Central Board of Secondary Education
Practice Question Paper — not an official CBSE document
Subject Code 041 · Set 3 of 3
Theory 80 + internal assessment 20.
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.
Objective type (MCQ and Assertion–Reason) · Q1–20 · 1 mark each · 20 marks
B. Bayes theorem
NoteBayes theorem. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Second order derivatives
NoteSecond order derivatives. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Every chapter ends with keywords or a summary that is useful for one-mark answers
NoteEvery 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.
A. Write three points from Inverse Trigonometric Functions in your own words; that is enough for a short-answer start
NoteWrite three points from Inverse Trigonometric Functions 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.
A. Anti-derivative
NoteAnti-derivative. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Corner-point method
NoteCorner-point method. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
NoteRead 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.
A. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
NoteIf 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.
B. Mix MCQs with short answers so you remember both facts and explanations from Relations and Functions
NoteMix MCQs with short answers so you remember both facts and explanations from Relations and Functions. The other options mix ideas from nearby topics or reverse the textbook fact.
B. Increasing/decreasing
NoteIncreasing/decreasing. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Three Dimensional Geometry is an NCERT chapter taught in CBSE Class 12 Mathematics
NoteThree Dimensional Geometry is an NCERT chapter taught in CBSE Class 12 Mathematics. The other options mix ideas from nearby topics or reverse the textbook fact.
C. CBSE often tests a concept by asking a daily-life example from the same chapter
NoteCBSE 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.
A. Use the terms used in the NCERT book; do not replace them with unofficial names
NoteUse 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.
C. Bayes theorem
NoteBayes theorem. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Second order derivatives
NoteSecond order derivatives. The other options mix ideas from nearby topics or reverse the textbook fact.
B. Every chapter ends with keywords or a summary that is useful for one-mark answers
NoteEvery 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.
D. Write three points from Inverse Trigonometric Functions in your own words; that is enough for a short-answer start
NoteWrite three points from Inverse Trigonometric Functions 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.
A. Anti-derivative
NoteAnti-derivative. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Both A and R are true, and R is the correct explanation of A.
NoteRead Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
A. Both A and R are true, and R is the correct explanation of A.
NoteRead Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Very Short Answer · Q21–25 · 2 marks each · 10 marks
1. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
1. Mix MCQs with short answers so you remember both facts and explanations from Relations and Functions.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
1. Increasing/decreasing.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR
1. Three Dimensional Geometry is an NCERT chapter taught in CBSE Class 12 Mathematics.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR — marking points1. Use the terms used in the NCERT book; do not replace them with unofficial names.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
OR
1. CBSE often tests a concept by asking a daily-life example from the same chapter.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR — marking points1. Bayes theorem.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Short Answer · Q26–31 · 3 marks each · 18 marks
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.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Bayes theorem. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Second order derivatives. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Every chapter ends with keywords or a summary that is useful for one-mark answers. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR
Write three points from Inverse Trigonometric Functions in your own words; that is enough for a short-answer start. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR — marking pointsCorner-point method. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
OR
Anti-derivative. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR — marking pointsRead 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.
Long Answer · Q32–35 · 5 marks each · 20 marks
Linear Programming — Corner-point method. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Textbook first — Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR
Diagrams — If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR — marking pointsApplication of Derivatives — Increasing/decreasing. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
OR
Practice — Mix MCQs with short answers so you remember both facts and explanations from Relations and Functions. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR — marking pointsThree Dimensional Geometry — Three Dimensional Geometry is an NCERT chapter taught in CBSE Class 12 Mathematics. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Case-study based · Q36–38 · 4 marks each · 12 marks
(i) Application of Derivatives.
(ii) Increasing/decreasing.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
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.
(i) Three Dimensional Geometry.
(ii) Three Dimensional Geometry is an NCERT chapter taught in CBSE Class 12 Mathematics.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
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.
(i) Examples.
(ii) CBSE often tests a concept by asking a daily-life example from the same chapter.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
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.
*** End of paper ***
No. The layout (sections, question numbers, marks and time) follows the 2025-26 sample paper. The questions are original GKSchools practice.
MCQ, assertion–reason and reading MCQ parts are auto-scored when you submit. Written answers are for self-check against the key.
Download it from CBSE Academic: https://cbseacademic.nic.in/web_material/SQP/ClassXII_2025_26/Maths-SQP.pdf
Follow this loop every day: mixed test, current affairs, then today's subject. A new set arrives tomorrow.
After this page, use these three links — do not open a random page.
More sets from the same cluster — stay on this topic.
Timed papers with a scorecard — start any time, then return to a related quiz above.
