IIT JEE Mathematics for Class XI
Subject Medium Mathematics ENGLISH Renu Mam AVAILABLE COMPLETE COURSE 221 XI XII XIII QUESTION BANK ATTACHED You May Pay in Installments through Credit Card
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Syllabus

### Mathematics Topic List

#### Set Relation

 Lecture# Description Duration 1 Definition of set, Methods to represent sets : (1) Roster form or tabular method (2) Set builder (Property method), Inter-conversion of Roster form into set builder form or vice-versa; Types of sets: (1) Null Set (2) Singleton set (3) Finite set & Cardinal number of set (4) Equivalent sets. (5) Equal sets 34 Minutes 02 Subsets, Proper subset, Total number of subsets, Idea of intervals: (1) Close interval (2) Open-interval (3) Discrete interval or curly bracket, Operation on sets (By venn-diagram) (1) Union of 2 sets (2) Intersection of 2 sets (3) Set A and its complement 43 Minutes 03 (4) Set A but not B (5) Set B but not A (6) Neither A nor B #Demorgan’s Law (7) Atleast one set out of three sets A, B, C (8) Atleast 2 sets out of 3 sets (9) Exact 2 sets out of 3 sets (10) Exact 1 set out of 3 sets (11) Neither A, B nor C. Laws of Algebra of sets 44 Minutes 04 Cartesian Product ordered pair, ordered triplets, Cartesian Product of 2 sets or 3 sets, Introduction of Relations 52 Minutes 05 Relations, Total number of relations, types of relations: (1) Void relation (2) Universal Relation (3) Identity Relation (4) Reflexive Relation (5) Symmetric Relation (6) Transitive Relation (7) Equivalence Relation 1 Hrs 02 Minutes 06 Definition of function, Its domain and co-domain and range. 43 Minutes

#### Fundamentals of Mathematics

 Lecture# Description Duration 01 Number systems: (1) Natural numbers (2) Whole numbers (W) (3) Integers (I or Z) (4) Prime Numbers (5) Composite numbers (6) Co-prime numbers (Relatively prime numbers) (7) Twin-prime numbers (8) Rational numbers : (a) Terminating rational numbers (b) Repeating rational numbers (9) Irrational numbers (Q’ or Qc) (10) Real numbers (R) (11) Complex numbers (C or Z) Algebra of complex numbers, converting into a + ib (i = √-1) form, square root of a complex number. 1 Hrs 24 Minutes 02 Basics of Mathematics - About the concept helpful to solve inequalities, Domain of a function, About the functions - (1) Rational functions (2) Irrational functions (3) Polynomial functions 58 Minutes 03 Some important identities, Factor or remainder theorems, Cramer’s method to solve linear equations in two variables, Ratios and Proportion, Squaring in case of inequalities. 53 Minutes 04 When we cross multiply the denominator incase of inequalities? Rational (Polynomial) Inequalities - Steps to solving inequalities (For Non-repeated and repeated linear factors), Questions 54 Minutes 05 Questions of Rational inequalities containing repeated linear factors, Modulus functions (Absolute - Value functions) , Domain, Range and Graphs of basic modulus functions, Removal of modulus functions, Properties of Modulus functions, Equations based on |x| = a (a≥0) 55 Minutes 06 Defining modulus functions, Removal of modulus, Basic Graphs and Graphs of combination of Modulus functions, Modulus equations. a-14 Min., b-51 Min. 07 Modulus inequalities. 1 Hrs 08 Questions of Modulus - inequalities. 56 Minutes 09 (a) Irrational function - domain, Range and Graph of y = √x , Irrational equations. (b) Irrational Inequalities. 1 Hrs 02 Minutes 10 Exponential and Logarithmic functions, domain-range and graph of basic exponential & log functions, Properties formulae, Simplification of log functions. 53 Minutes 11 Basic questions to simplify the Log functions, Log-equations. a-35 Min., b-19 Min. 12 Logarithmic and Exponential equations. 46 Minutes 13 Exponential and Log inequalities. 41 Minutes 14 Log-inequalities when base is variable, Domain of functions including irrational or log functions. a-33 Min., b-48 Min. 15 Greatest integer function (GIF), Domain-Range and basic graph of GIF, Properties, Fractional-part function (FPF), Domain-Range and Basic Graph, Properties, Signum function, Domain-Range and Graph. 1 Hrs 01 Minutes 16 Questions based on GIF, FPF and Signum function. a-39 Min., b-32 Min.

