ClearStepsCLEARSTEPS
NCERT Solutions›Class 11 Mathematics
📐

NCERT Solutions
Class 11 Mathematics

14 chapters · 76 important questions · Updated 2025-26

Ch 1

Sets

Introduces the concept of a set as a well-defined collection of objects. Students learn set representations (roster and set-builder form), types of sets, and operations such as union, intersection, difference, and complement. Venn diagrams are used to visualise relationships between sets. The chapter also covers De Morgan's laws and practical applications involving counting using the inclusion-exclusion principle.

Key Topics

Set representations: roster form and set-builder formTypes: empty set, finite/infinite sets, universal set, power setSubsets and proper subsets: A ⊆ B iff every element of A is in BSet operations: A ∪ B, A ∩ B, A − B, A′ (complement)De Morgan's laws: (A ∪ B)′ = A′ ∩ B′; (A ∩ B)′ = A′ ∪ B′Number of elements in power set P(A): n(P(A)) = 2ⁿ where n = n(A)Inclusion-exclusion principle: n(A ∪ B) = n(A) + n(B) − n(A ∩ B)Venn diagrams for visualising union, intersection, and difference

Important Questions

Q1

If A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8}, find A − B, B − A, and A △ B (symmetric difference).

Long Answer3M
Q2

In a survey of 600 students in a school, 150 students were found to drink Tea and 225 students to drink Coffee, while 100 students drink both Tea and Coffee. Find the number of students who drink neither Tea nor Coffee.

Long Answer3M
Q3

Let A = {x : x ∈ N, x ≤ 6} and B = {x : x ∈ N, 3 < x < 8}. Find A ∪ B, A ∩ B, and verify De Morgan's law.

Long Answer4M
Q4

If A and B are two sets such that A ∪ B has 18 elements, A has 8 elements and B has 15 elements, how many elements does A ∩ B have?

MCQ / 1 Mark1M
Q5

Write the following sets in roster form: (i) A = {x : x is a two-digit natural number such that the sum of its digits is 8} (ii) B = {x : x ∈ N, x² < 25}.

Short Answer2M
Ch 2

Relations and Functions

Builds on sets to define ordered pairs, Cartesian products, and relations. Students learn to distinguish between relations and functions, identify domain and range, and work with different types of functions (one-one, onto, into). The chapter also covers the algebra of real functions including sum, difference, product, and quotient.

Key Topics

Cartesian product: A × B = {(a, b) : a ∈ A, b ∈ B}n(A × B) = n(A) × n(B)Relation R from A to B: R ⊆ A × B; domain = set of first elementsFunction: every element of domain has exactly one imageTypes of functions: one-one (injective), onto (surjective), bijectiveAlgebra of functions: (f + g)(x) = f(x) + g(x); (fg)(x) = f(x)·g(x)Domain of f/g: {x : g(x) ≠ 0}; domain of √f: {x : f(x) ≥ 0}Range of a function: set of all actual output values

Important Questions

Q1

If f(x) = x² − 3x + 2, find f(1), f(−1), and f(1/2). Also find the values of x such that f(x) = 0.

Long Answer3M
Q2

Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x, y) : y = x + 1}. Write R, domain, and range of R.

Long Answer3M
Q3

Find the domain and range of the function f(x) = (x² − 4)/(x − 2).

Short Answer2M
Q4

If f and g are two real functions defined as f(x) = √(x + 1) and g(x) = 1/(x − 2), find (f + g)(x), (fg)(x), and their domains.

Long Answer4M
Q5

The function f is defined by f(x) = 1 − x for x < 0; 1 for x = 0; x + 1 for x > 0. Draw the graph of this function.

Long Answer3M
Ch 3

Trigonometric Functions

Extends trigonometric ratios to all real numbers via the unit circle, introducing radian measure and relationships between degree and radian. Students learn values of trigonometric functions for standard angles, fundamental identities, and formulas for compound, multiple, and sub-multiple angles. Finding the general solution of trigonometric equations is an important board exam skill.

