Practice Question Paper — not an official CBSE document
Class 10 · Mathematics (Standard)
Subject Code 041 · Set 1 of 3
Time allowed: 3 hoursMaximum marks: 8038 questions
General instructions
This practice paper has 38 questions in five sections. All questions are compulsory.
Section A: Q1–18 are MCQs and Q19–20 are Assertion–Reason, 1 mark each.
Section B: Q21–25 are very short answers of 2 marks each. Internal choice is given in 2 questions.
Section C: Q26–31 are short answers of 3 marks each. Internal choice is given in 2 questions.
Section D: Q32–35 are long answers of 5 marks each. Internal choice is given in 2 questions.
Section E: Q36–38 are case-study questions of 4 marks each (typical split 1 + 1 + 2). Internal choice is given on the 2-mark part.
Use of calculator is not allowed. Take π = 22/7 wherever required.
Practice questions aligned to NCERT topics used in CBSE classrooms. These are original exam-oriented questions for revision — not official CBSE board papers and not a guarantee of any exam question. Always match the textbook issued by your school and the latest PDFs on ncert.nic.in and cbseacademic.nic.in.
Section A
Objective type (MCQ and Assertion–Reason) · Q1–20 · 1 mark each · 20 marks
Q.1MCQPair of Linear Equations in Two Variables[1]
Choose the correct statement related to Textbook first in the chapter Pair of Linear Equations in Two Variables.
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Answer / marking points
A. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
Note
Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.2MCQIntroduction to Trigonometry[1]
Choose the correct statement related to Diagrams in the chapter Introduction to Trigonometry.
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Answer / marking points
B. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
Note
If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.3MCQStatistics[1]
Choose the correct statement related to Practice in the chapter Statistics.
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Answer / marking points
C. Mix MCQs with short answers so you remember both facts and explanations from Statistics
Note
Mix MCQs with short answers so you remember both facts and explanations from Statistics. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.4MCQQuadratic Equations[1]
Choose the correct statement related to Quadratic Equations in the chapter Quadratic Equations.
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Answer / marking points
C. D>0 two distinct real roots
Note
D>0 two distinct real roots. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.5MCQSome Applications of Trigonometry[1]
Choose the correct statement related to Some Applications of Trigonometry in the chapter Some Applications of Trigonometry.
Show answer / marking points
Answer / marking points
B. Some Applications of Trigonometry is an NCERT chapter taught in CBSE Class 10 Mathematics
Note
Some Applications of Trigonometry is an NCERT chapter taught in CBSE Class 10 Mathematics. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.6MCQProbability[1]
Choose the correct statement related to Examples in the chapter Probability.
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Answer / marking points
B. CBSE often tests a concept by asking a daily-life example from the same chapter
Note
CBSE often tests a concept by asking a daily-life example from the same chapter. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.7MCQArithmetic Progressions[1]
Choose the correct statement related to Accuracy in the chapter Arithmetic Progressions.
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Answer / marking points
C. Use the terms used in the NCERT book; do not replace them with unofficial names
Note
Use the terms used in the NCERT book; do not replace them with unofficial names. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.8MCQCircles[1]
Choose the correct statement related to Circles in the chapter Circles.
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Answer / marking points
D. Two tangents from an external point are equal
Note
Two tangents from an external point are equal. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.9MCQReal Numbers[1]
Choose the correct statement related to Irrational numbers in the chapter Real Numbers.
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Answer / marking points
A. √2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0
Note
√2, √3 and √5 are irrational; they cannot be written as p/q with integers p, q ≠ 0. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.10MCQTriangles[1]
Choose the correct statement related to Keywords in the chapter Triangles.
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Answer / marking points
B. Every chapter ends with keywords or a summary that is useful for one-mark answers
Note
Every chapter ends with keywords or a summary that is useful for one-mark answers. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.11MCQAreas Related to Circles[1]
Choose the correct statement related to Revision in the chapter Areas Related to Circles.
