NCERT Solutions for Class 11 Maths

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