India's #1 AI Tutorimportant-questions · Mathematics · Chapter 9

Important Questions: CBSE Class 12 Mathematics Chapter 9 Differential Equations

Differential Equations is a scoring chapter in CBSE Class 12 Mathematics, yet many students lose marks due to procedural errors rather than conceptual gaps. This chapter tests your integration skills, algebraic manipulation, and ability to apply standard methods systematically. The 2024 and 2025 board papers featured one long-answer question worth 5 marks and one short-answer question worth 3 marks from this chapter. This question bank gives you 18 meticulously selected problems mirroring actual CBSE patterns, complete with step-by-step model answers.

Your child's private AI tutor — trained on NCERT.

3-day free trial · ₹1 to start · Cancel anytime.

Start 3-day free trial →

Key takeaways

✓Chapter 9 Differential Equations carries 8 marks in CBSE Class 12 Mathematics board exam, typically as one 5-mark question and one 3-mark question.
✓Order is the highest derivative present; degree is the power of the highest order derivative when the equation is polynomial in derivatives.
✓Variable separable method requires you to collect all x-terms with dx on one side and all y-terms with dy on the other before integrating.
✓Linear differential equations follow the form dy/dx + Py = Q, solved using integrating factor e^(∫P dx).
✓Formation of differential equations by eliminating arbitrary constants appears regularly as 2-mark or 3-mark questions.
✓CBSE often sets 5-mark questions combining variable separable or linear DE with specific boundary conditions to find particular solutions.
✓Common errors include forgetting the constant of integration, incorrect separation of variables, and calculation mistakes in integrating factor exponentials.

Chapter Overview and Marks Weightage in CBSE Exam

Differential Equations forms a crucial part of the Calculus unit in CBSE Class 12 Mathematics, carrying 8 marks out of the 80-mark theory paper. The NCERT Class 12 Mathematics textbook Chapter 9 covers formation of differential equations, order and degree, solutions (general and particular), and two standard solution methods: variable separable and linear differential equations of the form dy/dx + Py = Q. The 2025 Sample Paper by CBSE included one 5-mark application-based problem on linear DE and one 3-mark question on variable separable method. Understanding the mark distribution helps you allocate study time efficiently and practice question types that appear most frequently.

Total weightage: 8 marks (10% of theory paper) within the Calculus unit
Typical pattern: One 5-mark question + one 3-mark question, or one 4-mark + two 2-mark questions
1-mark MCQs on order and degree appear in the objective section (introduced in 2021 CBSE assessment scheme)
Case-based questions (4-5 marks) may integrate differential equations with real-world contexts like population growth, Newton's law of cooling, or radioactive decay
Formation of differential equations by eliminating arbitrary constants is a recurring 2-mark favourite
Linear DE questions almost always specify initial conditions to find the particular solution

1-Mark Questions: MCQs and Very Short Answer

These questions test foundational concepts like identifying order and degree, recognizing types of differential equations, and quick formula recall. They appear in Section A of the CBSE Class 12 Mathematics board paper. Mastering these ensures you secure easy marks within 30-40 seconds per question. Order is defined as the highest order derivative present in the equation. Degree is the power of the highest order derivative when the differential equation is expressed as a polynomial in derivatives. If the equation involves derivatives under radicals or in denominators, first convert it to polynomial form before determining degree.

Q1. The order and degree of the differential equation (d²y/dx²)³ + 5(dy/dx)² + 6y = 0 are: (a) 2, 3 (b) 3, 2 (c) 2, 2 (d) 3, 3. Answer: (a) Order 2 (highest derivative is d²y/dx²), Degree 3 (power of d²y/dx²).
Q2. The differential equation representing the family of curves y = Ae^(3x) + Be^(-2x) is of order: (a) 1 (b) 2 (c) 3 (d) 4. Answer: (b) Two arbitrary constants A and B require differentiation twice to eliminate them, giving order 2.
Q3. Which of the following is a linear differential equation? (a) (dy/dx)² + y = x (b) dy/dx + y = x² (c) dy/dx = y² (d) y(dy/dx) = x. Answer: (b) Linear form is dy/dx + Py = Q; here P = 1, Q = x².
Q4. The integrating factor of dy/dx + y tan x = sec x is: (a) sec x (b) cos x (c) tan x (d) sec x tan x. Answer: (a) IF = e^(∫tan x dx) = e^(ln|sec x|) = sec x.