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Answer / marking points
A. Write three points from Areas Related to Circles in your own words; that is enough for a short-answer start
Note
Write three points from Areas Related to Circles in your own words; that is enough for a short-answer start. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.12MCQPolynomials[1]
Choose the correct statement related to Polynomials in the chapter Polynomials.
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Answer / marking points
D. A quadratic has at most two zeros
Note
A quadratic has at most two zeros. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.13MCQCoordinate Geometry[1]
Choose the correct statement related to Coordinate Geometry in the chapter Coordinate Geometry.
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Answer / marking points
A. Area of triangle from coordinates
Note
Area of triangle from coordinates. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.14MCQSurface Areas and Volumes[1]
Choose the correct statement related to Textbook first in the chapter Surface Areas and Volumes.
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Answer / marking points
D. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
Note
Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.15MCQPair of Linear Equations in Two Variables[1]
Choose the correct statement related to Diagrams in the chapter Pair of Linear Equations in Two Variables.
Show answer / marking points
Answer / marking points
C. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
Note
If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.16MCQIntroduction to Trigonometry[1]
Choose the correct statement related to Practice in the chapter Introduction to Trigonometry.
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Answer / marking points
C. Mix MCQs with short answers so you remember both facts and explanations from Introduction to Trigonometry
Note
Mix MCQs with short answers so you remember both facts and explanations from Introduction to Trigonometry. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.17MCQStatistics[1]
Choose the correct statement related to Statistics in the chapter Statistics.
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Answer / marking points
C. Mode class
Note
Mode class. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.18MCQQuadratic Equations[1]
Choose the correct statement related to Quadratic Equations in the chapter Quadratic Equations.
Show answer / marking points
Answer / marking points
A. Quadratic Equations is an NCERT chapter taught in CBSE Class 10 Mathematics
Note
Quadratic Equations is an NCERT chapter taught in CBSE Class 10 Mathematics. The other options mix ideas from nearby topics or reverse the textbook fact.
Q.19Assertion and ReasonSome Applications of Trigonometry[1]
Assertion (A): CBSE often tests a concept by asking a daily-life example from the same chapter.
Reason (R): Examples is a key idea in the chapter Some Applications of Trigonometry.
Choose the correct option.
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Answer / marking points
A. Both A and R are true, and R is the correct explanation of A.
Note
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Q.20Assertion and ReasonProbability[1]
Assertion (A): Use the terms used in the NCERT book; do not replace them with unofficial names.
Reason (R): Accuracy is a key idea in the chapter Probability.
Choose the correct option.
Show answer / marking points
Answer / marking points
A. Both A and R are true, and R is the correct explanation of A.
Note
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Section B
Very Short Answer · Q21–25 · 2 marks each · internal choice in 2 questions · 10 marks
Q.212 MarkArithmetic Progressions[2]
Give two points to explain Arithmetic Progressions as used in Arithmetic Progressions.
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Answer / marking points
1. an = a+(n−1)d.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Note
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Q.222 MarkCircles[2]
Give two points to explain Circles as used in Circles.
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Answer / marking points
1. Contact point.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Note
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Q.232 MarkReal Numbers[2]
Give two points to explain Real number as used in Real Numbers.
Show answer / marking points
Answer / marking points
1. Real numbers include all rationals and irrationals and fill the number line.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Note
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
Q.242 MarkTriangles[2]
Give two points to explain Revision as used in Triangles.
OR
Give two points to explain Some Applications of Trigonometry as used in Some Applications of Trigonometry.
Show answer / marking points
Answer / marking points
1. Write three points from Triangles in your own words; that is enough for a short-answer start.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Note
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR — marking points
1. Draw a figure first.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Q.252 MarkAreas Related to Circles[2]
Give two points to explain Areas Related to Circles as used in Areas Related to Circles.
OR
Give two points to explain Textbook first as used in Probability.
