Class 12 Maths Half-Yearly Exam 2026: Important Questions & Complete Revision

The Class 12 Maths Half-Yearly Exam 2026 requires clear concepts, regular practice and effective revision. Students can prepare with Class 12 Maths Half-Yearly Important Questions 2026, solved answers, syllabus details and exam pattern to prioritise key topics.

This revision covers important questions from Relations and Functions and Inverse Trigonometric Functions, along with key topics from other chapters. Practise numerical problems, revise formulas and solve timed sample papers to identify weak areas before the exam.

Class 12 Maths Half-Yearly Exam 2026: Important Topics

Focus on these topics first, then solve important questions from each one. 

• Relations and functions: types of relations, counting total, reflexive, symmetric and one-one functions.

• Inverse trigonometric functions: principal value ranges and simplifying expressions.

• Matrices and determinants: matrix operations, symmetric and skew-symmetric matrices, determinants and inverses.

• Continuity and differentiability: continuity at a point and derivatives of piecewise functions.

• Applications of derivatives: tangents and normals, rate of change, and maxima and minima.

Class 12 Maths Half-Yearly Exam 2026: Important Questions with Answers

Relations and Functions is a high-scoring chapter. Questions often ask you to count relations and functions, check properties, or identify one-one and onto functions. 

Useful formulas for this chapter:

• Total relations from A to B: 2^(n(A) × n(B))

• Reflexive relations on A: 2^(n² − n)

• Symmetric relations on A: 2^(n(n + 1)/2)

• Total functions from A to B: n(B)^n(A)

Q1. If sets A and B have 2 and 5 elements, respectively, then the total number of relations from A to B is:

(a) 10

(b) 7

(c) 64

(d) None of the above

Q2. Let A = {3, 5}. Then the number of reflexive relations on A is:

(a) 2

(b) 4

(c) 0

(d) 8

Q3. If set A has 2 elements, how many symmetric relations can be formed from A to A?

(a) 2

(b) 4

(c) 8

(d) 64

Q4. A relation R on the set A = {1, 2, 3, 4} is given by R = {(1, 4)}. Then R is:

(a) Only reflexive

(b) Only symmetric

(c) Only transitive

(d) None of the above

Q5. The relation "x is the father of y" on the set of all people is:

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) None of these

Q6. A relation R on the set of real numbers is defined by R = {(a, b): 2a² − 3ab + b² = 0}. Check whether R is reflexive, symmetric, or transitive.

(a) Only reflexive

(b) Only symmetric

(c) Reflexive and transitive

(d) None of the above

Q7. Let R be an equivalence relation on the set A = {0, 1, 2, 3, 4, 5}, defined by R = {(a, b): 2 divides (a − b)}. Write the equivalence class [0].

Q8. Show that the function f: [0, ∞) → [2, ∞), defined by f(x) = x² + 2, is bijective.

Q9. Let f: R → R be defined by f(x) = x² − 4x + 5. Then f is:

(a) Injective but not surjective

(b) Surjective but not injective

(c) Both injective and surjective

(d) Neither injective nor surjective

Q10. If n(A) = 4 and n(B) = 3, then the total number of functions from A to B is:

(a) 81

(b) 12

(c) 64

(d) 4096

Q11. If n(A) = 4 and n(B) = 5, then the total number of one-one (injective) functions from A to B is:

(a) 20

(b) 9

(c) 24

(d) 120

Q12. The value of sin[π/3 + sin⁻¹(1/2)] is:

(a) 1

(b) 1/2

(c) 1/3

(d) 1/4

Q13. Evaluate cos(2 cos⁻¹(2/5)).

(a) 13/25

(b) 17/25

(c) −13/25

(d) −17/25

Q14. sin(tan⁻¹x), where |x| < 1, is equal to:

(a) x/√(1 − x²)

(b) 1/√(1 − x²)

(c) 1/√(1 + x²)

(d) x/√(1 + x²)

Q15. Find the value of sin⁻¹(sin 3π/5).

(A) 3π/5

(B) 2π/5

(C) π/5

(D) −3π/5

Q16. Write in simplest form: tan⁻¹√((1 − cos x)/(1 + cos x)).

(A) x/2

(B) x

(C) (π − x)/2

(D) π/2 − x/2

Q17. Solve sin{cot⁻¹(x + 1)} = cos(tan⁻¹x).

(a) 0

(b) 1

(c) −1

(d) None

Q18. Find the value of sin⁻¹(sin 10), where 10 is in radians.

(A) 10

(B) π + 10

(C) 3π − 10

(D) 2π − 10

Q19. The domain of the function cos⁻¹(2x − 1) is:

(a) [0, 1]

(b) [−1, 1]

(c) (−1, 1)

(d) [0, π]

Q20. The domain of f(x) = sin⁻¹x + cos x is:

(a) [−1, 1]

(b) [−1, π + 1]

(c) (−∞, ∞)

(d) ∅

Q21. If cos⁻¹α + cos⁻¹β + cos⁻¹γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals:

(a) 0

(b) 1

(c) 6

(d) 12

Q22. Evaluate tan[sin⁻¹(8/17) + sin⁻¹(3/5)].

(A) 36/77

(B) 77/36

(C) 15/8

(D) 60/77

Class 12 Maths Half-Yearly Exam Important Questions PDF

Students who prefer offline revision can use the Half-Yearly revision PDF, which puts the important questions, notes and solutions in one file. It focuses on Relations and Functions and Inverse Trigonometric Functions, so use it alongside the other chapters.

How to Revise Class 12 Maths for the Half-Yearly Exam

A Class 12 Maths Half-Yearly Revision works best with a short daily routine rather than long study sessions in the final week. Use the steps below for Class 12 Mathematics Revision 2026 before the paper, so each chapter gets proper attention.

• Make a one-page sheet of key formulas, especially for matrices, determinants and derivatives.

• Solve the important questions for each chapter and spend extra time on weak areas.

• Attempt one or two sample papers under timed conditions, and keep within each section's time limit.

• Focus on understanding concepts rather than memorising answers.

• Do not start new chapters in the last few days before the exam.

For detailed chapter notes, students can read the Class 12 Maths notes and revise them alongside the questions above.

Solving important questions every day and revising formulas before the test can make the Class 12 Mathematics Half-Yearly Exam 2026 far less stressful. Review every mistake and give each chapter its fair share of time. 

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