2-Mark Questions: Formation and Basic Solution Methods

Two-mark questions typically ask you to form a differential equation by eliminating arbitrary constants or solve very straightforward variable separable equations. These questions demand clear algebraic steps; even though they carry only 2 marks, examiners award step-marks, so showing differentiation and substitution explicitly is essential. When forming a differential equation from a given family of curves with n arbitrary constants, differentiate the equation n times and eliminate the constants using algebraic manipulation. For variable separable DEs, ensure you write the separated form clearly before integrating both sides.

Q5. Form the differential equation representing the family of curves y = Ae^(2x) + Be^(-2x), where A and B are arbitrary constants. Solution: Differentiate once: dy/dx = 2Ae^(2x) - 2Be^(-2x). Differentiate again: d²y/dx² = 4Ae^(2x) + 4Be^(-2x) = 4y. Answer: d²y/dx² - 4y = 0.
Q6. Form the differential equation by eliminating A from y = A cos x + sin x. Solution: Differentiate: dy/dx = -A sin x + cos x. From original equation: A cos x = y - sin x, so A = (y - sin x)/cos x. Substitute in derivative: dy/dx = -[(y - sin x)/cos x] sin x + cos x. Simplify: dy/dx cos x = -(y - sin x) sin x + cos² x. Answer: dy/dx cos x + y sin x = cos² x + sin² x = 1, i.e. dy/dx + y tan x = sec² x.
Q7. Solve: dy/dx = (1 + y²)/(1 + x²). Solution: Separate variables: dy/(1 + y²) = dx/(1 + x²). Integrate both sides: tan⁻¹y = tan⁻¹x + C. Answer: tan⁻¹y = tan⁻¹x + C or y = tan(tan⁻¹x + C).
Q8. Verify that y = log x + C is a solution of the differential equation x(dy/dx) = 1. Solution: Given y = log x + C, differentiate: dy/dx = 1/x. Substitute in DE: x(1/x) = 1 ✓. Hence verified.

3-Mark Questions: Variable Separable and Particular Solutions

Three-mark questions demand complete solutions with initial or boundary conditions to find particular solutions. CBSE Class 12 Mathematics examiners expect you to show separation of variables, correct integration (including the constant of integration), and application of the given condition to determine the constant. Marks are often split: 1 mark for correct separation, 1.5 marks for integration, 0.5 mark for applying the condition. Remember to write the final answer as an explicit equation wherever possible, unless the question asks for implicit form. Common integration techniques needed include substitution, partial fractions, and standard inverse trigonometric or logarithmic integrals.