Show answer / marking points
Answer / marking points
1. Area of circle = πr².
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Note
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR — marking points
1. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Section C
Short Answer · Q26–31 · 3 marks each · internal choice in 2 questions · 18 marks
Q.263 MarkPolynomials[3]
Explain Polynomials in about three points, with one example.
Show answer / marking points
Answer / marking points
Division algorithm as retained. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Note
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Q.273 MarkCoordinate Geometry[3]
Explain Textbook first in about three points, with one example.
Show answer / marking points
Answer / marking points
Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Note
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Q.283 MarkSurface Areas and Volumes[3]
Explain Diagrams in about three points, with one example.
Show answer / marking points
Answer / marking points
If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Note
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Q.293 MarkPair of Linear Equations in Two Variables[3]
Explain Practice in about three points, with one example.
Show answer / marking points
Answer / marking points
Mix MCQs with short answers so you remember both facts and explanations from Pair of Linear Equations in Two Variables. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Note
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Q.303 MarkIntroduction to Trigonometry[3]
Explain Introduction to Trigonometry in about three points, with one example.
OR
Explain Examples in about three points, with one example.
Show answer / marking points
Answer / marking points
tanθ = sinθ/cosθ. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Note
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR — marking points
CBSE often tests a concept by asking a daily-life example from the same chapter. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Q.313 MarkStatistics[3]
Explain Statistics in about three points, with one example.
OR
Explain Accuracy in about three points, with one example.
Show answer / marking points
Answer / marking points
Statistics is an NCERT chapter taught in CBSE Class 10 Mathematics. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Note
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR — marking points
Use the terms used in the NCERT book; do not replace them with unofficial names. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Section D
Long Answer · Q32–35 · 5 marks each · internal choice in 2 questions · 20 marks
Q.325 MarkQuadratic Equations[5]
Write a long answer on Examples. Include definition, explanation and one application.
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Answer / marking points
Examples — CBSE often tests a concept by asking a daily-life example from the same chapter. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Note
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Q.335 MarkSome Applications of Trigonometry[5]
Write a long answer on Accuracy. Include definition, explanation and one application.
Show answer / marking points
Answer / marking points
Accuracy — Use the terms used in the NCERT book; do not replace them with unofficial names. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Note
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Q.345 MarkProbability[5]
Write a long answer on Probability. Include definition, explanation and one application.
OR
Write a long answer on Keywords. Include definition, explanation and one application.
Show answer / marking points
Answer / marking points
Probability — 0 ≤ P(E) ≤ 1. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Note
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR — marking points
Keywords — Every chapter ends with keywords or a summary that is useful for one-mark answers. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Q.355 MarkArithmetic Progressions[5]
Write a long answer on Arithmetic Progressions. Include definition, explanation and one application.
OR
Write a long answer on Revision. Include definition, explanation and one application.
Show answer / marking points
Answer / marking points
Arithmetic Progressions — Apply to real sequences. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Note
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR — marking points
Revision — Write three points from Introduction to Trigonometry in your own words; that is enough for a short-answer start. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Section E
Case-study based · Q36–38 · 4 marks each (1 + 1 + 2) · 12 marks
Q.36Case BasedCircles[4]
A student is revising Circles and notes: “Every chapter ends with keywords or a summary that is useful for one-mark answers.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Show answer / marking points
Answer / marking points
(i) Keywords.
(ii) Every chapter ends with keywords or a summary that is useful for one-mark answers.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Note
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
Q.37Case BasedReal Numbers[4]
A student is revising Real Numbers and notes: “Terminating decimals: denominator 2^m 5^n after simplifying.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Show answer / marking points
Answer / marking points
(i) Terminating decimals.
(ii) Terminating decimals: denominator 2^m 5^n after simplifying.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Note
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
Q.38Case BasedTriangles[4]
A student is revising Triangles and notes: “AA, SSS, SAS similarity.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Show answer / marking points
Answer / marking points
(i) Triangles.
(ii) AA, SSS, SAS similarity.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Note
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