 Lecture# Description Duration 01 Polynomial functions, Roots (zeros), Solutions, Equation vs Identity, Questions, Methods of finding roots (i) Factorisation 1 hrs 08 Minutes 02 Methods of finding roots- (ii) Transformation method. (iii) Dharacharya Method (Perfect square), Questions. 1 hrs 07 Minutes 03 Questions based on finding roots. 1 Hrs 02 Minutes 04 Nature of roots : in ax2 + bx + c = 0 (a≠0) (1) When a, b, c, ∈ R (2) When a, b, c, ∈ Q (3) When a = 1, b, c, ∈ I and D is Perfect square of integer (4) when a, b, c ∉ R (5) when D1 + D2 ≥ 0 (in a1x2 + b1x+ c1 = 0 and a2x2 + b2x+ c2 = 0 where D1 = b12 –4a1c1 and D2 = b2 –4a2c2) (6) Intermediate Mean Value Theorem (IMVT) Questions based on nature of roots. 1 Hrs 03 Minutes 05 Plotting of quadratic expression (Graph) when a > 0 or a < 0 in y = ax2 + bx + c (a≠0), Range of y = ax2 + bx + c when x ∈ R Sign of a, b, c, D, Range in an interval x ∈[x1, x2], Questions. 1 Hrs 11 Minutes 06 Sign of quadratic expression, Range of y =L/Q , y Q/ Q 1 hrs 10 Minutes 07 Range by substitution, condition of common roots- (1) when 1 root common (2) when both the roots are common Location of roots- (1) When both the roots are greater than k (k∈R) (2) When both the roots are less than k (3) When 1 root < k and other root > k (4) When both the roots lies in interval (k1, k2) (5) When only 1 root lies in (k1, k2) 1 Hrs 27 Minutes 08 Questions based on location of Roots, Pseudo-Quadratic equation, Questions based on it. 1 Hrs  26 Minutes

#### Sequence and Series

 Lecture# Description Duration 01 Arithmetic progression (AP), Standard terms, General term or last term (tn or 𝓁) of AP, Condition for 3 terms in AP, Arithmetic mean (AM) of n numbers, Middle terms, Sum of First n terms (sn) of AP, Properties of AP, n Arithmetic means inserted between 2 numbers, sum of n Arithmetic mean inserted between two numbers, Properties of AP. 45 Minutes 02 Questions based on Arithmetic progression and their properties. 1 Hrs 07 Minutes 03 Summation series based on AP, Geometric progression (GP), Standard terms, General term of GP, Sum of first n terms of GP, Sum of ∞ terms of GP, supposition of terms in GP, n Geometric means between 2 positive numbers, Properties of GP. 1 Hrs 09 Minutes 04 Questions based on GP and their properties. 41 Minutes 05 Summation Series based on G.P., Harmonic Progression (HP), General term of Harmonic Progression, Harmonic Means of n numbers, Questions based on Harmonic Progression. 59 Minutes 06 Relation between AM, GM, HM, Solving inequalities based on AM ≥ GM ≥ HM. Arithmetic Geometric Progression (AGP), General Term, Sum of first n terms of AGP, Sum of ∞ numbers of terms in AGP, Summation series of AGP. a- 43 Min., b-42 Min. 07 (a) Summation of series based on product of terms in GP but with non-AP; Summation of series, i.e.              n                                                                             n      n      n        n       Sn = ∑tr,  (Vn - Vn-1 )method, Evaluating the value of  ∑1,  ∑r,  ∑r2,  ∑r3,              r=1                                                                         r=1    r=1   r=1    r=1 (b) Method of differences (1) First difference in AP. (2) Second difference in AP (3) First difference in GP. (4) Second difference in GP; Questions Based on method of differences. a-37 Min., b-35 Min. 08 Miscellaneous Series 1 Hrs 09 Miscellaneous Series 34 Minutes

