The NIOS Class 12 Mathematics 311 Solved TMA for the 2026 session is ready, with every assignment question answered after a close reading of the official NIOS Mathematics (311) textbook. Each solution is written in plain, exam friendly language so a learner can follow the working, grasp the method, and reproduce it during submission.
Last updated: 18 July 2026 | Written by Prateek Talwar | Reviewed by Jyoti Sharma, Senior NIOS Counsellor
- Prepared for the 2026 TMA
- All questions answered
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Below you will find the full question list, two complete sample answers so you can judge the quality yourself, the fifteen lessons the assignment draws from, and the exact steps to receive the entire solved set. The internal assessment, known across the board as the NIOS TMA, carries real weight in your final result, so getting these answers right matters.
NIOS Class 12 Mathematics 311 Solved TMA for the 2026 Session
Mathematics is the subject where a well presented assignment quietly protects your result. The theory paper carries eighty marks and the TMA carries twenty, so a clean, correct set of answers here gives you a comfortable cushion before you even sit the exam.
This solved set covers the whole assignment as issued for the current session. It runs from the Sets and functions questions at the start, through the sequences, trigonometry and complex number tasks in the middle, to the statistics and probability items and the final project question. Nothing is skipped, and every internal choice is answered so you are never left guessing which option to attempt.
You do not have to take our word for the standard. Two questions are fully worked out lower down the page, exactly as they appear in the file, so you can read the method and decide whether it fits the way you study.
Complete Question List in the Mathematics 311 TMA
Here is the entire question paper for the Mathematics 311 assignment, laid out with each internal choice and the lesson it tests. Read through it first, then check the two sample solutions to see how each one is handled.
Question 1 · Answer any one
Option A · Lesson 1: Sets
In a survey of 100 students the numbers studying various languages were recorded: English only 18, English but not Hindi 23, English and Punjabi 8, English total 26, Punjabi total 48, Punjabi and Hindi 8, and no language 24. Find (i) how many students were studying Hindi and (ii) how many were studying English and Hindi.
Option B · Lesson 2: Relations and Functions
Check whether the function f(x) = x ÷ √(x² − 5x + 4) is even, and find its domain.
Question 2 · Answer any one
Option A · Lesson 19: Probability
Ramesh tosses a coin three times. Find the probability of getting head and tail alternately (i) if the first toss is a head and (ii) if the first toss is a tail.
Option B · Lesson 19: Probability
Two numbers are chosen, one from each of the sets {1,2,3,4,5,6,7,8,9}. Ram finds the probability that their sum is 10 and Shyam finds the probability that their sum is 8. What is the product of the two probabilities?
Question 3 · Answer any one, 40 to 60 words
Option A · Lesson 6: Sequences and Series
A factory produces 680 mobile handsets in the 4th year and 780 in the 8th year, with production rising by a fixed number each year. Find (i) the production in the first year, (ii) the production in the 11th year and (iii) the total production over 11 years.
Option B · Lesson 7: Some Special Sequences
Find the value of (1³ + 2³ + 3³ + … + 15³) divided by (1² + 2² + 3² + … + 15²) using the standard sum formulae.
Question 4 · Answer any one, 100 to 150 words
Option A · Lesson 4: Trigonometric Functions II
(i) Prove that tan(60° + A) tan(60° − A) = (2 cos 2A + 1) ÷ (2 cos 2A − 1). (ii) Find the general value of θ satisfying tan θ + tan 2θ + tan 3θ = 0.
Option B · Lesson 5: Sides and Angles of a Triangle
Kiran designs a triangular park whose angles are in arithmetic progression, with two fence sides in the ratio √3 : √2 lying opposite the smallest and the larger angle. Find (i) the three angles and (ii) which side lies opposite the largest angle.
Question 5 · Answer any one, 100 to 150 words
Option A · Lesson 17: Measures of Dispersion
For a frequency distribution of the monthly data usage of 800 internet users, find (i) the upper limit of the fifth class, (ii) the lower limit of the eighth class, (iii) the class interval size, (iv) the frequency of the fourth class, (v) the cumulative frequency of the sixth class, (vi) the percentage of users on 100 GB or more and (vii) the median.
Option B · Lesson 17: Measures of Dispersion
An assertion and reason item comparing Set A and Set B using their means, variances and dot diagrams. Choose the correct code and justify it with reasons.
Question 6 · Prepare any one project
Option A, part I · Lesson 9: Quadratic Equations and Inequalities
A carpenter cuts three lengths from a 101 cm cardboard piece where the second is 11 cm longer than the shortest and the third is thrice the shortest. Find the possible lengths of the shortest piece if the third is at least 8 cm longer than the second.
Option A, part II · Lesson 8: Complex Numbers
For z₁ = 3 − 2i, z₂ = 3 + 2i and z₃ = 1 + i, find α, β and γ as defined, represent them on the Argand plane, and find the modulus and argument of each.
Option B, part i · Lesson 11: Permutations and Combinations
Mr. Rohan has 7 relatives (4 ladies, 3 men) and his wife Sunita has 7 relatives (3 ladies, 4 men). In how many ways can they invite 3 ladies and 3 men so that 3 guests are Rohan's relatives and 3 are Sunita's?