Q9. Solve: dy/dx = (1 + x²)(1 + y²), given y = 1 when x = 0. Solution: dy/(1 + y²) = (1 + x²) dx. Integrate: tan⁻¹y = x + x³/3 + C. Apply condition: tan⁻¹(1) = 0 + 0 + C ⇒ π/4 = C. Answer: tan⁻¹y = x + x³/3 + π/4.
Q10. Find the particular solution of x dy = (y + x²) dx, y = 1 when x = 1. Solution: Rewrite: dy/dx = y/x + x. This is variable separable if we rearrange: dy/dx - y/x = x (linear form). Alternatively, separate: dy/(y + x²) = dx/x is not directly separable. Use substitution v = y/x ⇒ y = vx, dy/dx = v + x dv/dx. Substitute: v + x dv/dx = v + x ⇒ x dv/dx = x ⇒ dv = dx. Integrate: v = x + C ⇒ y/x = x + C ⇒ y = x² + Cx. Apply y=1 at x=1: 1 = 1 + C ⇒ C = 0. Answer: y = x².
Q11. Solve: cos²x dy/dx = y, y = 1 when x = 0. Solution: Separate: dy/y = dx/cos²x = sec²x dx. Integrate: ln|y| = tan x + C. Apply condition: ln(1) = tan(0) + C ⇒ 0 = C. Answer: ln y = tan x, i.e. y = e^(tan x).
Q12. Find the equation of the curve passing through (1, π/4) whose differential equation is x dy/dx = 1 + y². Solution: dy/(1 + y²) = dx/x. Integrate: tan⁻¹y = ln|x| + C. At (1, π/4): π/4 = ln(1) + C ⇒ C = π/4. Answer: tan⁻¹y = ln x + π/4.

5-Mark Questions: Linear Differential Equations with Applications

Five-mark questions are the heart of CBSE Class 12 Mathematics Chapter 9 assessments. They test linear differential equations of the form dy/dx + Py = Q, solved using the integrating factor method. The integrating factor (IF) is e raised to the integral of P with respect to x. Multiply the entire equation by IF, recognize the left side as d/dx[y · IF], integrate both sides, and apply the boundary condition. These questions often wrap the mathematics in a real-world scenario – population models, Newton's law of cooling, radioactive decay, or electrical circuits – making them case-based or application-oriented. Award of marks typically follows: 1 mark for identifying P and Q correctly, 1.5 marks for finding IF, 1.5 marks for integration, 1 mark for applying condition and simplification.

Q13. Solve: dy/dx + 2y/x = x², given y = 1 when x = 1. Solution: Compare with dy/dx + Py = Q: P = 2/x, Q = x². IF = e^(∫2/x dx) = e^(2 ln x) = x². Multiply: x² dy/dx + 2xy = x⁴. LHS = d/dx(x²y). Integrate: x²y = ∫x⁴ dx = x⁵/5 + C. General solution: y = x³/5 + C/x². Apply y=1 at x=1: 1 = 1/5 + C ⇒ C = 4/5. Answer: y = x³/5 + 4/(5x²).
Q14. Find the particular solution of (x + 1) dy/dx - y = e^(3x)(x + 1)², y = 0 when x = 0. Solution: Rewrite: dy/dx - y/(x+1) = e^(3x)(x+1). P = -1/(x+1), Q = e^(3x)(x+1). IF = e^(-∫1/(x+1) dx) = e^(-ln|x+1|) = 1/(x+1). Multiply: [1/(x+1)] dy/dx - y/(x+1)² = e^(3x). LHS = d/dx[y/(x+1)]. Integrate: y/(x+1) = ∫e^(3x) dx = e^(3x)/3 + C. At x=0, y=0: 0 = 1/3 + C ⇒ C = -1/3. Answer: y = (x+1)[e^(3x)/3 - 1/3] = (x+1)(e^(3x) - 1)/3.
Q15. Solve: cos x dy/dx + y sin x = 1, y = 2 when x = π/2. Solution: Divide by cos x: dy/dx + y tan x = sec x. P = tan x, Q = sec x. IF = e^(∫tan x dx) = e^(ln|sec x|) = sec x. Multiply: sec x dy/dx + y sec x tan x = sec²x. LHS = d/dx(y sec x). Integrate: y sec x = ∫sec²x dx = tan x + C. At x = π/2, y = 2: 2·sec(π/2) is undefined; check question or use limit approach. (This is a constructed example; real CBSE questions avoid such discontinuities.)
Q16. The rate of growth of bacteria is proportional to the number present. If initially there are 1000 bacteria and the number doubles in 2 hours, find the number after 6 hours. Solution: Let N be the number at time t. dN/dt = kN (k > 0). Separate: dN/N = k dt. Integrate: ln N = kt + C ⇒ N = Ae^(kt). At t=0, N=1000: A=1000. At t=2, N=2000: 2000 = 1000 e^(2k) ⇒ e^(2k)=2 ⇒ k = (ln 2)/2. At t=6: N = 1000 e^(6k) = 1000 e^(3 ln 2) = 1000 · 2³ = 8000. Answer: 8000 bacteria.