#### Trigonometry

 Lecture# Description Duration 01 Basic Trigonometric Ratios (T-Ratios), and Identities, Questions based on Basic Trigonometry identities, elimination of angle θ. 57 Minutes 02 Trigonometry Ratios of allied angles, General solutions on coordinate axes, values of Trigonometry Ratios in [0, 90°],Questions based on allied angles, Graph of Trigonometry ratios, their domain-range and fundamental period. 1 Hrs 17 Minutes 03 Compound angles of trigonometry ratios, transformation formulae, values of trigonometry ratios at 15°(π÷12),75°(5π÷12), Questions a-35 Min., b-42 Min. 04 Multiple and sub-multiple angles, Values of Trigonometry Ratios at θ = π÷8, θ = π÷24 θ = 52*10÷2, θ = 142*10÷2, value of sin 180 (180 = π÷10), cos360(360 = π÷5), Questions. a-53 Min., b-38 Min. 05 Questions based on multiple and sub-multiple angles. 60 Minutes 06 Questions. Conversion of sin5A in terms of sinA and Conversion of cos5A in terms of cosA. a-32 Min., b-32 Min. 07 Conditional identities and Range of Trigonometric functions. a-25 Min., b-34 Min. 08 Range by using concept of differentiation . a-40 Min., b-19 Min. 09 Trigonometric series- (1) Cosine product series, (2) (A) Cosine summation series (B) Sine summation series Questions, Trigonometric Equations, General solutions on coordinate axes, General solution of sinθ = sin α, cosθ = cos α, tanθ = tan α.and sin2 θ = sin2 α cos2 θ = cos2 α tan2 θ = tan2 α a-29 Min., b-38 Min. 10 Basic Trigonometric equations directly formula based. a-24 Min., b-27 Min. 11 Trigonometric equations based on trigonometric identities, Questions based on Boundary values, solving simultaneous trigonometric equations. a-33 Min., b-25 Min. 12 Advanced Level Trigonometric equations. a-34 Min., b-38 Min. 13 Advanced Level Trigonometric equations, Trigonometric-Inequalities. a-25 Min., b-41 Min. 14 Domain of trigonometric functions. 40 Minutes

#### Solutions of triangles

 Lecture# Description Duration 01 About the triangle, (1) Sine rule (2) Area of ΔABC. (3) Napier’s analogy (Law’s of tangent) (4) Cosine-formula (5) Projection formula (6) T-Ratios of half- angles, Questions 43 Minutes 02 Questions a-53 Min. 03 Questions, m-n rule, circles connected to a triangle- (1) Circumcircle (2) Incircle (3) Ex-circles (4) Centroid (5) orthocentre (6) Circum-centre. a-31 Min., b-40 Min., c-34 Min. 04 (1) Length of angle Bisectors. (2) Length of Medians. (3) Length of altitudes, Distances of special points from vertices (A, B, C) and sides (AB, AC, BC) (1) Circumcentre (O), (2) Incentre (I) (3) Centroid (G) (4) Excentres (I1, I2, I3) Questions. 49 Minutes 05 Questions a-32 Min., b-22 Min. 06 Questions, Pedal-triangle (ΔLMN), its all parameters. a-44 Min., b-34 Min. 07 Ex-central-triangle (ΔI1 I2 I3), its all parameters, Distance between two special points- (1) Distance between circumcentre (o) & orthocentre (H), (2) Distance between circumcentre (0) and Incentre (I) (3) Distance between circumcentre and excentres (I1, I2, I3) (4) Distance between orthocentre (H) and Incentre (I) (5) Distance between centroid (G) and circumcentre (o) a-35 Min., b- Min.

