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By Shailendra Singh
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Updated on 18 Jun 2025, 10:34 IST
NCERT Solutions for Class 11 Maths include step-by-step answers for every chapter and exercise. These solutions are very helpful for students preparing for their Class 11 exams. All the answers follow the NCERT syllabus and are made by experts in a simple way that’s easy for students to understand.
If you’re getting ready for your Class 11 Maths exam, these NCERT Solutions for Class 11 maths pdf are super useful. They have answers to sample questions, quick tips, summaries, and notes that can clear up any confusion you might have.
When you’re preparing for exams that help you get into Engineering institutes, the questions often come from your textbook. So, practicing with our NCERT Solutions for Class 11 Maths exercises can really improve your exam scores. We also suggest trying out the tougher problems and using our online solutions. The Class 11 Maths Solutions guide you through a strong learning journey. You can explore the solutions for each chapter in the table we’ve provided to understand better.
NCERT Solutions Class 11 Maths Chapter 1 : Sets
Q1. Define a set. Give an example.
A: A set is a well-defined collection of distinct objects.
Example: A = {2, 4, 6, 8} is a set of even numbers less than 10.
Q2. What is the power set of A = {a, b}?
A: Power set of A is the set of all subsets of A.
P(A) = { {}, {a}, {b}, {a, b} }
Q3. If A = {1, 2, 3} and B = {3, 4, 5}, find A ∩ B.
A: A ∩ B = {3}, as it is the common element.
NCERT Solutions Class 11 Maths Chapter 2 : Relations and Functions
Q1. What is a function?
A: A function is a relation in which every element of the domain has exactly one image in the codomain.
Q2. If A = {1, 2}, B = {3, 4}, list all possible functions from A to B.
A: Total functions = 2² = 4.
Functions: {(1,3),(2,3)}, {(1,3),(2,4)}, {(1,4),(2,3)}, {(1,4),(2,4)}
Q3. What is the domain of f(x) = √(x - 2)?
A: x - 2 ≥ 0 ⇒ x ≥ 2. So, domain = [2, ∞)
NCERT Solutions Class 11 Maths Chapter 3: Trigonometric Functions
Q1. Convert 90° to radians.
A: 90° = (π/180) × 90 = π/2 radians
Q2. What is sin(0) and cos(0)?
A: sin(0) = 0, cos(0) = 1
Q3. Prove: sin²θ + cos²θ = 1
A: It’s a fundamental identity in trigonometry, derived from the Pythagorean theorem on the unit circle.
NCERT Solutions Class 11 Maths Chapter Chapter 4: Principle of Mathematical Induction
Q1. What is the Principle of Mathematical Induction?
A: It's a method to prove statements for all natural numbers by verifying:
(i) The base case is true, and
(ii) If true for k, then also true for k + 1.
Q2. Prove that 1 + 2 + 3 + ... + n = n(n+1)/2 using induction.
A: Base case (n = 1): 1 = 1(1+1)/2 = 1 — true.
Assume true for n = k: 1 + 2 + ... + k = k(k+1)/2
For n = k+1:
1 + 2 + ... + k + (k+1)
= [k(k+1)/2] + (k+1) = (k+1)(k+2)/2 — proved.
NCERT Solutions Class 11 Maths Chapter Chapter 5: Complex Numbers and Quadratic Equations
Q1. What is the imaginary unit 'i'?
A: i is defined as √(-1)
Q2. Find the square root of -16.
A: √(-16) = √(16) × √(-1) = 4i
Q3. Solve x² + 4 = 0
A: x² = -4 → x = ±2i
NCERT Solutions Class 11 Maths Chapter Chapter 6: Linear Inequalities
Q1. Solve: 3x – 5 < 7
A:
3x – 5 < 7
⇒ 3x < 12
⇒ x < 4
Q2. Solve and graph: x – 2 ≥ 0
A:
x ≥ 2
Graph: A number line with a solid dot at 2 and arrow towards right.
NCERT Solutions Class 11 Maths Chapter Chapter 7: Permutations and Combinations
Q1. How many 3-letter words can be formed from the letters A, B, C without repetition?
A:
P(3,3) = 3! = 6
Words: ABC, ACB, BAC, BCA, CAB, CBA
Q2. How many ways can 5 books be arranged on a shelf?
A: 5! = 120 ways
Q3. How many ways can we choose 2 students out of 5?
A: ⁵C₂ = 5! / (2!×3!) = 10 ways
NCERT Solutions Class 11 Maths Chapter Chapter 8: Binomial Theorem
Q1. State the Binomial Theorem for (x + y)ⁿ.
A:(x + y)ⁿ = Σ (nCr)(xⁿ⁻ʳ)(yʳ) for r = 0 to n
Q2. Find the middle term in (x + 1)⁴⁰.