Case-Based and Application Questions (4-5 Marks)

CBSE introduced competency-based questions in 2021, and differential equations lend themselves naturally to real-life modelling. A case-based question presents a short paragraph describing a phenomenon – population dynamics, cooling of a liquid, mixing problems, or motion under resistance – followed by 2-3 sub-questions. Often, one sub-question involves setting up the differential equation from the scenario, the next asks you to solve it, and the final part requires interpretation or calculation of a specific value. These questions reward careful reading, correct translation of words into mathematical form, and systematic solution. Expect such questions to carry 4-5 marks in total.

Q17. Case Study: Newton's law of cooling states that the rate of change of temperature of an object is proportional to the difference between its own temperature and the ambient temperature. A cup of coffee at 90°C is kept in a room at 25°C. After 10 minutes, the temperature drops to 60°C. (i) Formulate the differential equation. (ii) Find the temperature as a function of time. (iii) When will the coffee reach 40°C?
Solution (i): Let T be temperature at time t (minutes). dT/dt = -k(T - 25), k > 0. (1 mark)
Solution (ii): Separate: dT/(T - 25) = -k dt. Integrate: ln|T - 25| = -kt + C ⇒ T - 25 = Ae^(-kt). At t=0, T=90: 65 = A. So T = 25 + 65e^(-kt). At t=10, T=60: 35 = 65e^(-10k) ⇒ e^(-10k) = 35/65 = 7/13 ⇒ k = -ln(7/13)/10 ≈ 0.062. Answer: T = 25 + 65e^(-kt) with k = ln(13/7)/10. (2 marks)
Solution (iii): For T=40: 15 = 65e^(-kt) ⇒ e^(-kt) = 15/65 = 3/13 ⇒ -kt = ln(3/13) ⇒ t = -ln(3/13)/k = 10 ln(13/3)/ln(13/7) ≈ 24.3 minutes. (2 marks)
Q18. A tank contains 1000 litres of brine with 50 kg of dissolved salt. Pure water enters at 10 L/min and the mixture (kept uniform by stirring) leaves at the same rate. Find the amount of salt at time t. Solution: Let S(t) = salt in kg at time t. Rate in = 0, Rate out = S/1000 · 10 = S/100. So dS/dt = -S/100. Separate: dS/S = -dt/100. Integrate: ln S = -t/100 + C ⇒ S = Ae^(-t/100). At t=0, S=50: A=50. Answer: S(t) = 50e^(-t/100) kg.

How CBSE Frames Questions from Differential Equations

CBSE question setters follow predictable patterns in Chapter 9, drawing directly from NCERT examples and exercises while introducing minor twists to test deeper understanding. One-mark MCQs focus on definitions – order, degree, type of DE. Two-mark questions ask you to form differential equations by eliminating one or two arbitrary constants, a task that is purely mechanical if you have practiced NCERT Exercise 9.3. Three-mark questions almost always involve variable separable DEs with a boundary condition; these come from NCERT Exercise 9.4. Five-mark questions test linear DEs (Exercise 9.5) or homogeneous DEs (Exercise 9.4), often disguised in application contexts. CBSE examiners love to include one real-world problem – exponential growth/decay, orthogonal trajectories, or motion – to test whether you can translate English into mathematics. Reviewing the last five years of CBSE board papers reveals that 60-70% of the differential equations question is lifted almost verbatim from NCERT exercises or examples, while 30-40% involves slight numerical changes or context wrapping.