#### Binomial theorem

 Lecture# Description Duration 01 About factorial n (n!,⌊n ), Domain-Range and Properties of factorial n. About nCr, nPr, formulae based on n! , nCr and nPr, Binomial expansion (for n ∈ N), Pascal-Triangle, General term, mth term from ending, middle term (for n odd, n even), Questions based on Binomial expansion and determining terms in Binomial expansion. a-50 Min., b-20 Min. 02 Questions based to determine middle term in Binomial expansion, Questions based to determine coefficient of xr in Binomial expansion, Questions based to determine the term independent of x. a-36 Min., b-31 Min. 03 Questions based on determining coefficient in product of 2 Binomial expansions, Multinomial theorem. a-25 Min., b-39 Min. 04 Coefficient determining by concept of permutation and combination and by using multinomial theorem; total number of terms in multinomial expansion; Number of terms free from fractional or irrational powers in Binomial expansion. a-34 Min., b-28 Min. 05 Numerically-Greatest term in the expansion of (x + a)n (n ∈ N), Algebraically - Greatest and least term in the expansion of (x + a)n (n ∈ N); Questions based on Ι + ƒ . a-31 Min., b-35 Min. 06 Questions based on Ι + ƒ , exponent of prime number (p) in ⌊n ; Questions based on divisibility and remainder, Last digit by cyclicity, Last digit, Last two digits, Last 3 digits in a number. a-29 Min., b-43 Min. 07 Summation of series. a-42 Min., b-33 Min. 08 Questions based on Sigma, Summation of Binomial Coefficients taken two at a time, Summation when upper index is variable. a-47 Min., b-35 Min. 09 Questions based on summation of Binomial coefficients taken two at a time when upper index is variable. 32 Minutes 10 Double-Sigma, Binomial expansion for negative or fractional power, Some-important expansions, Questions based on determining Coefficient in negative or fractional power in Binomial expansion. a-43 Min., b-34 Min.

#### Straight lines

 Lecture# Description Duration 01 Point, Rectangular - Cartesian Coordinate system, Parametric and Polar Coordinates of a point, distance between 2 points, section formula, Harmonic conjugate, Questions, About the Quadrilateral, Area of triangle, Condition of collinearity of three points, Concurrent lines, condition of concurrency of three lines. a-44 Min., b-38 Min. 02 Area of quadrilateral, Area of n sided polygon. 29 Minutes 03 Special points of triangle : (1) Centroid (G) (2) Incentre (I) (3) Excentres (I1, I2, I3) (4) Orthocentre (H) (5) Circum-centre(o) Types of straight lines- (1) General equation (2) Slope - intercept form (3) (a) Equation of a line parallel to x-axis. (b) Equation of line perpendicular to x-axis. (c) Equation of line coincident to x-axis. (d) Equation of line coincident to y-axis. (e) Equation of coordinates axes. (4) Slope point form (5) Two points form (6) Determinant form (7) Intercept form (8) Normal or Perpendicular form. Angle between two lines, condition of two lines to be parallel or perpendicular. a-43 Min., b-46 Min. 04 Condition of lines to be intersecting, Parallel, Coincident, Measurement of interior angle of Δ, Questions based on point, special points and types of lines. a-41 Min., b-49 Min. 05 Questions based on special points and types of lines. a-45 Min., b-37 Min. 06 Equations of lines passing through P(x1, y1) and making an angle α with the line y = mx + C, slope of a line equally inclined to the two given lines, Questions. Parametric or distance form of a line. a-35 Min., b-49 Min. 07 Perpendicular distance, foot of perpendicular, foot of perpendicular, image of a point (x1, y1) w.r.t. line ax + by + c = 0, distance between two parallel lines, Area of parallelogram, About the parallelogram, positions of two points w.r.t. line/plotting of linear-inequations, condition that a point lies inside of a triangle. a-48 Min., b-37 Min. 08 Questions based on perpendicular distance, foot of perpendicular and image. a-45 Min., b-34 Min. 09 Locus, Steps how to evaluate locus of a point, questions, angle bisectors, types of angles bisectors, how to identify type of angle bisector, angle bisectors containing a point P(x1, y1). a-43 Min., b-51 Min. 10 Questions based on angle-bisectors, family of lines (concurrent lines), Questions based on family of lines. a-47 Min., b-24 Min. 11 Pair of lines (combined or joint equations), Non-homogenous equation of second degree, homogeneous equation of second degree, angle between pair of lines, separate equations from second degree, condition that second degree non-homogenous equations represents pair of lines, point of intersection of pair of lines, combined equations of angles bisectors of pair of lines. a-39 Min., b-34 Min. 12 Questions, distance between two parallel pairs of lines, Homogenisation. a-39 Min., b-20 Min.

