Mathematics – Important Question Bank for CBSE Class XII HSC Board Exam 2026 – HSC

Disclaimer: This question bank is for practice and revision purposes. It is curated using leading sources, teacher insights, and previous board trends, but does not guarantee actual board appearance.

As we approach the CBSE Class XII HSC Board Exam 2026, our expert faculty has analyzed emerging board trends and examination patterns to create this comprehensive question bank. This strategic compilation benefits students by providing targeted practice aligned with the latest CBSE guidelines, ensuring thorough preparation for the upcoming mathematics examination.

Why This Matters

Your performance in the CBSE Class XII Mathematics examination directly impacts your academic future and career opportunities. Our comprehensive trend analysis reveals that students who practice with expertly curated question banks score significantly higher than those relying solely on textbooks. This collection has undergone rigorous expert review to ensure alignment with current board expectations and emerging examination patterns.

Mathematics is the foundation of logical thinking and problem-solving skills, requiring mastery of concepts, formulas, and application techniques. This comprehensive question bank has been designed to help students prepare effectively for their HSC Board Exam 2026, covering all important topics and providing practice questions that mirror the actual exam pattern.

Key Topics Covered

This question bank covers all essential mathematics topics from the CBSE Class XII syllabus:

Relations and Functions
Inverse Trigonometric Functions
Matrices
Determinants
Continuity and Differentiability
Applications of Derivatives
Integrals
Applications of Integrals
Differential Equations
Vector Algebra
Three Dimensional Geometry
Linear Programming
Probability

Question Types and Format

This question bank includes various types of questions designed to test different levels of understanding and application:

Multiple Choice Questions (MCQs) – Test conceptual understanding and quick recall
Very Short Answer Questions – Brief numerical problems and formula applications
Short Answer Questions – Step-by-step problem solving
Long Answer Questions – Comprehensive mathematical proofs and complex problems
Case Study Questions – Real-world applications and analysis
Assertion-Reason Questions – Critical thinking and logical reasoning

Study Tips and Exam Strategy

To maximize your performance in the CBSE Class XII Mathematics exam, follow these essential study tips:

Master fundamental concepts before attempting complex problems
Practice numerical problems regularly to build speed and accuracy
Create formula sheets for quick revision
Solve previous year question papers to understand exam patterns
Focus on high-weightage topics like Calculus, Algebra, and Probability
Time yourself while practicing to improve exam speed
Review and understand your mistakes to avoid repetition
Practice step-by-step solutions for better presentation
Use graphical representations wherever applicable

This comprehensive question bank serves as your complete preparation guide for the CBSE Class XII Mathematics examination. Regular practice with these questions, combined with a thorough understanding of concepts and consistent revision, will significantly boost your confidence and performance in the 2026 HSC Board Exam. Remember, success in mathematics comes from consistent practice and understanding of fundamental principles.

Access our complete question bank with detailed solutions and expert explanations. Unlock premium content to boost your CBSE Class XII Mathematics preparation.

2026 Board-Ready Mathematics Important Questions

🔢 COMPREHENSIVE MATHEMATICS QUESTION BANK – CBSE CLASS XII 2026

BOARD-READY MATHEMATICS IMPORTANT QUESTIONS (CBSE CLASS XII 2026)

Relations and Functions

MCQ: If f(x)=x2f(x)=x2, is ff one-to-one, onto, or both over RR?
Short Answer: Define equivalence relation, and give one example.
Long Answer: Prove that the relation “is congruent to modulo n” is an equivalence relation.

Inverse Trigonometric Functions

MCQ: Find the principal value of sin⁡−1(12)sin−1(21).
Short Answer: Evaluate tan⁡−11+tan⁡−12+tan⁡−13tan−11+tan−12+tan−13.
Long Answer: Prove that sin⁡−1x+cos⁡−1x=π2sin−1x+cos−1x=2π, for x∈[−1,1]x∈[−1,1].

Matrices

MCQ: If A=[1201]A=[1021], find ∣A∣∣A∣.
Short Answer: Find the inverse of A=[2314]A=[2134].
Long Answer: If AA and BB are two invertible matrices, show that inverse of ABAB is B−1A−1B−1A−1.

Determinants

MCQ: For what value of kk is the determinant ∣12345678k∣=014725836k=0 ?
Short Answer: Expand the determinant ∣2031∣2301.
Long Answer: Solve the system{2x+3y=54x+5y=11{2x+3y=54x+5y=11using Cramer’s Rule.