Key Topics

Radian-degree conversion: 1 radian = 180°/π; arc length l = rθSigns of trig functions in all four quadrants (ASTC rule)Compound angle formulas: sin(A ± B), cos(A ± B), tan(A ± B)Double angle formulas: sin 2A = 2 sin A cos A; cos 2A = cos²A − sin²A = 1 − 2sin²AProduct-to-sum formulas: 2 sin A cos B = sin(A+B) + sin(A−B)General solutions: sin θ = sin α ⟹ θ = nπ + (−1)ⁿα; cos θ = cos α ⟹ θ = 2nπ ± αSine rule: a/sin A = b/sin B = c/sin C = 2RFundamental identities: sin²x + cos²x = 1; 1 + tan²x = sec²x; 1 + cot²x = cosec²x

Important Questions

Q1

Prove that: cos(π/4 + x) + cos(π/4 − x) = √2 cos x.

Long Answer3M
Q2

Find the general solution of: cos 4x = cos 2x.

Long Answer3M
Q3

Prove: (cos x − cos y)² + (sin x − sin y)² = 4 sin²((x − y)/2).

Long Answer3M
Q4

If tan x = 3/4 and x is in the third quadrant, find the values of sin x/2, cos x/2, and tan x/2.

Long Answer4M
Q5

Prove that: sin 20° sin 40° sin 80° = √3/8.

Long Answer4M
Q6

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

MCQ / 1 Mark1M
Ch 4

Complex Numbers and Quadratic Equations

Introduces complex numbers as numbers of the form a + ib where i = √(−1). Students learn algebraic operations on complex numbers, the modulus-argument (polar) form, and the Argand plane representation. The chapter culminates in the fundamental theorem of algebra — every polynomial equation has a root in C — and solving quadratic equations with complex roots using the discriminant.

Key Topics

Imaginary unit: i = √(−1); i² = −1; i³ = −i; i⁴ = 1; i⁴ⁿ = 1Complex number z = a + ib; Re(z) = a, Im(z) = bModulus: |z| = √(a² + b²); Argument: arg(z) = θ = tan⁻¹(b/a)Conjugate: z̄ = a − ib; |z|² = z · z̄Polar form: z = r(cos θ + i sin θ) where r = |z|Algebra: (a+ib)(c+id) = (ac−bd) + i(ad+bc)Division: z₁/z₂ = z₁ · z̄₂ / |z₂|²Quadratic with D < 0: x = (−b ± i√|D|) / 2a

Important Questions

Q1

Express (3 + 2i)(2 − 3i) in the form a + ib and find its modulus and argument.

Long Answer3M
Q2

Solve: x² + 3x + 5 = 0 over the complex number field.

Short Answer2M
Q3

If z₁ = 2 + 3i and z₂ = 1 − 2i, find z₁/z₂ in the form a + ib.

Long Answer3M
Q4

Find the modulus and argument of the complex number (1 + i)/(1 − i).

Long Answer3M
Q5

If (a + ib)² = x + iy, prove that (a² − b²)² + (2ab)² = (x² + y²).

Long Answer4M
Ch 5

Linear Inequalities

Covers one-variable and two-variable linear inequalities and their graphical solutions. Students learn rules for manipulating inequalities (sign reversal on multiplication/division by a negative number) and solve systems of linear inequalities to find the feasible region. Word problems involving inequalities from daily life are important for exams.

Key Topics

Properties of inequalities: if a > b and c < 0 then ac < bcSolution set of a linear inequality in one variable on the number lineIntersection and union of solution sets for a system of inequalitiesGraphical solution: half-plane representation of ax + by ≤ cFeasible region: intersection of half-planes for a system of inequalitiesSolving word problems using linear inequalities

Important Questions

Q1

Solve: 3x − 7 > 5x − 1 and represent the solution on a number line.

Short Answer2M
Q2

Solve the system of inequalities graphically: x + y ≤ 4, 2x − y > 0.

Long Answer4M
Q3

Solve: (x − 2)/(x + 5) > 2. Find the solution set and represent it on the number line.

Long Answer3M
Q4

A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added so that the resulting mixture will contain more than 15% but less than 18% acid?

Long Answer4M
Q5

Solve: −5 ≤ (5 − 3x)/2 ≤ 8.