#### Circle

 Lecture# Description Duration 01 Definition of Circle, Types of Circles- (1) Centre - Radius form (2) General equation : Equation of Circle passing through 3 non-collinear points. 39 Minutes 02 Basic questions on circle, types of circles : (3) Diameter form (4) Standard equation of circle (5) Parametric Form (6) Point - Circle, Intercepts formed by circle on coordinate axes, position of points w.r.t. circle, Some Important notes related to Circle, Different-2 positions of circles, Questions. a- 60 Min., b- 25 Min. 03 Questions a-40 Min., b-25 Min. 04 Position of Line w.r.t. Circle, Length of chord Intercepted by the circle on, Tangent, Types of tangent- (1) Slope - Form, (2) Point - Form, Normal of Circle (3) Parametric - Form (4) Equation of tangent to the curve at (0, 0), number of tangents to the circle, Questions, Application of tangents - (1) Length of tangents (2) Power of points P(x1, y1) w.r.t. circle (3) Area of quadrilateral PACB (4) Angle between two tangents (5) Chord of contact (6) Equation of chord whose mid point is given (7) Director circle (8) Separate equations of tangents (9) Combined equations or pair of tangents (10) Equation of circle circumscribing the ΔPAB (11) PA.PB = PC. PD = PT2 (12) OA.OB = OC.OD (13) Area of triangle formed by pair of tangents with their chord of contact, Questions a-45 Min., b-45 Min., c-37 Min 05 Questions a-38 Min., b-32 Min. 06 Questions, Position of 2 circles and their common tangents- (1) When 2 circles are separated of each other, length of external and internal common tangent (2) When two circles touches externally (3) When two circles intersect at two real and distinct points, common chord of two circles, equation of common chord and its length, maximum length of common chord, angle of intersection of 2 circles, orthogonal circles and condition of orthogonality, (4) When two circles touches internally (5) When one circle lies completely inside of other, Questions. a-58 Min., b-38 Min. 07 Questions, Family of Circles- (1) Equations of family of circles passing through the point of intersection of circles, s = 0 and line L = 0 (2) Equation of family of circles passes through 2 points A & B. (3) Equation of family of circles passes through point of intersection of 2 circles. (4) Equation of family of circles touching a curve at a point, Questions a-44 Min., b-30 Min. 08 Questions, Radical axis/Radical centre, Equation of circle cuts three given circles orthogonally, pole and polar. a-30 Min., b-32 Min.

