NIOS Class 12 Maths 311 Important Questions 2026

Mathematics is the one subject where students lose objective marks not because they do not understand the concept, but because they have never practised the formula as a question. If you are preparing for NIOS Class 12 Maths 311 in 2026 and want to know which chapter-wise objective questions actually matter, this page puts it all together. For the complete solution booklet, contact Unnati Education at 9654279279 or 9899436384

NIOS Mathematics 311 – Quick Overview

What Are NIOS Class 12 Maths 311 Important Questions for 2026?

Here is something most students find out too late. Reading a chapter in Mathematics and solving that chapter as objective questions are two completely different activities. You can know exactly how integration works and still mark the wrong MCQ option because the four choices are designed to catch common errors. A derivative question with options like 3x², 3x, x², and x⁴/4 looks straightforward — until you are under exam pressure and pick the second one by habit. The objective section of NIOS Mathematics 311 covers 10 modules and 38 lessons. It tests formula recall, direct substitution, and conceptual understanding across everything from sets and trigonometry to calculus, vectors, and linear programming. Practising these chapter by chapter is the only preparation that actually works. This page gives you the most important sample questions from each module. For the full booklet with complete working, reach out to Unnati Education directly.

Module I – Sets, Relations, Functions and Trigonometry

Sets and relations are where the paper begins, and most students underestimate them. The exam does not just ask for definitions — it asks you to apply set operations, count subsets, and identify function types. A set with n elements has exactly 2ⁿ subsets. That single fact alone appears as a question in practically every exam.

Students who need their NIOS Class 12 TMA for Mathematics 311 solved accurately and ready for submission can get it from Unnati Education in both typed and handwritten formats.

Sample Questions

• The number of subsets of a set with 4 elements is: A. 8 B. 16 C. 4 D. 12
  Answer: B (2⁴ = 16)
• If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B is: A. {1, 2, 3, 4} B. {1, 4} C. {2, 3} D. {}
  Answer: C
• Fill in the Blank: A function f : A → B is called a bijection if it is both __________ and onto.
  Answer: one-one
• True or False: Every function is a relation, but not every relation is a function.
  Answer: True

Trigonometric Functions (Lessons 3 and 4) build on identity recall. The Pythagorean identity sin²θ + cos²θ = 1 is the foundation, and the exam uses it in all three derived forms. If you know all three — 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ — you will answer multiple trigonometry MCQs correctly without doing any real calculation.

Sample Questions

• The value of sin 30° + cos 60° is: A. √3 B. √3/2 C. 1 D. 1/2
  Answer: C (1/2 + 1/2 = 1)
• True or False: sin(90° − θ) = cos θ for all values of θ.
  Answer: True

Module II – Sequences and Series

AP and GP come back in objective questions year after year because the formulas are clean, the substitution is quick, and the exam knows you will miscalculate under pressure if you have not practised.

For AP: aₙ = a + (n − 1)d

For GP: aₙ = arⁿ⁻¹

The sum of the first n natural numbers is n(n + 1)/2. Sum of squares is n(n + 1)(2n + 1)/6. These appear in the fill-in-the-blank section regularly.

Sample Questions

• The 4th term of a GP with first term 2 and common ratio 3 is: A. 18 B. 162 C. 54 D. 6
  Answer: C (2 × 3³ = 2 × 27 = 54)
• Fill in the Blank: The sum of the first n natural numbers is __________.
  Answer: n(n + 1)/2
• True or False: In an AP, the common difference can be negative.
  Answer: True

Students who want to practise all 38 chapters in one structured resource can get the complete NIOS Class 12 Important Questions booklet for Mathematics 311 from Unnati Education with full solutions and step-by-step working.

Module III – Algebra I

Lessons 8 to 12 cover complex numbers, quadratic equations, mathematical induction, permutations, combinations, and the binomial theorem. This is the module with the highest density of formula-based MCQs in the entire paper.

The modulus of a complex number z = a + bi is |z| = √(a² + b²). For z = 3 + 4i, that is √(9 + 16) = √25 = 5. This question appears every year in some form. Know the formula and it takes under ten seconds.

For permutations and combinations: nPr = n! / (n − r)! and nCr = n! / (r!(n − r)!)

The fact that ⁿCr = ⁿCₙ₋ᵣ is tested repeatedly. ⁵C₂ = ⁵C₃ = 10. The exam puts both values as wrong options to catch students who do not know this.

Sample Questions

• The modulus of the complex number z = 3 + 4i is: A. 7 B. 25 C. 5 D. 1
  Answer: C
• The discriminant of ax² + bx + c = 0 is b² − 4ac. If b² − 4ac = 0, the roots are: A. Imaginary B. Real and distinct C. Irrational D. Real and equal
  Answer: D
• Fill in the Blank: The value of 5! is __________.
  Answer: 120
• True or False: ⁵C₂ = ⁵C₃.
  Answer: True

Module IV – Co-ordinate Geometry

Lessons 13 to 16 cover the Cartesian system, straight lines, circles, and conic sections. This module has the highest number of numerical MCQs in the paper. You are given coordinates and asked to calculate — and four close-looking options mean one calculation error loses the mark.

