Top 5 Repeated CBSE Class 12 Maths Previous Year Questions

For the school board exams, you need not only basic memorisation to get a top score, but you must also know how questions are trending. However, you can easily overcome these exam hurdles by focusing your practice on CBSE Class 12 Maths previous year questions. It helps you gain confidence in your revision and ensure that you obtain maximum marks in your final board exam

This article has summarised patterns of frequently asked questions, along with step-by-step methodologies to better understand them.

Importance of Previous Year Questions in CBSE Class 12 Maths

Solving previous-year board papers connects basic theoretical concepts and provides a realistic exam experience. It also changes your approach to the question paper on exam day.

Understanding the Blueprint and Real Weightage

The syllabus may tell you chapter-wise marks, but working through actual papers tells you exactly where those marks appear. Example: Calculus carries an approximate 35 marks out of a total of 80. If you track past papers, you will see the same concepts (which carry higher weight) very frequently; only the numbers used are different.

Enhancing Time Management and Speed

The overall paper consists of several sections, with 1-mark multiple-choice questions and 5-mark long-answer problems. Practising past papers in an exam setting will condition your mind to spend the appropriate time on each section, meaning long-answer questions are not left abandoned in the closing minutes of the exam.

Highlighting Examiner Expectations

Each previous solution shows the precise, detailed marking scheme used by the markers. Nonetheless, being able to write your steps down succinctly and clearly state formulas and final units gets you step-marking scores. Step marks may still be awarded if the method is correct.

Most Common CBSE Class 12 Maths Previous Year Questions

These 5 specific question types seem to be used most frequently in board exams, based on a detailed analysis of CBSE class 12 previous year papers and study material.

1. Matrix Method to Solve Linear Equations

Question: Solve the system of equations using the matrix method:

3x−2y+3z=8
2x+y−z=1
4x−3y+2z=4

Write the equations in matrix form:

AX=B

Find the determinant of matrix A.

Since ∣A∣≠0, an inverse exists.

Using the inverse matrix method:

X=A^−1B

After calculation:

x = 1, y = 2, z = 3

Therefore, the solution is:

• x=1

• y=2

• z=3

2. Shortest Distance Between Two Skew Lines

Question: Find the shortest distance between the skew lines:

Vec r=(i^+2j^+k^)+λ(i^−j^+k^)
Vec r=(2i^−j^−k^)+μ(2i^+j^+2k^)

Use the formula:

d = |(a⃗₂ − a⃗₁) ⋅ (b⃗₁ × b⃗₂) / |b⃗₁ × b⃗₂∣|​​|

Find:

• difference vector

• cross product

• magnitude

Substitute values in the formula and simplify.

The obtained value gives the shortest distance between the two skew lines.

3. Area Bounded by Curves Using Integration

Question: Find the area bounded by:

y=x²

and

y = ∣x∣

The curves intersect at:

(0,0) and (1,1)

Using symmetry:

Area=2∫₀¹(x−x²)dx

Integrating:

2[x²−x³]₀¹/2

After simplification:

Area=1/3 square units.

Therefore, the required area is 1/3 square units.

4. Application of Bayes’ Theorem

Question: Two bags contain red and black balls. Find the probability that the selected balls came from bag B.

Let:

• E₁: Choosing Bag A

• E₂: Choosing Bag B

• A: One red and one black ball drawn

Probabilities:

P(E₁)=1/3, P(E₂)=2/3

Using combinations:

P(A∣E₁)=24/45​

P(A∣E₂)=21/45

Apply Bayes’ theorem:

P(E₂∣A) = P(E₂)P(A∣E₂)/[P(E₁)P(A∣E₁) + P(E₂)P(A∣E₂)]

After simplification:

P(E₂∣A)=7/11

Therefore, the required probability is 7/11​.

5. Linear Programming Problem (LPP)

Question: Minimise:

Z=3x+9

Subject to:

X+3y≤60, X+y≥10,
x≤y

Plot all boundary lines on the graph and identify the feasible region.

The corner points obtained are the following:

• (0, 10)

• (5, 5)

• (15, 15)

• (0, 20)

Substitute in the objective function:

At (0,10):

Z=90

At (5, 5):

Z=60

At (15, 15):

Z=180

At (0, 20):

Z=180

The minimum value of Z is:

Z=60

The minimum value of Z occurs at the point (5, 5).

Benefits of Solving CBSE Class 12 Maths Previous Year Questions

There are many practical benefits to combining continuous practice with CBSE Class 12 mathematics previous year question papers in your study plan.

• Pinpoints High-Yield Topics: Practising on past papers will reveal what you need to pay most attention to and give an indication of high-yield topics, so that these can be prioritised over the less frequent ones in revision.

• Exposes Structural Patterns: Many questions have similar patterns, so the specific numbers might change, but actual board questions will feel familiar.

• Eliminates Exam Anxiety: When you practise real CBSE 12th maths last year's previous question papers with solutions, it helps to normalise the exam structure and thus removes anxiety-fuelled stress when facing the actual test.

• Refines Step-by-Step Presentation: By looking through model answers, you learn how to present your work in a way that gives examiners as much opportunity to give each and every mark available for steps as possible.

For more complete preparation, students can combine PYQ practice with CBSE Class 12 Books, which provide structured theory, concept clarity, and additional exam-oriented practice for stronger board performance.

Read More: CBSE Class 12 Maths 2026: Chapter-Wise Weightage & Marking Scheme

CBSE Class 12 Maths Previous Year Questions FAQs

Q1. How many past years of CBSE Mathematics Class 12 previous year question papers should I solve?

You must try solving the past board papers of at least the last 7–10 years. This will help you cover a few syllabus variations, some wordings (types of questions), and the repetitive structure in high-weightage areas.

Q2. Are questions from CBSE Class 12 maths PYQs repeated exactly in the final board exam?

Exact numerical values may differ. The structural format, fundamental formula requirements and step-by-step methodologies are the same, except that now those numbers have changed.

Q3. Where can I find reliable CBSE 12th Maths previous year question papers with solutions?

You can directly check the official papers from the CBSE website or use curation for your revision. If you are looking for organised, step-by-step solutions, then opt for practice material that accurately meets your study requirements.

Q4. Can I pass the board exam by only preparing for the CBSE PYQ class 12 maths?

Practising the past papers teaches you a lot about how an exam is designed, what the important topics are for each subject and so on, but still prefer to work around concepts asked in your NCERT textbook because it will help you answer any variation of question that can be framed through it, which might not generally happen with some questions.

Q5. How should I allocate my time when solving maths previous year question papers class 12 CBSE?

Match the real 3-hour exam timer by setting a strict time limit for yourself. Total Time Taken per Area: Allocate approximately half an hour for Level I, one-mark MCQs; around 50 minutes for Level II (2 and 3 marks) requires at least 80 to 90 minutes or more for some long-answer questions.