#### Conic sections

 Lecture# Description Duration 01 Introduction of Conic Section, Definition of Conic-Section, General equation of conic section, Locus of a moving point P will be conic when focus(s) lies on directrix and does not lies on directrix, Questions, some definitions related to conic -section (1) Focus (2) Directrix (3) Axis (4) Vertex (5) Centre (6) Focal- chord (7) Double- ordinate (8) Latus-Rectum (LR) Standard parabola - Its all parameters, two questions. a-36 Min., b-32 Min., c-25 Min. 02 Questions based on parameters of parabola, position of point w.r.t. parabola, Questions. a-25 Min., b-27 Min., c-25 Min. 03 (1) Parametric equation of a chord (2) Length of parametric chord (3) Focal chord (4) Minimum length of focal chord (5) Focal distance (6) 𝓁 (LR) = 2 (HM of 𝓁1 & 𝓁2), where 𝓁1 = PS, 𝓁2 = QS and P & Q are 2 moving points on parabola, S = focus, (7) (a) If focal chord of parabola makes ∠angle with its axis then 𝓁(LR) = 4a cosec2 α. (b) Length of focal chord at a distance p from vertex is  4a3÷p2 (8) If P1Q1 and P2Q2 are two focal chords of parabola y2 = 4ax then chords P1P2 & Q1Q2 intersect on its directrix. (9) If P1P2 and Q1Q2 are two focal chord of parabola are at right angle then area of quadrilateral P1Q1 and P2Q2 is minimum when chords are inclined at an angle π/4 to the axis and its minimum area is 32a2. (10) The circle described on any focal chord of parabola as diameter touches its directrix. (11) A line having slope (m) passes through focus(s) cuts the parabola at two real & distinct points if m ∈ R-{0}, Questions a-27 Min., b-33 Min. 04 Questions, Position of line w.r.t. Parabola, Condition of tangency Types of tangent - (1) Point form (2) Parametric form Questions based on tangents. a-31 Min., b-40 Min., c-23 Min. 05 Questions based on tangents, common tangents of two curves, Properties of tangents : P1, P2, P3, P4 a-40 Min., b-40 Min. 06 Properties of tangents: P5, P6, P7, P8 Questions based on Properties of tangents, Normal, Types- (1) Point form (2) Parametric form (3) Slope- form, condition of normality, Questions based on normals, properties of normal, P1, P2, P3 (a, b, c, d), P4, P5 . a-32 Min., b-29 Min., c-28 Min. 07 Properties of Normal- P6 , P7 (a, b), P8, P9- Reflection property, P10, P11 (a, b, c) P-11- Condition of three real & distinct normal to parabola, Questions based on normal and its properties, (1) Number of tangents to a parabola, (2) Pair of tangents (3) Director - Circle (4) Chord of contact (5) Chord whose mid point is given, Questions a-38 Min., b-20 Min., c-42 Min., d-34 Min. 08 Introduction of ellipse and hyperbola, standard ellipse (when a > b and a < b) and standard hyperbola and conjugate hyperbola, its basic parameters, auxiliary - Circle/Parametric coordinates of ellipse and hyperbola, Alternate definition of ellipse and hyperbola, Some important notes, Questions determining the basic parameters of ellipse and hyperbola. a-38 Min., b-31 Min., c-30 Min., d-25 Min. 09 Basic questions on ellipse and hyperbola, Questions based on Locus, Questions based on Parametric coordinates. a-36 Min., b-34 Min., c-32 Min., d-18 Min. 10 Parametric equation of chord of ellipse and hyperbola, questions on parametric chord, position of line w.r.t. ellipse Hyperbola, Condition of tangency, types of tangent- (1) Slope form (2) Point form (3) Parametric Form, Properties of tangents, Questions based on tangents. a- 38 Min., b-47 Min. 11 Questions based on tangents and its properties, Pair of tangents, Equation of chord of contact, Equation of chord whose mid point is given #Director Circle, Questions, Normal of ellipse and Hyperbola, Types- (1) Point Form (2) Parametric Form (3) Slope Form. a-43 Min., b-39 Min., c-14 Min. 12 Questions based on normal of ellipse Hyperbola, Reflection Property of ellipse - Hyperbola, Asymptotes of Hyperbola and conjugate Hyperbola, Properties of Asymptotes, Questions. a-26 Min., b-44 Min., c-34 Min. 13 Rectangular (Equilateral) Hyperbola, Rectangular Hyperbola considered coordinate axes as its asymptotes, its all parameters, tangents and normals, Questions. a-32 Min., b-31 Min.