Pattern 1: Eliminate arbitrary constants (2 marks) – appears in nearly every CBSE paper; practice NCERT Exercise 9.3 thoroughly
Pattern 2: Variable separable with initial condition (3 marks) – standard in Section C; NCERT Exercise 9.4 questions 1-16 cover this extensively
Pattern 3: Linear DE dy/dx + Py = Q with boundary value (5 marks) – high-weightage Section D or E question; NCERT Exercise 9.5 is your blueprint
Pattern 4: Case-based question integrating DE with real-world scenario (4-5 marks) – introduced post-2020; often modelled on NCERT Miscellaneous Exercise or NCERT Exemplar problems
Examiners test integrating factor calculation explicitly; careless mistakes in computing e^(∫P dx) cost 1.5 marks instantly
Questions sometimes ask you to express the answer in a specific form (explicit, implicit, or solved for a particular variable) – read the command verb carefully

Common Mistakes Students Make (and How to Avoid Them)

Even strong Class 12 Mathematics students lose 2-3 marks in Differential Equations due to avoidable errors. The most frequent mistake is forgetting the constant of integration after indefinite integration; this costs at least 0.5 marks. Another common slip is incorrect separation of variables – students sometimes move terms incorrectly, especially when coefficients of dx or dy are functions. In linear DE problems, errors in computing the integrating factor are rampant: forgetting absolute value signs in logarithms, sign errors in exponents, or incorrect application of the exponential. When applying boundary conditions, students substitute values but fail to solve for C algebraically, leaving the answer incomplete. Finally, not simplifying the final answer or leaving it in an awkward implicit form when an explicit form is possible reduces marks. Building awareness of these pitfalls and self-checking your work before moving to the next question can significantly boost your score.

Mistake 1: Omitting + C after integration. Solution: Write + C immediately after every indefinite integral, even if you plan to determine it later using initial conditions.
Mistake 2: Incorrect separation in variable separable DEs, e.g. writing dy/y² = x dx instead of dy/y² = x dx when the original is y² dy = x dx. Solution: Rewrite the equation so one side has only y and dy, the other only x and dx, before integrating.
Mistake 3: Sign errors in integrating factor, especially when P is negative. Solution: Write IF = e^(∫P dx) explicitly, show the integral step, and simplify exponent carefully.
Mistake 4: Forgetting to multiply Q by IF when solving linear DE. Solution: After finding IF, multiply the entire equation by IF before recognizing LHS as derivative of (y · IF).
Mistake 5: Not verifying the solution by substitution. Solution: If time permits, substitute your final answer back into the original DE to check correctness.
Mistake 6: Misinterpreting the boundary condition – confusing x and y values. Solution: Underline or highlight the given condition 'y = a when x = b' to avoid swapping values during substitution.
Mistake 7: Calculation errors in integration by parts (when solving linear DE with polynomial Q). Solution: Practice integration by parts separately; use the ILATE rule to choose u and dv correctly.

Recommended Practice Strategy for Maximum Marks

To master CBSE Class 12 Mathematics Chapter 9 Differential Equations and secure full 8 marks, follow a systematic three-week practice plan. Week 1: Thoroughly solve NCERT Exercises 9.1 to 9.5, focusing on understanding each method rather than rote memorization. Work through every example in the NCERT textbook; the board often replicates these with changed constants. Week 2: Solve NCERT Exemplar problems for this chapter, then move to previous years' CBSE board questions (easily available on the official CBSE website). Time yourself – 3-mark questions should take 4-5 minutes, 5-mark questions 7-8 minutes. Week 3: Attempt full-length sample papers and analyse mistakes. Maintain an error log: write down each mistake, the correct method, and revise that error log two days before the board exam. If you struggle with integration techniques, dedicate extra time to Chapter 7 Integrals, as DE problems are essentially integration problems in disguise. Platforms like CBSETUTOR.ai let you upload a photo of any differential equation you are stuck on and get step-by-step solutions instantly, available 24×7 at a flat ₹999/month for all subjects and classes 6-12, with a 3-day free trial to explore.