Option B, part ii · Lesson 12: Binomial Theorem
The 5th, 6th and 7th terms in the expansion of (1 + y)ⁿ form an arithmetic progression. Prove that the two possible values of n are such that one is double the other.
Option B, part iii · Lesson 9: Quadratic Equations and Inequalities
A rectangular table is (x + 3) feet long and (x + 1) feet wide, and its area must be less than 30 square feet. Write and solve an inequality to find the possible values of x.
Sample Solved Answers from the Mathematics 311 TMA
These two answers are lifted straight from the file so you can see the presentation before you ask for the full set. One is a short sequences question and the other is a function question, which together show how both the quick items and the reasoning items are handled.
Sample 1 · Question 3, Option A · Lesson 6
Factory production as an arithmetic progression
Let the yearly production form an arithmetic progression with first term a and common difference d.
4th year: a + 3d = 680 (1)
8th year: a + 7d = 780 (2)Subtracting (1) from (2) gives 4d = 100, so d = 25. From (1), a = 680 − 3(25) = 680 − 75 = 605.
(i) First year = a = 605 units.
(ii) 11th year = a + 10d = 605 + 250 = 855 units.
(iii) Total in 11 years = S₁₁ = (11 ÷ 2)(2a + 10d) = (11 ÷ 2)(1210 + 250) = (11 ÷ 2)(1460) = 8030 units.So first year production is 605 units, eleventh year production is 855 units, and the total across eleven years is 8030 units.
Sample 2 · Question 1, Option B · Lesson 2
Is f(x) = x ÷ √(x² − 5x + 4) even, and what is its domain?
Domain. The expression under the root must be positive and the denominator non zero.
x² − 5x + 4 = (x − 1)(x − 4) > 0 ⇒ x ∈ (−∞, 1) ∪ (4, ∞).
So the domain is (−∞, 1) ∪ (4, ∞).
Evenness. Replacing x with −x gives f(−x) = −x ÷ √(x² + 5x + 4), which is not equal to f(x) or to −f(x) in general. For example f(5) = 5 ÷ 2 while f(−5) = −5 ÷ √54. The domain is also not symmetric about 0, since 3 is not in the domain but −3 is.
Therefore f is neither even nor odd.
The remaining questions, including the trigonometric proof, the triangle in arithmetic progression, the grouped median and the complex number project, are worked out to the same standard in the complete file.
How We Prepare the NIOS Class 12 Mathematics 311 Solved TMA
Every answer starts with the source, not a shortcut. Our subject team reads the relevant lesson in the official Mathematics (311) book, confirms the concept the question is testing, and then writes the solution so the working leads cleanly to the result. Nothing is copied blindly from an old set.
Once a draft is written, a second reviewer checks the arithmetic, the final answer, and the presentation against NIOS assignment norms. Word limits are respected where the paper specifies them, such as the forty to sixty word items and the hundred to fifty word ones, so the response never looks padded or thin.
Because the assignment mixes proofs, calculations and a project task, we treat each type differently. Proofs are laid out step by step, numerical answers show the formula before the substitution, and the project questions include the reasoning a study centre expects to see. Learners who also want lesson notes alongside the answers can pair this file with our wider NIOS Study Material for the same subject.
Chapters and Lessons Covered in the Mathematics 311 TMA
The Mathematics 311 TMA is built only from the fifteen self paced lessons that carry internal assessment. The table below lists all of them by module, along with the specific ideas each lesson contributes to this assignment, so you can see exactly where every question comes from.
| Module | Lesson | Key ideas tested in this TMA |
|---|---|---|
| Sets, Relations and Functions | Lesson 1: Sets | Venn diagrams, overlapping set regions, cardinality of unions |
| Lesson 2: Relations and Functions I | Domain and range, testing even and odd functions, symmetry about zero | |
| Lesson 3: Trigonometric Functions I | Radian measure, basic ratios, fundamental identities | |
| Lesson 4: Trigonometric Functions II | Compound angle formulae, tan(A ± B), general solutions of equations | |
| Lesson 5: Sides and Angles of a Triangle | Sine rule, cosine rule, angles in arithmetic progression | |
| Sequences and Series | Lesson 6: Sequences and Series | Arithmetic progression, nth term, sum of n terms |
| Lesson 7: Some Special Sequences | Sum of squares, sum of cubes, evaluating combined series | |
| Algebra I | Lesson 8: Complex Numbers | Argand plane, modulus and argument, products and quotients |
| Lesson 9: Quadratic Equations and Linear Inequalities | Sign analysis, roots by formula, solving word based inequalities | |
| Lesson 10: Principle of Mathematical Induction | Base step, inductive step, proving sum and divisibility results | |
| Lesson 11: Permutations and Combinations | Selection with conditions, grouping constraints, counting cases | |
| Lesson 12: Binomial Theorem | General term, coefficients, terms forming a progression | |
| Statistics and Probability | Lesson 17: Measures of Dispersion | Grouped median, variance, cumulative frequency, spread of dot plots |
| Lesson 18: Random Experiments and Events | Sample space, events, equally likely outcomes | |
| Lesson 19: Probability | Conditional probability, favourable outcomes, product of probabilities |
The other twenty three lessons in the book belong to the public examination, not the assignment, so they are correctly left out of this solved set.