A: Number of terms = 41 (odd), so middle term = 21st term
T₂₁ = ⁴⁰C₂₀·x²⁰
NCERT Solutions Class 11 Maths Chapter Chapter 9: Sequences and Series
Q1. What is the nth term of an AP with first term a and common difference d?
A:
Tₙ = a + (n - 1)d
Q2. Find the sum of first 10 terms of AP: 2, 4, 6, ...
A: a = 2, d = 2, n = 10
S₁₀ = n/2 [2a + (n - 1)d] = 10/2 [4 + 18] = 5 × 22 = 110
Q3. Find the 5th term of GP: 3, 6, 12,...
A: a = 3, r = 2
T₅ = ar⁴ = 3 × 16 = 48
NCERT Solutions Class 11 Maths Chapter Chapter 10: Straight Lines
Q1. What is the slope of the line 3x + 4y = 7?
A: Convert to y = mx + c → 4y = –3x + 7 ⇒ y = –3/4x + 7/4
So, slope m = –3/4
Q2. Find the distance between points (1,2) and (4,6).
A: Distance = √[(4–1)² + (6–2)²] = √[9 + 16] = √25 = 5
NCERT Solutions Class 11 Maths Chapter Chapter 11: Conic Sections
Q1. What is the standard equation of a circle with center (0, 0) and radius r?
A: x² + y² = r²
Q2. Write the equation of a parabola with vertex at origin and axis along x-axis.
A: y² = 4ax
Q3. Find the coordinates of the focus of y² = 8x.
A: Compare with y² = 4ax ⇒ 4a = 8 ⇒ a = 2
Focus = (2, 0)
NCERT Solutions Class 11 Maths Chapter Chapter 12: Introduction to Three-Dimensional Geometry
Q1. Find the distance between points A(1,2,3) and B(4,6,3).
A: Distance = √[(4–1)² + (6–2)² + (3–3)²] = √[9 + 16] = √25 = 5
Q2. Find the coordinates of the midpoint of line joining (2,3,4) and (4,5,6).
A: Midpoint = ((2+4)/2, (3+5)/2, (4+6)/2) = (3, 4, 5)
NCERT Solutions Class 11 Maths Chapter Chapter 13: Limits and Derivatives
Q1. Find limₓ→0 (sin x)/x
A: limₓ→0 (sin x)/x = 1
Q2. Differentiate f(x) = x²
A: f’(x) = d/dx (x²) = 2x
Q3. Find the derivative of f(x) = sin x
A: f’(x) = cos x
NCERT Solutions Class 11 Maths Chapter 14: Mathematical Reasoning
Q1. What is a statement in logic?
A: A statement is a sentence that is either true or false but not both.
Q2. What is the contrapositive of "If it rains, then I stay home"?
A: Contrapositive: If I don't stay home, then it doesn't rain.
NCERT Solutions Class 11 Maths Chapter 15: Statistics
Q1. Find the mean of: 2, 4, 6, 8, 10
A: Mean = (2+4+6+8+10)/5 = 30/5 = 6
Q2. What is the formula for variance?
A: Variance (σ²) = Σ(xᵢ – x̄)² / n
NCERT Solutions Class 11 Maths Chapter 16: Probability
Q1. What is the probability of getting a head when a coin is tossed?
A:Favourable outcomes = 1, Total outcomes = 2
P(Head) = 1/2
Q2. A die is rolled. What is the probability of getting an even number?
A: Even numbers = {2, 4, 6} → 3 outcomes
Total = 6
P(even) = 3/6 = 1/2
Regular practice is essential. You can practice these solutions alongside your regular studies to reinforce your understanding of concepts. Consistent practice can improve your problem-solving skills and boost your confidence in math.
While NCERT Solutions provide a strong foundation, competitive exams might require additional preparation. However, practicing these solutions can help you build a solid understanding of concepts that might be useful in competitive exams as well.
Yes, NCERT Solutions cover the entire syllabus outlined in the NCERT Class 11 Maths textbook. They provide solutions for all the exercises and problems given in the textbook, ensuring comprehensive coverage.
NCERT Solutions provide clear explanations and solutions to each problem, helping you grasp the concepts in a structured manner. They offer step-by-step guidance, making it easier to understand and solve complex math problems.
Chapter 11 of NCERT Solutions Class 11 Maths PDF revolves around significant concepts like parts of a cone, which covers topics such as parabola, ellipse, circle, degenerate conic sections, and hyperbola. Additionally, it delves into crucial subjects like the interplay between semi-minor axis, semi-major axis, the distance of the focus from the center of the ellipse, and standard equations of parabola and ellipse. This chapter holds particular importance in Class 11 as it explores fundamental conic section concepts that will continue to be relevant in higher classes.