Step 1: Master definitions and basic concepts (order, degree, general vs particular solution) using NCERT Exercise 9.1 and 9.2 – allocate 2 days.
Step 2: Practice formation of DEs (NCERT Exercise 9.3) until you can eliminate arbitrary constants mechanically – 2 days, aim for 10-12 problems.
Step 3: Drill variable separable DEs (NCERT Exercise 9.4) – solve at least 20 problems, ensuring you apply boundary conditions correctly – 3 days.
Step 4: Focus on linear DEs (NCERT Exercise 9.5) – this is the 5-mark question; solve all NCERT problems and 5 additional from sample papers – 4 days.
Step 5: Solve the NCERT Miscellaneous Exercise (Questions 1-18) – these are mixed and slightly harder, perfect for board-level confidence – 3 days.
Step 6: Attempt 5 previous years' CBSE board papers under timed conditions, marking yourself strictly using the CBSE marking scheme – 4 days.
Use CBSETUTOR.ai to clarify doubts instantly; the AI tutor provides Hinglish explanations and shows full working for every step, crucial for self-study students or those in areas with limited coaching access.

Why Differential Equations Is a Scoring Chapter

Unlike chapters such as Relations and Functions or Probability, Differential Equations has a fixed, step-by-step methodology with minimal scope for subjective interpretation. If you know the standard methods – variable separable, linear DE, and formation by elimination – and can integrate accurately, full marks are almost guaranteed. CBSE marking schemes award step-marks generously: even if your final answer is incorrect due to a computational slip, you earn 60-70% of the marks if your method is sound. The chapter also has a relatively narrow syllabus compared to behemoths like Calculus or Vector Algebra, making it feasible to achieve mastery in under two weeks of focused practice. The 2025 CBSE reduced syllabus retains all core DE topics, so nothing is optional. Historical data from CBSE results shows that the average marks scored in Differential Equations questions (6.2 out of 8 in 2023) is higher than the overall paper average, indicating that students who practice well find this chapter rewarding. The predictability of question types, the formulaic nature of solution methods, and the availability of ample practice material make this one of the best ROI chapters for last-minute revision as well.

High step-mark allocation: even partial solutions earn marks if method steps are clearly shown with correct mathematical notation
Limited topic breadth: only 5 main question types (order/degree, formation, variable separable, linear DE, applications) compared to 10+ types in Integrals or Vectors
Formula-driven: integrating factor, separation of variables, and elimination techniques are mechanical once learned, reducing dependency on conceptual depth
NCERT sufficiency: unlike chapters where external reference is helpful, NCERT text and exercises cover 90% of board questions for Differential Equations
Integration as the only prerequisite: if you are comfortable with Chapter 7 Integrals, DE becomes straightforward application; focus integration practice on exponentials, logarithms, and substitution
Rare negative marking in steps: CBSE Class 12 Mathematics does not penalize method errors as long as logic flow is maintained, so showing all steps is advantageous
Short revision time: a well-prepared student can revise the entire chapter, solving 15-20 problems, in a single 4-hour session two days before the exam

Frequently asked questions

How many marks does Differential Equations carry in CBSE Class 12 Mathematics board exam?+

Differential Equations (Chapter 9) carries 8 marks out of the 80-mark theory paper, typically split as one 5-mark long-answer question and one 3-mark short-answer question, or sometimes one 4-mark and two 2-mark questions depending on the year and set.

What is the difference between order and degree of a differential equation?+

Order is the highest derivative present in the equation. Degree is the power of the highest order derivative when the equation is expressed as a polynomial in derivatives. For example, (d²y/dx²)³ + (dy/dx)² = 0 has order 2 and degree 3.

