Class 12 Mathematics Application of Integrals Previous Year Style Questions
Previous Year Style Questions for Class 12 Mathematics Application of Integrals. Try first, then reveal the answer. These are exam-oriented practice items, not copied board papers.
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.
Answers opened: 0
Practice set
Q1MCQ1 markEasyRevision pick
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. CBSE often tests a concept by asking a daily-life example from the same chapter
B. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
C. Vertical vs horizontal strips
D. Area = ∫ y dx
Answer
D. Area = ∫ y dx
Explanation
Area = ∫ y dx. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q2MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
B. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
C. Area between curves
D. Standard curves: line, circle, parabola, ellipse
Answer
C. Area between curves
Explanation
Area between curves. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q3MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Sketch first
B. Every chapter ends with keywords or a summary that is useful for one-mark answers
C. Write three points from Application of Integrals in your own words; that is enough for a short-answer start
D. Vertical vs horizontal strips
Answer
D. Vertical vs horizontal strips
Explanation
Vertical vs horizontal strips. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q4MCQ1 markEasy
Choose the correct statement related to Standard curves in the chapter Application of Integrals.
A. Use the terms used in the NCERT book; do not replace them with unofficial names
B. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
C. Standard curves: line, circle, parabola, ellipse
D. CBSE often tests a concept by asking a daily-life example from the same chapter
Answer
C. Standard curves: line, circle, parabola, ellipse
Explanation
Standard curves: line, circle, parabola, ellipse. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q5MCQ1 markModerateRevision pick
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals
B. Sketch first
C. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
D. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
Answer
B. Sketch first
Explanation
Sketch first. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q6MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
B. Write three points from Application of Integrals in your own words; that is enough for a short-answer start
C. Every chapter ends with keywords or a summary that is useful for one-mark answers
D. Standard curves: line, circle, parabola, ellipse
Answer
A. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
Explanation
Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q7MCQ1 markEasy
Choose the correct statement related to Textbook first in the chapter Application of Integrals.
A. The textbook says the opposite of this statement
B. CBSE often tests a concept by asking a daily-life example from the same chapter
C. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
D. Use the terms used in the NCERT book; do not replace them with unofficial names
Answer
C. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q8MCQ1 markEasy
Choose the correct statement related to Keywords in the chapter Application of Integrals.
A. This happens only in a laboratory and never in daily life
B. Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals
C. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
D. Every chapter ends with keywords or a summary that is useful for one-mark answers
Answer
D. Every chapter ends with keywords or a summary that is useful for one-mark answers
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q9MCQ1 markEasyRevision pick
Choose the correct statement related to Examples in the chapter Application of Integrals.
A. Area = ∫ y dx
B. This idea is not part of the NCERT chapter
C. Write three points from Application of Integrals in your own words; that is enough for a short-answer start
D. CBSE often tests a concept by asking a daily-life example from the same chapter
Answer
D. CBSE often tests a concept by asking a daily-life example from the same chapter
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q10MCQ1 markModerate
Choose the correct statement related to Diagrams in the chapter Application of Integrals.
A. Use the terms used in the NCERT book; do not replace them with unofficial names
B. The textbook says the opposite of this statement
C. Area between curves
D. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
Answer
D. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q11MCQ1 markEasy
Choose the correct statement related to Revision in the chapter Application of Integrals.
A. Vertical vs horizontal strips
B. This happens only in a laboratory and never in daily life
C. Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals
D. Write three points from Application of Integrals in your own words; that is enough for a short-answer start
Answer
D. Write three points from Application of Integrals in your own words; that is enough for a short-answer start
Explanation
Write three points from Application of Integrals 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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q12MCQ1 markEasy
Choose the correct statement related to Accuracy in the chapter Application of Integrals.
A. This idea is not part of the NCERT chapter
B. Use the terms used in the NCERT book; do not replace them with unofficial names
C. Standard curves: line, circle, parabola, ellipse
D. Area = ∫ y dx
Answer
B. Use the terms used in the NCERT book; do not replace them with unofficial names
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q13MCQ1 markEasyRevision pick
Choose the correct statement related to Practice in the chapter Application of Integrals.