Short Answer2M
Ch 6

Permutations and Combinations

Covers the fundamental counting principle and factorial notation, then builds up to permutations (arrangements) and combinations (selections). Students learn when to use nPr versus nCr and handle problems involving repetition, identical objects, and circular arrangements. This chapter is heavily tested in board and competitive exams.

Key Topics

Fundamental counting principle: m × n ways for two independent choicesFactorial: n! = n × (n−1) × ... × 1; 0! = 1Permutations: ⁿPᵣ = n! / (n−r)!Combinations: ⁿCᵣ = n! / (r!(n−r)!); ⁿCᵣ = ⁿCₙ₋ᵣPermutations with identical objects: n! / (p! q! r!)Circular permutations: (n−1)! arrangementsProperty: ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ (Pascal's identity)

Important Questions

Q1

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Long Answer3M
Q2

In how many ways can 6 people be seated at a round table? How many of these arrangements will have two specific people always together?

Long Answer3M
Q3

If ⁿC₈ = ⁿC₁₂, find ⁿC₁₇ and ²²Cₙ.

Short Answer2M
Q4

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

Long Answer3M
Q5

How many 4-letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

MCQ / 1 Mark1M
Q6

Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these, do all vowels always occur together?

Long Answer5M
Ch 7

Binomial Theorem

States and proves the Binomial Theorem for positive integral indices. Students learn to expand (a + b)ⁿ using the general term Tᵣ₊₁, find the middle term(s), and identify specific terms in binomial expansions. Properties of binomial coefficients, including Pascal's triangle and the sum of coefficients, are important exam topics.

Key Topics

Binomial Theorem: (a + b)ⁿ = Σ(r=0 to n) ⁿCᵣ aⁿ⁻ʳ bʳGeneral term: Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳMiddle term: T(n/2 + 1) for even n; T((n+1)/2) and T((n+3)/2) for odd nSum of all binomial coefficients: 2ⁿ (put a = b = 1)Pascal's triangle: each entry is sum of two entries aboveTerm independent of x: find r such that power of x = 0Greatest binomial coefficient: ⁿCₙ/₂ for even n

Important Questions

Q1

Find the 4th term from the end in the expansion of (x³/2 − 2/x²)⁹.

Long Answer3M
Q2

If the coefficients of (r − 5)th and (2r − 1)th terms in the expansion of (1 + x)³⁴ are equal, find r.

Long Answer3M
Q3

Using the Binomial Theorem, evaluate (101)⁴.

Long Answer3M
Q4

Find the term independent of x in the expansion of (√x − √(3/x²))¹⁰.

Long Answer3M
Q5

If the 21st and 22nd terms in the expansion of (1 + x)⁴⁴ are equal, find x.

Short Answer2M
Q6

Prove that Σ(r=0 to n) 3ʳ · ⁿCᵣ = 4ⁿ.

Long Answer3M
Ch 8

Sequences and Series

Covers arithmetic progressions (AP), geometric progressions (GP), and the special sums Σn, Σn², and Σn³. Students learn to find the nth term and sum of n terms of both AP and GP, including the sum of infinite GP when |r| < 1. Arithmetic-geometric mean inequality and insertion of means between two numbers are also tested.

Key Topics

AP: nth term aₙ = a + (n−1)d; sum Sₙ = n/2 [2a + (n−1)d]GP: nth term aₙ = arⁿ⁻¹; sum Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1Infinite GP sum: S∞ = a/(1 − r) when |r| < 1Arithmetic mean: AM = (a + b)/2; Geometric mean: GM = √(ab)AM ≥ GM for positive realsInsertion of n AMs: d = (b − a)/(n + 1)Insertion of n GMs: r = (b/a)^(1/(n+1))Special sums: Σn = n(n+1)/2; Σn² = n(n+1)(2n+1)/6; Σn³ = [n(n+1)/2]²

Important Questions

Q1

The sum of first three terms of a GP is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio, and the sum to n terms of the GP.

Long Answer4M
Q2

Find the sum to n terms of the series: 3 × 8 + 6 × 11 + 9 × 14 + ...