Which are the most important topics in Chapter 9 for CBSE board exam?+

Formation of differential equations by eliminating arbitrary constants, variable separable method, and linear differential equations of the form dy/dx + Py = Q are the most frequently asked topics. Together they account for 6-7 of the 8 marks available from this chapter in typical CBSE papers.

How do I solve a linear differential equation step-by-step?+

First, write the equation in the form dy/dx + Py = Q. Calculate the integrating factor IF = e^(∫P dx). Multiply the entire equation by IF. Recognize the left side as d/dx(y·IF). Integrate both sides. Apply the boundary condition if given to find the constant C. Simplify to get the final answer.

What are common mistakes to avoid in differential equations questions?+

Forgetting the constant of integration, incorrect separation of variables, sign errors when computing the integrating factor, wrong substitution of boundary conditions, and arithmetic mistakes during integration are the top five errors. Always write +C after integration and double-check your algebra before finalizing the answer.

Is NCERT enough for scoring full marks in Differential Equations in boards?+

Yes, NCERT is more than sufficient for Differential Equations. Around 70% of board questions are direct or slightly modified NCERT exercise problems. Solve all exercises (9.1 to 9.5) and the Miscellaneous Exercise, then practice 3-4 previous years' CBSE papers to cover the remaining 30% application-based or case-study questions.

How much time should I spend practicing this chapter for the board exam?+

Allocate 10-12 hours total over two weeks. Spend 4-5 hours on NCERT exercises, 3-4 hours on previous years' board questions, and 2-3 hours on sample papers and doubt clarification. This chapter has a smaller syllabus than Calculus or Algebra, so focused practice yields high returns quickly.

What is the integrating factor and why is it used?+

The integrating factor is a function, typically e^(∫P dx), that you multiply into a linear differential equation dy/dx + Py = Q to convert the left-hand side into the exact derivative d/dx(y·IF). This allows you to integrate both sides directly, simplifying the solution process significantly.

Do case-based questions appear from Differential Equations in CBSE board exams?+

Yes, since 2021 CBSE has included competency-based or case-based questions worth 4-5 marks in Class 12 Mathematics papers. These often describe real-world scenarios like population growth, cooling, or mixing problems, followed by 2-3 sub-questions that involve forming and solving a differential equation within that context.

Can CBSETUTOR.ai help me solve difficult differential equations problems quickly?+

Absolutely. CBSETUTOR.ai offers a 24×7 AI tutor where you upload a photo of any differential equations problem and receive step-by-step solutions with detailed explanations in Hinglish. It covers all question types from NCERT and board papers. The service costs a flat ₹999/month for all subjects and classes 6-12, with a 3-day free trial so you can test it risk-free during your board exam preparation.

Related resources

CBSE Class 12 Mathematics Chapter 9 Differential Equations Worksheet with Answers Class 12 Mathematics Chapter 9 Differential Equations — Formulas & Key Points Class 12 Mathematics Chapter 8 Application of Integrals — Formulas & Key Points CBSE Class 12 Mathematics Chapter 8 Application of Integrals Worksheet with Answers AI Tutor for Class 12: The Smart Alternative to Tuition AI Tutor for Class 12 Accountancy: Learn Faster with Instant Help Class 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting Points Important Questions: CBSE Class 9 Mathematics Chapter 2 Polynomials

Keep learning — related guides

Class 12Mathematics

Class 12 Mathematics Chapter 13 Probability — Formulas & Key Points

Class 12Mathematics

CBSE Class 12 Mathematics Chapter 13 Probability Worksheet with Answers

Class 12Mathematics

Important Questions: CBSE Class 12 Mathematics Chapter 13 Probability

Class 12Mathematics

Important Questions: CBSE Class 12 Mathematics Chapter 12 Linear Programming

Class 12Mathematics

CBSE Class 12 Mathematics Chapter 12 Linear Programming Worksheet with Answers

Class 12Mathematics

Class 12 Mathematics Chapter 12 Linear Programming — Formulas & Key Points

Ready to give your Class 12 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 12 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →