Class 12 Maths · CBSE 2025–26 · Arvind Academy
A targeted question bank covering 59 Sure Shot Questions across Relations & Functions and Inverse Trigonometric Functions — with complete, detailed solutions for CBSE Class 12 Maths Board Exam 2026.
ConTent4U Editorial
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CBSE 2025–26
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Class 12 Mathematics
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Arvind Academy
If you are targeting high marks in the CBSE Class 12 Mathematics Board Exam 2026,
the Arvind Academy Sure Shot Questions 2025-26 is a must-have practice resource.
This carefully curated question bank covers the most important and frequently asked questions
from Chapter 1 — Relations and Functions and Chapter 2 — Inverse Trigonometric Functions,
complete with step-by-step solutions. With 28 questions in Ch. 1 and 31 questions in Ch. 2,
this PDF is designed to maximise your score in the exam.
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Maths Sure Shot Questions — Arvind Academy 2025-26 · PDF Preview
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📥 Free Download — Maths Sure Shot Questions Arvind Academy 2025-26
📚 Chapter-wise Coverage at a Glance
| Chapter |
Topic |
No. of Questions |
Key Focus Areas |
| Ch. 1 |
Relations and Functions |
28 Questions |
Injective, Surjective, Bijective; Equivalence Relations; Pre-image & Domain |
| Ch. 2 |
Inverse Trigonometric Functions |
31 Questions |
Evaluation; Proofs & Simplification; Domain & Range; Solving ITF Equations |
| Total |
2 Chapters |
59 Questions |
Full solutions provided for every question |
📐 Chapter 1 — Relations and Functions (28 Questions)
This chapter tests your ability to analyse properties of functions and relations — a key 8-mark unit in the board exam. The sure shot questions cover:
01
Function Properties
Determine if functions are injective (one-one), surjective (onto), or bijective — for linear, cubic, quadratic, and trigonometric functions like f(x) = x² + x, f(x) = 4x³ + 7, f(x) = sin x.
02
Types of Relations
Check and prove whether given relations are reflexive, symmetric, and/or transitive — covering all standard question patterns asked in CBSE boards.
03
Equivalence Relations
Prove that specific relations are equivalence relations — e.g., R = {(a,b) : |a−b| is divisible by 4} on A = {x ∈ Z : 0 ≤ x ≤ 12}, and (a,b)R(c,d) ⟺ a² + d² = b² + c².
04
Pre-image and Domain
Find pre-images such as f⁻¹(17) and f⁻¹(−3) for f(x) = x² + 1, and determine the domain of relations like R = {(a,b) : a² + b² = 25} on Z.
📐 Chapter 2 — Inverse Trigonometric Functions (31 Questions)
This chapter covers one of the most formula-heavy and conceptually tricky topics in Class 12 Maths. The sure shot questions span every question type asked in CBSE exams:
01
Evaluation of Expressions
Calculate values of complex ITF expressions involving principal value branches — e.g., sin⁻¹(cos 43π/5), cos⁻¹(cos(−7π/3)).
02
Simplification and Proofs
Prove identities using ITF formulas — e.g., 2tan⁻¹(1/2) + tan⁻¹(1/7) = tan⁻¹(31/17); cos⁻¹(12/13) + sin⁻¹(3/5) = sin⁻¹(56/65).
03
Domain and Range
Find domain/range of ITF expressions like f(x) = sin⁻¹(x² − 4), and determine principal value branches for functions like cos⁻¹x.
04
Solving ITF Equations
Solve equations involving multiple ITF terms — e.g., sin⁻¹x + sin⁻¹y + sin⁻¹z = 3π/2; simplify forms like cos⁻¹(3/5 · cos x + 4/5 · sin x).
💡 Board Exam Strategy
Ch. 1 (Relations & Functions) and Ch. 2 (Inverse Trigonometric Functions) together form Unit I — 8 marks in the CBSE board paper. These chapters frequently appear as 2-mark VSA and 3-mark SA questions. Mastering the equivalence relation proofs and ITF identity proofs can alone secure 5–6 marks with certainty.
🎯 How to Use This Question Bank for Board 2026
1
Attempt Questions First
Try solving each question independently before looking at the solution to build genuine problem-solving ability.
2
Check Every Step
Compare your steps with the provided solutions — CBSE awards marks stepwise, so presentation matters as much as the final answer.
3
Revise Equivalence Proofs
The equivalence relation proof structure (prove reflexive + symmetric + transitive) repeats almost every year — master the template.
4
Memorise ITF Formulas
Ch. 2 proofs require command over addition/subtraction formulas for tan⁻¹, sin⁻¹, cos⁻¹. Revise these daily in the final weeks.
“Sure Shot Questions are called that for a reason — these are the questions most likely to appear in your board exam. Practise them until they become second nature.”
🔔 Important Note
This PDF is shared only for educational purposes to help students prepare for the CBSE Class 12 Mathematics Board Exam 2026. All credit goes to Arvind Academy for this excellent resource. Please support their work by subscribing to their YouTube channel.
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