Long Answer4M
Q3

If A and G be respectively the AM and GM between two positive numbers, prove that the numbers are A ± √(A² − G²).

Long Answer4M
Q4

The sum of three numbers in GP is 56. If we subtract 1, 7, 21 from these numbers in that order, we get an AP. Find the numbers.

Long Answer4M
Q5

Find the 20th term and sum to 20 terms of the series 2 + 6 + 18 + 54 + ...

Short Answer2M
Q6

Evaluate: Σ(k=1 to 10) (2 + 3k).

Short Answer2M
Ch 9

Straight Lines

Provides a thorough treatment of lines in the Cartesian plane, covering slope, various forms of the equation of a line (slope-point, slope-intercept, two-point, intercept, and normal forms), distance of a point from a line, and the angle between two lines. Students also learn to find the family of lines passing through the intersection of two given lines.

Key Topics

Slope of a line: m = tan θ; m = (y₂ − y₁)/(x₂ − x₁)Condition for parallel lines: m₁ = m₂; perpendicular: m₁ × m₂ = −1Slope-intercept form: y = mx + cTwo-point form: (y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁)Normal form: x cos α + y sin α = pGeneral form Ax + By + C = 0; slope = −A/BDistance of point (x₁, y₁) from line Ax + By + C = 0: |Ax₁ + By₁ + C|/√(A² + B²)Distance between parallel lines Ax+By+C₁=0 and Ax+By+C₂=0: |C₁−C₂|/√(A²+B²)

Important Questions

Q1

Find the equation of the line passing through (−1, 1) and (2, −4). Find its x-intercept and y-intercept.

Long Answer3M
Q2

Find the distance of the point (3, −5) from the line 3x − 4y − 26 = 0.

Short Answer2M
Q3

Find the equation of the line which is equidistant from parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0.

Long Answer4M
Q4

Prove that the three lines 3x + y + 2 = 0, 2x − y + 3 = 0, and x + 2y − 3 = 0 form a triangle. Also find the area of the triangle.

Long Answer5M
Q5

Find the angles between the lines y = (2 − √3)x + 5 and y = (2 + √3)x − 7.

Long Answer3M
Ch 10

Conic Sections

Introduces the four conic sections — circle, parabola, ellipse, and hyperbola — as intersections of a plane with a double-napped cone. Students derive and apply standard equations for each conic, identify key parameters (centre, radius, foci, vertices, eccentricity, latus rectum), and solve problems involving equations of conics given geometric conditions.

Key Topics

Circle: (x − h)² + (y − k)² = r²; general equation x² + y² + 2gx + 2fy + c = 0Parabola: y² = 4ax (focus: (a,0), directrix: x = −a, latus rectum: 4a)Ellipse: x²/a² + y²/b² = 1 (a > b > 0); b² = a²(1 − e²); sum of focal radii = 2aEllipse: foci: (±ae, 0); vertices: (±a, 0); latus rectum: 2b²/aHyperbola: x²/a² − y²/b² = 1; b² = a²(e² − 1); e > 1; asymptotes: y = ±(b/a)xEccentricity e: circle e = 0; parabola e = 1; ellipse 0 < e < 1; hyperbola e > 1Focal chord: chord passing through the focusStandard equations for horizontal and vertical conics

Important Questions

Q1

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

Long Answer4M
Q2

Find the coordinates of the foci, vertices, eccentricity, and length of latus rectum of the ellipse x²/25 + y²/9 = 1.

Long Answer4M
Q3

Find the equation of the parabola with focus (2, 0) and directrix x = −2.

Short Answer2M
Q4

Find the equation of the hyperbola with foci at (±5, 0) and the length of the transverse axis = 8.

Long Answer3M
Q5

Find the equation of the ellipse whose foci are (±4, 0) and the sum of distances from a point on the ellipse to the two foci is 10.

Long Answer4M
Q6

Find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the endpoints of the latus rectum.

Long Answer3M
Ch 11

Introduction to Three-Dimensional Geometry

Extends coordinate geometry to three dimensions, introducing the three coordinate axes, octants, and three-dimensional coordinates. Students learn to calculate the distance between two points in 3D and apply the section formula to find coordinates of a point dividing a line segment in a given ratio. The midpoint formula is a special case of the section formula.

Key Topics

3D coordinate system: x, y, z axes; eight octantsDistance formula: PQ = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]Section formula (internal): P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n))Midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)Centroid of a triangle: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3, (z₁+z₂+z₃)/3)Section formula (external): m:n externally — use (mx₂−nx₁)/(m−n)

Important Questions

Q1

Find the distance between the points (2, −1, 3) and (−2, 1, 3).

MCQ / 1 Mark1M
Q2

Show that the points (−2, 3, 5), (1, 2, 3), and (7, 0, −1) are collinear.

Long Answer3M
Q3

Find the coordinates of the point which divides the join of (−2, 3, 5) and (1, −4, 6) in the ratio 2:3 internally.

Long Answer3M
Q4

Find the centroid of a triangle whose vertices are (1, 1, 1), (0, −1, 0), and (2, 1, −1).

Short Answer2M
Q5

The mid-point of a segment joining A(a, b, c) and B is (4, −1, 2). If B = (6, −7, 4), find A.

Short Answer2M
Ch 12

Limits and Derivatives

Introduces the concept of a limit intuitively and develops the algebra of limits (sum, product, quotient rules). Students evaluate standard limits including lim(x→0) sin x/x = 1 and lim(x→a) (xⁿ − aⁿ)/(x − a) = naⁿ⁻¹. The derivative is defined as the first principle (limit of the difference quotient), and differentiation rules (product rule, quotient rule) are developed.

Key Topics

Limit: lim(x→a) f(x); left-hand limit, right-hand limit; existence condition: LHL = RHLAlgebra of limits: lim(fg) = lim f · lim g; lim(f/g) = lim f/lim g (g ≠ 0)Standard limit: lim(x→0) sin x / x = 1; lim(x→0) tan x / x = 1Standard limit: lim(x→a) (xⁿ − aⁿ)/(x − a) = naⁿ⁻¹Derivative from first principles: f′(x) = lim(h→0) [f(x+h) − f(x)] / hStandard derivatives: d/dx(xⁿ) = nxⁿ⁻¹; d/dx(sin x) = cos x; d/dx(cos x) = −sin xProduct rule: (uv)′ = u′v + uv′; Quotient rule: (u/v)′ = (u′v − uv′)/v²Derivatives of tan x, cot x, sec x, cosec x using quotient rule

Important Questions

Q1

Evaluate: lim(x→3) (x⁴ − 81)/(2x² − 5x − 3).

Long Answer3M
Q2

Find the derivative of f(x) = sin x from first principles.

Long Answer4M
Q3

Evaluate: lim(x→0) (sin 2x + sin 3x) / (2x + sin 3x).

Long Answer3M
Q4

Find the derivative of (x² + 5x + 3)(x³ − 7x + 1) using the product rule.

Long Answer3M
Q5

Evaluate: lim(x→π/2) (tan 2x) / (x − π/2).

Short Answer2M
Q6

Find the derivative of (5x³ + 3x − 1)(x − 1) and hence find the slope of the tangent at x = 1.

Long Answer4M
Ch 13

Statistics

Extends the study of statistics to measures of dispersion — range, mean deviation, variance, and standard deviation — for both ungrouped and grouped data. Students learn to calculate mean deviation about the mean and median, and standard deviation using the direct and assumed mean methods. Coefficient of variation is used to compare variability of two series.

Key Topics

Range = Maximum value − Minimum valueMean Deviation (MD) about mean: MD = Σ|xᵢ − x̄| / n (ungrouped)Mean Deviation for grouped data: MD = Σfᵢ|xᵢ − x̄| / ΣfᵢVariance: σ² = Σ(xᵢ − x̄)² / n; Standard Deviation: σ = √(Σ(xᵢ − x̄)²/n)Shortcut for variance: σ² = (Σxᵢ²)/n − (x̄)²Coefficient of Variation (CV) = (σ/x̄) × 100; lower CV ⟹ more consistentVariance of grouped data: σ² = (1/N) Σfᵢ(xᵢ − x̄)²

Important Questions

Q1

Find the mean deviation about the mean for the data: 4, 7, 8, 9, 10, 12, 13, 17.

Long Answer3M
Q2

Find the mean, variance, and standard deviation for the following data: 6, 7, 10, 12, 13, 4, 8, 12.

Long Answer4M
Q3

The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect, the correct value is 12. Find the correct mean and standard deviation.

Long Answer5M
Q4

Calculate the coefficient of variation for scores in Mathematics (mean = 57.5, SD = 1.5) and Statistics (mean = 31.2, SD = 0.6). Which subject shows greater variability?

Long Answer4M
Q5

Find the standard deviation for the following frequency distribution: class 0-10 (f = 5), 10-20 (f = 8), 20-30 (f = 15), 30-40 (f = 16), 40-50 (f = 6).

Long Answer5M
Ch 14

Probability

Introduces the axiomatic approach to probability alongside the classical definition. Students learn sample space, events, algebra of events (complementary, mutually exclusive, exhaustive), and basic laws including the addition rule. The chapter contrasts empirical (experimental) probability with theoretical (classical) probability and applies them to dice, cards, and general sample spaces.

Key Topics

Sample space S and events as subsets of SAxiomatic definition: 0 ≤ P(A) ≤ 1; P(S) = 1; P(A ∪ B) = P(A) + P(B) for mutually exclusive eventsClassical probability: P(A) = n(A)/n(S)Complementary event: P(A′) = 1 − P(A)Addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)Mutually exclusive events: P(A ∩ B) = 0 ⟹ P(A ∪ B) = P(A) + P(B)Exhaustive events: P(A₁ ∪ A₂ ∪ ... ∪ Aₙ) = 1

⚠️ Deleted from Syllabus 2025-26

  • — Principle of Mathematical Induction (separate chapter removed from 2025-26 board exam syllabus)
  • — Mathematical Reasoning (entire chapter removed from 2025-26 board exam syllabus)

Important Questions

Q1

A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random. Find the probability that it is (i) red (ii) yellow (iii) blue (iv) not blue.

Long Answer4M
Q2

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify is 0.05 and Ashima will qualify is 0.10. The probability that both will qualify is 0.02. Find the probability that (a) both will not qualify (b) at least one of them will qualify.

Long Answer4M
Q3

In a class of 60 students, 30 opted for NCC, 32 opted for NSS, and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that the student opted for NCC or NSS.

Long Answer3M
Q4

Three coins are tossed simultaneously. Write the sample space and find the probability of getting (i) exactly two heads (ii) at most two heads.

Long Answer4M
Q5

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a king or a heart.

Short Answer2M

Frequently Asked Questions

Is NCERT enough for CBSE Class 11 Mathematics board exam?

Yes. CBSE board exams are designed entirely around NCERT. 80–90% of questions in the Class 11 Mathematics paper are directly based on NCERT concepts — sometimes reworded, never from outside NCERT. Completing all 76 important questions listed here is the minimum you need.

How to study NCERT Class 11 Mathematics for board exams?

Go chapter-by-chapter. Read the chapter first, then attempt the important questions without looking at answers. Check your answer structure — CBSE gives marks per point, so structure matters as much as content. For 5-mark answers: brief intro + 4–5 numbered points with keywords + conclusion.

Which chapters are most important in Class 11 Mathematics for CBSE boards?

Chapters with the most long-answer (5-mark) important questions carry the most marks in the board paper. Look at which chapters here have the highest question count — those are the ones CBSE has historically focused on. Don't skip any chapter, but spend extra time on these.

How many questions come from NCERT in CBSE Class 11 Mathematics exam?

Nearly all 76 questions in the Class 11 Mathematics board paper are rooted in NCERT. The exact question may be reworded, but the concept, definition, or formula always comes from the NCERT textbook. Practicing these 76 important questions covers the vast majority of what can be asked.

Complete Study Pack — Class 11 Mathematics

Chapter Summaries →Important Questions →Sample Papers 2025-26 →Previous Year Papers →Revision Checklist →Topper Answer Sheets →