Why Students Trust This Mathematics 311 TMA Solution Set
Trust in an assignment file comes down to two things: are the answers correct, and are they presented the way a checker wants to read them. This set is built for both, which is why learners return session after session rather than hunting for a new source each year.
The answers are original working, not recycled screenshots, so the file reads naturally in your own hand when you copy it out. Students juggling several senior secondary submissions at once often pick up the full NIOS Class 12 Solved TMA set from the same team, because the standard and the support stay consistent across every subject.
You also get a real person to talk to. If a study centre uses a slightly different question set or asks for a particular format, we adjust the affected answers rather than sending a fixed file and disappearing. That responsiveness is what keeps our Mathematics 311 answers reliable through the whole session.
How to Get the Full Mathematics 311 Solved TMA on WhatsApp
The complete file is shared over WhatsApp so you receive it quickly and can ask follow up questions in the same chat. There is no long form to fill and no waiting for an email that never arrives.
Send us the subject name and code, tell us whether you want the typed PDF or a ready to submit handwritten copy, and confirm your session. We reply with the delivery details and timeline, and most files reach the student the same day. This page is part of our full range of NIOS solved help, so if you study more than one subject you can request them together and reviewers will guide you through our complete NIOS Solved TMA collection.
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TMA Marks, Format and Submission Rules for Mathematics 311
The Mathematics 311 TMA carries twenty marks out of the hundred for the subject, drawn from the fifteen internal assessment lessons. Those twenty marks are among the easiest to secure in the whole course, because you prepare them at home without exam pressure, which is exactly why a careful submission is worth the effort.
Write the assignment on plain sheets, copy each answer in your own handwriting, and keep the working visible rather than jumping to the final line. Attempt the required number of choices only, since answering extra parts does not add marks and only crowds the file. Submit the completed set at your study centre before the deadline it announces for the session.
If you are planning your registration or clearing an earlier backlog, our resources cover the full senior secondary level. Learners frequently check the NIOS Class 12 Syllabus with us before deciding which subjects to register, and the same team handles every subject, so nothing gets lost along the way.
The exact deadline and any question revisions are set by NIOS and your study centre for the running session. Always confirm the current assignment against your centre before you submit.
Frequently Asked Questions on the Mathematics 311 Solved TMA
Is the NIOS Class 12 Mathematics 311 Solved TMA updated for the 2026 session?
Yes, this Mathematics 311 solved set is prepared for the 2026 assignment and matches the current questions issued by NIOS. Every answer is checked against the official textbook lessons before release. If NIOS revises any question during the session, we update the affected solution and reshare the corrected file so your submission always reflects the latest assignment paper.
How many questions does the Mathematics 311 TMA contain?
The Mathematics 311 TMA contains six main questions, and most of them offer an internal choice between two or three parts. Question six is a project task where you prepare any one option. Our solved set answers each listed question and every choice, so whichever version your study centre assigns, you already have a ready and accurate response to copy and submit.
Are the Mathematics 311 answers handwritten or typed?
Both formats are available for the Mathematics 311 solved set. You can request a clean typed PDF for quick reference or a handwritten copy that is ready to submit at your study centre. The handwriting is done on standard assignment sheets following NIOS presentation norms, so the file looks natural in your submission and reads well during internal assessment.
Will the Mathematics 311 Solved TMA help me score full internal marks?
The Mathematics 311 answers are written to earn maximum internal marks by showing complete working, correct final results and the format examiners expect. The TMA carries twenty marks in this subject, so an accurate submission lifts your overall result. You still need to copy the work in your own hand and submit it before the deadline set by your study centre.
Which lessons are covered in the Mathematics 311 Solved TMA?
The Mathematics 311 TMA draws from the fifteen self paced lessons that carry internal assessment, including Sets, Trigonometry, Sequences and Series, Complex Numbers, Inequalities, Permutations and Combinations, Binomial Theorem, Measures of Dispersion and Probability. Our solved set addresses each question from these lessons, so the full assignment is covered in one file with no gap left behind.
How do I get the complete Mathematics 311 Solved TMA?
Getting the complete Mathematics 311 solved set takes one message on WhatsApp. Send the subject name and code to our team, confirm whether you want the typed or handwritten version, and we share the delivery details and timeline. Most files are shared the same day, so you can review the solutions and submit your assignment well before the cut off date.
Ready when you are. One message puts the full solved file in your hands.
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Disclaimer. Unnati Educations is an independent academic support provider and is not affiliated with, endorsed by, or officially connected to the National Institute of Open Schooling (NIOS). All subject names, codes and assignment references belong to NIOS and are used only to help learners identify the correct study material.
Sources. Official NIOS Senior Secondary Mathematics (311) study material and syllabus, nios.ac.in.