Key formulas the exam tests directly:

• Distance between A(x₁, y₁) and B(x₂, y₂) = √((x₂ − x₁)² + (y₂ − y₁)²)
• Section formula (internal): x = (mx₂ + nx₁) / (m + n)
• Slope = (y₂ − y₁) / (x₂ − x₁)
• Two lines are perpendicular if a₁a₂ + b₁b₂ = 0

Students who want to see how questions were framed in previous years can get NIOS Class 12 question paper collections for Mathematics 311 from Unnati Education, with complete solutions across multiple exam cycles.

Sample Questions

• The distance between A(0, 0) and B(3, 4) is: A. 7 B. 5 C. 25 D. 1
  Answer: B (√(9 + 16) = 5)
• Two lines are perpendicular if the product of their slopes m₁ × m₂ equals: A. 0 B. 1 C. −1 D. ∞
  Answer: C
• True or False: Lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are perpendicular if a₁a₂ + b₁b₂ = 0.
  Answer: True

Module V – Statistics and Probability

Probability questions in Module V are the most straightforward MCQs in the paper if you know the basic rules. P(certain event) = 1. P(impossible event) = 0. P(A ∪ B) = P(A) + P(B) for mutually exclusive events. The complement rule P(A') = 1 − P(A) appears in at least one question every year.

Sample Questions

• A die is rolled once. The probability of getting a number greater than 4 is: A. 1/2 B. 1/6 C. 1/3 D. 2/3
  Answer: C (favourable outcomes: 5 and 6 = 2 out of 6 = 1/3)
• If P(A) = 0.4 and P(B) = 0.3 and A and B are mutually exclusive, then P(A ∪ B) is: A. 0.12 B. 1.0 C. 0.1 D. 0.7
  Answer: D
• Fill in the Blank: The probability of an impossible event is __________.
  Answer: 0

Module VI – Algebra II

Lessons 20 to 22 cover matrices, determinants, and inverse of a matrix. The exam tests order of a matrix, types of matrices, determinant calculations, and the condition for invertibility.

For a 2 × 2 matrix |a b; c d|, determinant = ad − bc. If det(A) = 0, the matrix is singular and has no inverse. These two facts together answer multiple questions in this module.

Students who need NIOS Class 12 Intext and Terminal Questions for Mathematics 311 can get the complete chapter-wise set from Unnati Education.

Sample Questions

• The determinant of the matrix |2 3; 1 4| is: A. 11 B. 8 C. 5 D. −5
  Answer: C (2 × 4 − 3 × 1 = 8 − 3 = 5)
• Fill in the Blank: A square matrix A is singular if det(A) = __________.
  Answer: 0
• True or False: The inverse of a matrix exists only if its determinant is non-zero.
  Answer: True

Module VIII – Calculus

Calculus is the largest module in Mathematics 311 and covers eight full lessons — from limits and continuity through differentiation, integration, and differential equations. The objective section here tests standard formulas directly. There is no complex proof required. Know the formula, apply it, pick the answer.

Key formulas tested every year:

• d/dx(xⁿ) = nxⁿ⁻¹
• d/dx(eˣ) = eˣ
• d/dx(log x) = 1/x
• ∫xⁿ dx = xⁿ⁺¹/(n + 1) + C (where n ≠ −1)
• ∫(1/x) dx = log|x| + C
• lim(x → 0) sin x / x = 1

Sample Questions

• The derivative of x⁵ with respect to x is: A. 5x⁶ B. x⁴ C. 5x⁴ D. 4x⁵
  Answer: C
• ∫eˣ dx equals: A. eˣ⁺¹ + C B. eˣ/x + C C. eˣ + C D. xeˣ + C
  Answer: C
• Fill in the Blank: lim(x → 0) sin x / x = __________.
  Answer: 1
• True or False: The derivative of a constant is always zero.
  Answer: True

d/dx(xⁿ) = nxⁿ⁻¹ is the power rule and it is tested in more objective questions than any other calculus formula. For x⁵, n = 5, so derivative = 5x⁴. If you write this formula on a piece of paper and practise it five times today, you will never get that question wrong.

Module IX – Vectors and Three Dimensional Geometry

Vectors are tested for magnitude, dot product, cross product properties, and direction cosines. The magnitude formula is |a⃗| = √(a₁² + a₂² + a₃²) — the same structure as the modulus of a complex number. Students who recognize this pattern answer both question types with equal confidence.

