of the base is 28 m and the total height of the tent is 18.5 m.

Based on the above, answer the following questions:
(i) Find the slant height of the conical part. (1 mark)
(ii) Determine the floor area of the tent. (1 mark)
(iii) (a) Find the area of the cloth used for making the tent. (2 marks)
OR
(iii) (b) Find the total volume of air inside an empty tent. (2 marks)

38. In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.

Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she traveled by bus or ship. (1 mark)
(ii) Which is the most favorite mode of transport, and how many people used it? (1 mark)
(iii) (a) A person is selected at random. If the probability that he did not use the train is 4/5, find the number of people who used the train. (2 marks)
OR
(iii) (b) The probability that a randomly selected person used an aeroplane is 7/60. Find the revenue collected by the air company at the rate of ₹5,000 per person. (2 marks)

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Analysis of the Topper’s Answer Sheet

We have embedded the topper’s answer sheet PDF below for reference. While reviewing it, note these key points:

1. Answer serially as far as possible.
2. Draw neat and clean diagrams with pencils.
3. If you make a mistake in a calculation, simply cut it by drawing a line instead of scrubbing the pen over it. See the topper’s approach in Question No. 25 in the embedded PDF.
4. Don’t skip any step in overconfidence, as it will cause silly mistakes.
5. Don’t panic; instead, maintain a slow and steady pace.
6. While drawing graphs, write the scale in a box. See the topper’s approach—it’s perfect.

Maths_Stand_rotated

Download CBSE Class 10 Maths Topper’s Answer Sheet 2024

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Links for More Resources

Also See	Link
CBSE Class 10 Maths Topper’s Answer Sheet 2023	Click Here
CBSE Class 10 Maths Topper’s Answer Sheet 2022	Click Here
CBSE Class 10 Top Case-Based Questions	Click Here

Final Thoughts

Scoring 90+ marks in CBSE Class 10 Maths (Standard) is achievable if you follow a structured approach like toppers. Use this guide to improve your answer presentation and maximize your marks in the upcoming board exams.

Have questions? Drop them in the comments below!

For more CBSE updates, sample papers, and topper strategies, follow CBSE Guidance!