Continuity and Differentiability

MCQ: Is f(x)=∣x∣f(x)=∣x∣ differentiable at x=0x=0?
Short Answer: Prove f(x)=x3f(x)=x3 is continuous everywhere.
Long Answer: Find kk so that the functionf(x)={kx2+1,x<13x+2,x≥1f(x)={kx2+1,3x+2,x<1x≥1is continuous at x=1x=1.

Applications of Derivatives

MCQ: If y=x3y=x3, what is dydxdxdy at x=2x=2?
Short Answer: Find equation of the tangent to y=x2y=x2 at x=1x=1.
Long Answer: Find the maximum and minimum values of f(x)=−x2+4x+5f(x)=−x2+4x+5.

Integrals

MCQ: ∫02x dx=?∫02xdx=?
Short Answer: Evaluate ∫cos⁡x dx∫cosxdx.
Long Answer: Evaluate∫01×21+x4dx∫011+x4x2dx(Hint: Use substitution.)

Applications of Integrals

MCQ: Area under y=xy=x, x=0x=0 to x=2x=2?
Short Answer: Find the area between y=x2y=x2 and y=4y=4.
Long Answer: Find the area bounded by y2=4xy2=4x and x=4x=4.

Differential Equations

MCQ: Solution of dydx=kydxdy=ky is?
Short Answer: State order and degree of d2ydx2+y=0dx2d2y+y=0.
Long Answer: Solve dydx+y=exdxdy+y=ex, y(0)=1y(0)=1.

Vector Algebra

MCQ: If a⃗=i^+2j^a=i^+2j^ and b⃗=2i^−j^b=2i^−j^, find a⃗⋅b⃗a⋅b.
Short Answer: Find the projection of a⃗=3i^+4j^a=3i^+4j^ on i^i^.
Long Answer: If a⃗,b⃗,c⃗a,b,c are non-coplanar, show that [a⃗ b⃗ c⃗]≠0[a b c]=0.

Three-Dimensional Geometry

MCQ: Distance between points (1,2,3)(1,2,3) and (4,5,6)(4,5,6)?
Short Answer: Find the cosine of angle between two lines with direction ratios 2,3,4 and 1,2,2.
Long Answer: Find the equation of plane passing through three given points.

Linear Programming

MCQ: What type of region is formed by a set of linear inequalities?
Short Answer: Define ‘objective function’ in LPP.
Long Answer: Solve: Maximize Z=3x+2yZ=3x+2y subject to x+2y≤6x+2y≤6, x≥0,y≥0x≥0,y≥0.

Probability

MCQ: Probability of getting a sum 7 on two dice?
Short Answer: Define independent events with example.
Long Answer: A bag contains 4 red, 5 blue, 6 green balls. Three balls picked at random. Find probability all are different colors.

Practice Set (Sample Paper Pattern)

Section A: MCQs (10 × 1 = 10 marks)
Section B: Very Short Answers (5 × 2 = 10 marks)
Section C: Short Answers (4 × 3 = 12 marks)
Section D: Long Answers (3 × 5 = 15 marks)

High-Yield Topics for 2026:

Calculus (30%)
Algebra (20%)
Probability (15%)
Vectors & 3D Geometry (15%)
Matrices & Determinants (10%)
Linear Programming (10%)

This comprehensive question bank contains over 300 carefully selected questions aligned with CBSE guidelines and recent examination trends.

Focus on understanding mathematical concepts, formulas, and their applications as they carry maximum weightage in the CBSE Class XII Mathematics examination. Practice solving problems step-by-step and present solutions clearly with proper mathematical notation. Always show your work and use appropriate mathematical symbols. Time management is crucial – allocate specific time slots for different question types during your preparation.

Ready to Excel in Mathematics 2026?

This comprehensive question bank represents months of expert analysis and careful curation to ensure your success in the CBSE Class XII Mathematics examination. Regular practice with these questions will build your confidence and improve your problem-solving speed.

We’d love to hear about your preparation journey! Share your thoughts in the comments below and let us know which topics you find most challenging. Don’t forget to share this resource with your classmates and help them succeed too.

Best of luck for your 2026 board examinations!

Our question bank maintains the highest standards of academic accuracy and alignment with current CBSE examination patterns. Regular updates incorporate feedback from practicing teachers and recent board exam trends to provide students with the most relevant preparation material.

BOARD-READY MATHEMATICS IMPORTANT QUESTIONS (CBSE CLASS XII 2026)

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