Sample Questions

• The magnitude of the vector a⃗ = 3i⃗ + 4j⃗ is: A. 7 B. 25 C. 1 D. 5
  Answer: D (√(9 + 16) = 5)
• If a⃗ · b⃗ = 0, the vectors a⃗ and b⃗ are: A. Parallel B. Anti-parallel C. Perpendicular D. Equal
  Answer: C
• Fill in the Blank: The direction cosines of a line satisfy l² + m² + n² = __________.
  Answer: 1
• True or False: The cross product of two parallel vectors is a zero vector.
  Answer: True

Module X – Linear Programming and Mathematical Reasoning

Linear programming is one of the most reliable modules for objective marks because the rules are absolute. The optimal value of the objective function always occurs at a corner point of the feasible region. No exceptions. The exam tests this as both a true or false question and as a conceptual MCQ.

Mathematical reasoning tests negation, contrapositive, and the definition of different types of mathematical statements.

Sample Questions

• In linear programming, the optimal value of the objective function always occurs at: A. The centre of the feasible region B. Any interior point C. A corner point of the feasible region D. The midpoint of any boundary
  Answer: C
• The negation of the statement "All triangles are equilateral" is: A. No triangle is equilateral B. All triangles are isosceles C. Not all triangles are equilateral D. Some triangles are equilateral
  Answer: C
• Fill in the Blank: A region that satisfies all constraints in a linear programming problem is called the __________ region.
  Answer: feasible

Key Formula Reference Table

Common Mistakes Students Make in Mathematics 311 Exam

The most frequent error in Module IV is applying the external section formula when internal division is asked. Getting those two formulas mixed up under time pressure is very common and very avoidable if you write them both down and practise distinguishing between them.

In Module I, students confuse sin(90° − θ) = cos θ with sin(90° + θ) = cos θ and mark the wrong option in true or false.

In Module III, writing ⁵P₂ = 20 is correct, but writing ⁵C₂ = 20 is wrong — ⁵C₂ = 10. The difference between P and C trips up students who have not specifically practised the distinction in question format.

In Module VIII, the most common integration error is writing ∫(1/x) dx = −1/x² + C instead of log|x| + C. That single substitution error causes a wrong answer that students usually only catch after the exam.

In Module X, not knowing that the negation of "all" is "not all" (not "none") leads to wrong answers in mathematical reasoning MCQs every year.

About Unnati Education

Unnati Education has been helping NIOS students prepare since 2010. For Mathematics 311, we provide a complete chapter-wise objective question booklet covering all 38 lessons across all 10 modules with correct answers, full working, and clear explanations. We also offer solved TMAs, previous year question papers with complete solutions, and module-wise formula notes — all updated for the April and October 2026 NIOS exam cycles.

How to Get the Complete Solutions

If you want the full NIOS Class 12 Maths 311 important questions booklet with complete solutions for 2026, or if you need previous year question papers, solved TMAs, or any other study material, contact Unnati Education today.

Phone and WhatsApp: 9654279279 or 9899436384

Website: unnatieducations.com/nios

Frequently Asked Questions

Q1. Are these NIOS Class 12 Maths 311 important questions enough for the 2026 exam?

These chapter-wise questions cover the most important objective topics from all 10 modules and 38 lessons of NIOS Mathematics 311. They are a focused and reliable preparation resource for 2026. For the complete solution booklet with answers and full working for every chapter, contact Unnati Education at 9654279279 or 9899436384 and get your copy today.

Q2. Where can I get or download the NIOS Mathematics 311 important questions PDF for 2026?

Unnati Education provides a complete NIOS Mathematics 311 important questions PDF with MCQs, fill in the blanks, and true or false questions from all chapters, with full answers and step-by-step solutions included. Call or WhatsApp at 9654279279 or 9899436384 and our team will share the complete material with you quickly and directly.

Q3. Does the booklet include calculus and vector questions from NIOS Maths 311?

Yes, the Unnati Education booklet for NIOS Mathematics 311 covers objective questions from all modules including the full calculus section from Module VIII and vectors and three dimensional geometry from Module IX. Every question has a correct answer with working shown clearly. Contact us at 9654279279 or 9899436384 to get your complete 2026 solution booklet today.

Q4. Can I get previous year question papers for NIOS Mathematics 311 from Unnati Education?

Yes, Unnati Education provides previous year question papers with complete solutions for NIOS Mathematics 311. These papers show how questions are structured, what level of calculation is expected, and which chapters are weighted most heavily across different exam cycles. Call or WhatsApp 9654279279 or 9899436384 to get the full paper set for 2026.

Q5. Is the Unnati Education booklet valid for both April and October 2026 NIOS Maths exams?

Yes, the Unnati Education objective question booklet for NIOS Mathematics 311 is fully valid for both the April and October 2026 NIOS exam cycles. All content follows the current NIOS syllabus and is reviewed and updated throughout the year. Whichever session you are appearing for, this booklet prepares you completely for the objective section.