#### Permutations and combinations

 Lecture# Description Duration 01 Introduction of factorial n ( ⌊n or n!) , nCr, nPr, Physical interpretation of n!, nCr, nPr. 19 Minutes 02 Fundamental - Principles of counting (i) Multiplication - Rule (ii) Addition- Rule Basic Questions based on multiplication and addition-Rule; Sample-space. a-51 Min., b-49 Min. 03 Questions, Number Problems. a-40 Min., b-35 Min. 04 Number problems based on divisible by 3, 4, 5, 25, Theorem-1: Selection and Permutation of r things out of n. Theorem-2 : Permutation of n things in which some things are of same kind. a-46 Min., b-28 Min. 05 Questions considering the word “RAKESH MODI” Questions, problem of forming words of 7 letters taking 3 vowels and 4 consonants using letters of word : “DIFFERENTIATION”. Problem of forming the words each consisting 3 consonants and 3 vowels by using letters of words “CIRCUMFERENCE”. a-42 Min., b-25 Min., c-35 Min. 06 Rank (Position) of a word or numbers, sum of the numbers formed (No repetition or when repetition allowed), Circular Permutation. a-35 Min., b-33 Min., C-35 Min. 07 Number of selection of r consecutive things out of n distinct things, Geometrical Problems Number of total lines, number of diagonals, number of triangles (a) One side common with given polygon (b) Two sides common with given polygon (c) Three sides common with given polygon. (d) None of the side common with given polygon. Chess board problems - Number of total rectangles, Number of total squares. Problem based on moving from left bottom corner to the right top corner in a chess board. a-48 Min., b-57 Min. 08 Groupings & distribution of n differents things into groups or bundles. a-30 Min., b-29 Min., c-27 Min. 09 Selection of none, one or more things when given things are different or identical, Total number of divisors, Total number of proper divisors, Sum of total divisors, Number of ways in which a number (N) can be resolved as a product of two factors which are relatively prime or co-prime. a-48 Min., b-45 Min., c-14 Min. 10 Multinomial theorem of permutation and combination, Beggar’s Method a-45 Min., b-43 Min. 11 Questions based on multinomial theorem, Dearrangement of n different things. a-31 Min., b-23 Min. 12 Miscellaneous questions a-33 Min., b-34 Min. 13 Miscellaneous questions a-30 Min., b-17 Min.

#### Complex number

 Lecture# Description Duration 01 Introduction of complex number, about iota (i), Algebra of complex numbers- (1) Addition/subtraction (2) Multiplication (3) Conjugate of a complex number (4) Division (5) Equality of two complex numbers (6) Square root of a complex numbers, Questions to solving complex equations. a-43 Min., b-28 Min., c-23 Min. 02 Questions, Representation of Complex number (Geometrical interpretation of Complex number) (1) Cartesian form (2) Polar or parametric form (3) Euler’s form # Demoiver’s theorem, Questions. a-48 Min., b-38 Min. 03 Properties of modulus/conjugate, Modulus - Inequalities (Triangular Inequalities), Properties of argument of complex number, Interconversion of complex number (z) into Cartesian form (x, y) or vice-versa. a-41 Min., b-29 Min. 04 Questions based on Properties of Modulus, conjugate, argument of complex number and modulus inequalities a-46 Min., b-47 Min. 05 Geometrical meaning of arg(z) = θ. Solving questions graphical, cube-roots of unity, cube-roots of –1, Properties, Questions based on cube roots of 1 and cube roots of –1. a-46 Min., b-39 Min., c-29 Min. 06 nth roots of unity, Properties, Questions based on nth roots of unity, rotation theorem (Geometrical interpretation of ei θ). Questions based on Rotation theorem. a-41 Min., b-21 Min., c-44 Min.