A. Sketch first
B. Area between curves
C. The textbook says the opposite of this statement
D. Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals
Answer
D. Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals
Explanation
Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q14MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
B. Standard curves: line, circle, parabola, ellipse
C. This happens only in a laboratory and never in daily life
D. Area = ∫ y dx
Answer
D. Area = ∫ y dx
Explanation
Area = ∫ y dx. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q15MCQ1 markModerate
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Sketch first
B. Every chapter ends with keywords or a summary that is useful for one-mark answers
C. Area between curves
D. Area = ∫ y dx
Answer
C. Area between curves
Explanation
Area between curves. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q16MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Vertical vs horizontal strips
B. CBSE often tests a concept by asking a daily-life example from the same chapter
C. Area between curves
D. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
Answer
A. Vertical vs horizontal strips
Explanation
Vertical vs horizontal strips. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q17MCQ1 markEasyRevision pick
Choose the correct statement related to Standard curves in the chapter Application of Integrals.
A. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
B. Standard curves: line, circle, parabola, ellipse
C. Vertical vs horizontal strips
D. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
Answer
B. Standard curves: line, circle, parabola, ellipse
Explanation
Standard curves: line, circle, parabola, ellipse. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q18MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Standard curves: line, circle, parabola, ellipse
B. Sketch first
C. Every chapter ends with keywords or a summary that is useful for one-mark answers
D. Write three points from Application of Integrals in your own words; that is enough for a short-answer start
Answer
B. Sketch first
Explanation
Sketch first. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q19MCQ1 markEasy
Choose the correct statement related to Application of Integrals in the chapter Application of Integrals.
A. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
B. This topic is only for college
C. Sketch first
D. Area between curves
Answer
A. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
Explanation
Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics. The other options mix ideas from nearby topics or reverse the textbook fact.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q20MCQ1 markModerate
Choose the correct statement related to Textbook first in the chapter Application of Integrals.
A. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
B. Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics
C. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
D. Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals
Answer
A. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q413 Mark3 marksModerateRevision pick
Explain Application of Integrals in about three points, with one example.
Answer
Area between curves. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q423 Mark3 marksModerate
Explain Application of Integrals in about three points, with one example.
Answer
Vertical vs horizontal strips. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q433 Mark3 marksModerate
Explain Standard curves in about three points, with one example.
Answer
Standard curves: line, circle, parabola, ellipse. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q443 Mark3 marksDifficult
Explain Application of Integrals in about three points, with one example.
Answer
Sketch first. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q453 Mark3 marksModerateRevision pick
Explain Application of Integrals in about three points, with one example.
Answer
Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q463 Mark3 marksModerate
Explain Textbook first in about three points, with one example.
Answer
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.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q473 Mark3 marksModerate
Explain Keywords in about three points, with one example.
Answer
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.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q483 Mark3 marksDifficult
Explain Examples in about three points, with one example.
Answer
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.
Explanation
Three-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q555 Mark5 marksModerate
Write a long answer on Application of Integrals. Include definition, explanation and one application.
Answer
Application of Integrals — Vertical vs horizontal strips. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q565 Mark5 marksModerate
Write a long answer on Standard curves. Include definition, explanation and one application.
Answer
Standard curves — Standard curves: line, circle, parabola, ellipse. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q575 Mark5 marksDifficultRevision pick
Write a long answer on Application of Integrals. Include definition, explanation and one application.
Answer
Application of Integrals — Sketch first. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q585 Mark5 marksModerate
Write a long answer on Application of Integrals. Include definition, explanation and one application.
Answer
Application of Integrals — Application of Integrals 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.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q595 Mark5 marksModerate
Write a long answer on Textbook first. Include definition, explanation and one application.
Answer
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.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q605 Mark5 marksDifficult
Write a long answer on Keywords. Include definition, explanation and one application.
Answer
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.
Explanation
Long answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q61Assertion and Reason1 markModerate
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 Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q62Assertion and Reason1 markModerate
Assertion (A): If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures.
Reason (R): Diagrams is a key idea in the chapter Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q63Assertion and Reason1 markModerate
Assertion (A): Write three points from Application of Integrals in your own words; that is enough for a short-answer start.
Reason (R): Revision is a key idea in the chapter Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q64Assertion and Reason1 markDifficult
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 Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q65Assertion and Reason1 markModerate
Assertion (A): Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals.
Reason (R): Practice is a key idea in the chapter Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q66Assertion and Reason1 markModerate
Assertion (A): Area = ∫ y dx.
Reason (R): Application of Integrals is a key idea in the chapter Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q67Assertion and Reason1 markModerate
Assertion (A): Area between curves.
Reason (R): Application of Integrals is a key idea in the chapter Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q68Assertion and Reason1 markDifficult
Assertion (A): Vertical vs horizontal strips.
Reason (R): Application of Integrals is a key idea in the chapter Application of Integrals.
Choose the correct option.
A. Both A and R are true, and R is the correct explanation of A.
B. Both A and R are true, and R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
Answer
A. Both A and R are true, and R is the correct explanation of A.
Explanation
Read Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q69Case Based4 marksModerateRevision pick
A student is revising Application of Integrals and notes: “Standard curves: line, circle, parabola, ellipse.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Standard curves.
(ii) Standard curves: line, circle, parabola, ellipse.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q70Case Based4 marksModerate
A student is revising Application of Integrals and notes: “Sketch first.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Application of Integrals.
(ii) Sketch first.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q71Case Based4 marksModerate
A student is revising Application of Integrals and notes: “Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Application of Integrals.
(ii) Application of Integrals 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.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q72Case Based4 marksDifficult
A student is revising Application of Integrals and notes: “Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Textbook first.
(ii) Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q73Case Based4 marksModerateRevision pick
A student is revising Application of Integrals 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.
Answer
(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.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q74Case Based4 marksModerate
A student is revising Application of Integrals and notes: “CBSE often tests a concept by asking a daily-life example from the same chapter.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(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.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q75Case Based4 marksModerate
A student is revising Application of Integrals and notes: “If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Diagrams.
(ii) If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q76Case Based4 marksDifficult
A student is revising Application of Integrals and notes: “Write three points from Application of Integrals in your own words; that is enough for a short-answer start.” Using this case, answer: (i) Name the idea. (ii) State it in your own words. (iii) Give one classroom or daily-life use.
Answer
(i) Revision.
(ii) Write three points from Application of Integrals in your own words; that is enough for a short-answer start.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Explanation
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.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q77Competency Based3 marksModerateRevision pick
Competency practice: A classmate can recall the heading Accuracy but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Use the terms used in the NCERT book; do not replace them with unofficial names. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q78Competency Based3 marksDifficult
Competency practice: A classmate can recall the heading Practice but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Mix MCQs with short answers so you remember both facts and explanations from Application of Integrals. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q79Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Application of Integrals but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Area = ∫ y dx. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q80Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Application of Integrals but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Area between curves. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q81Competency Based3 marksDifficultRevision pick
Competency practice: A classmate can recall the heading Application of Integrals but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Vertical vs horizontal strips. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q82Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Standard curves but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Standard curves: line, circle, parabola, ellipse. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q83Competency Based3 marksModerate
Competency practice: A classmate can recall the heading Application of Integrals but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Sketch first. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
Q84Competency Based3 marksDifficult
Competency practice: A classmate can recall the heading Application of Integrals but cannot explain it. How will you teach it in two steps using the textbook idea?
Answer
Step 1: State the fact — Application of Integrals is an NCERT chapter taught in CBSE Class 12 Mathematics. Step 2: Show one example or diagram from the chapter and ask the classmate to repeat it in their own words.
Explanation
Competency-based items check whether you can use a concept, not only name it. Teach-back is a simple way to prove understanding.
Meta
Class: Class 12 · Subject: Mathematics · Chapter: Application of Integrals · Original GKSchools practice (NCERT-aligned, not an official CBSE paper).
FAQs
Are these official CBSE board questions?
No. They are original practice questions aligned to NCERT topics used in CBSE classrooms. Official sample papers are published on cbseacademic.nic.in.
Will these questions appear in the board exam?
Nobody can promise a question. Use them for revision of frequently tested concepts and exam-style practice.
Is the chapter list the latest NCERT list?
Yes, the catalog follows current NCERT textbooks used in CBSE schools (including new middle-stage books such as Ganita Prakash and Curiosity). Always match the book issued by your school.
How should I use the 100 questions?
Try the question first, then tap Show answer. Mix MCQs with long answers. Revise formulas and diagrams from the textbook alongside this set.
Where are NCERT solutions?
Open the NCERT-style practice link on this subject or chapter. For word-for-word textbook exercise answers, use the NCERT book itself; we do not copy solution keys from other websites.
What is the suggested URL pattern?
Hub /cbse/, then /cbse/class-12/, then subject and chapter slugs.
Why is this a separate URL?
So students searching for “Previous Year Style Questions” land on a filtered set, while the chapter page remains the full 100-question bank. Same facts, different search intent.
Today's 3-step path
Follow this loop every day: mixed test, current affairs, then today's subject. A new set arrives tomorrow.
