APC CBSE Mathematics - Class 12 - Avichal Publishing Company - Hints and SolutionsAvichal Publishing Company CBSE Mathematics, for class 12, has been written by Mr. M.L. Aggarwal (Former Head of P.G. Department of Mathematics, D.A.V. College, Jalandhar) strictly according to the latest syllabus prescribed by the CBSE, New Delhi and COBSE, New Delhi for students taking class 12 examination in the year 2015 and thereafter. The book has been thoroughly revised and a new feature - Typical Illustrative Examples and Typical Problems, has been added in some chapters for those students who want to attempt some more challenging problems. The question of NCERT Examplar Problems have also been included. Value Based Questions have also been added at the appropriate places. The book provides Hints & Solutions for the exercises of each chapter, at the end of the corresponding chapter. |
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Exercise 74
| 528 |
73 Four Standard Integrals
| 532 |
Exercise 75
| 535 |
74 Seven More Standard Integrals
| 536 |
Exercise 76
| 543 |
Exercise 77
| 552 |
Exercise 78
| 556 |
75 Integration by Partial Functions
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| 54 | |
| 57 | |
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| 62 | |
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| 71 | |
| 73 | |
| 99 | |
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| 105 | |
| 106 | |
| 107 | |
| 26 | |
| 108 | |
| 113 | |
| 115 | |
| 120 | |
| 122 | |
Exercise 33
| 136 |
34 Transpose of a Matrix
| 140 |
Exercise 34
| 148 |
35 Elementary Operations on a Matrix
| 150 |
36 Invertible Matrices
| 151 |
Exercise 35
| 156 |
Chapter Test
| 157 |
Answers
| 159 |
MATRICES HINTS AND SOLUTIONS
| 48 |
DETERMINANTS
| 82 |
Exercise 41
| 170 |
42 Properties of Determinants
| 171 |
Exercise 42
| 194 |
43 Area of a Triangle
| 200 |
Exercise 43
| 202 |
44 Adjoint and Inverse of a Square Matrix
| 203 |
Exercise 44
| 214 |
45 Solution of a System of Linear Equations
| 218 |
Exercise 45
| 228 |
46 Solutin of Linear Equations by Determinants
| 230 |
Exercise 46
| 238 |
Typical Illustrative Examples
| 239 |
Exercise 47 Typical Problems
| 246 |
Chapter Test
| 249 |
Answers
| 252 |
DETERMINANTS HINTS AND SOLUTIONS
| 82 |
CONTINUITY AND DIFFERENTIABILITY
| 123 |
Exercise 51
| 265 |
Exercise 52
| 275 |
Exercise 53
| 279 |
52 Continuity and Differentiability
| 280 |
Exercise 54
| 286 |
53 Derivatives of Composite Functions
| 287 |
Exercise 55
| 292 |
54 Derivatives of Inverse Trigonometric Functions
| 293 |
Exercise 56
| 302 |
55 Implicit Differentiation
| 304 |
Exercise 57
| 308 |
56 Exponential and Logarithmic Functions
| 309 |
Exercise 58
| 314 |
Exercise 59
| 320 |
57 Logarithmic Differentiation
| 322 |
Exercise 510
| 327 |
58 Derivatives of Functions in Parametric Forms
| 328 |
Exercise 511
| 333 |
59 Second Order Derivative
| 335 |
Exercise 512
| 343 |
510 Rolles Theorem
| 345 |
Exercise 513
| 351 |
511 Lagranges Mean Value Theorem
| 352 |
Exercise 514
| 356 |
Typical Illustrative Examples
| 357 |
Exercise 515 Typical Problems
| 370 |
Chapter Test
| 372 |
Answers
| 375 |
CONTINUITY AND DIFFERENTIABILITY HINTS AND SOLUTIONS
| 123 |
APPLICATIONS OF DERIVATIVES
| 383 |
Exercise 61
| 393 |
62 Tangents and Normals
| 395 |
Exercise 62
| 411 |
63 Approximations Errors and Differentials
| 413 |
Exercise 63
| 419 |
Exercise 64
| 422 |
Exercise 65
| 434 |
65 Maxima and Minima
| 436 |
Exercise 66
| 443 |
66 Local Maximum and Local Minimum Values
| 444 |
Exercise 67
| 452 |
Exercise 68
| 480 |
Typical Illustrative Examples
| 482 |
Exercise 69 Typical Problems
| 492 |
Chapter Test
| 494 |
Answers
| 496 |
APPLICATIONS OF DERIVATIVES HINTS AND SOLUTIONS
| 217 |
INTEGRALS
| 288 |
71 Indefinite Integrals
| 502 |
Exercise 71
| 503 |
Exercise 72
| 507 |
72 Integration by Substitution
| 509 |
Exercise 73
| 515 |
Exercise 79
| 569 |
76 Integration by Parts
| 571 |
Exercise 710
| 581 |
Exercise 711
| 586 |
Exercise 712
| 590 |
Exercise 713
| 593 |
Exercise 714
| 599 |
78 Fundamental Theorems of Integral Calculus
| 600 |
Exercise 715
| 609 |
Exercise 716
| 621 |
79 Properties of Definite Integrals
| 622 |
Exercise 717
| 644 |
Typical Illustrative Examples
| 648 |
Exercise 718 Typical Problems
| 658 |
Chapter Test
| 661 |
Answers
| 664 |
INTEGRALS HINTS AND SOLUTIONS
| 288 |
APPLICATIONS OF INTEGRALS
| 417 |
82 Area Between Two Curves
| 686 |
Exercise 81
| 706 |
Typical Illustrative Examples
| 709 |
Exercise 82 Typical Problems
| 711 |
Chapter Test
| 712 |
APPLICATIONS OF INTEGRALS HINTS AND SOLUTIONS
| 714 |
DIFFERENTIAL EQUATIONS
| 714 |
Exercise 91
| 716 |
Exercise 92
| 720 |
93 Formation of Differential Equations
| 721 |
Exercise 93
| 727 |
94 Solving a Differential Equation
| 728 |
Exercise 94
| 740 |
Exercise 95
| 745 |
Exercise 96
| 758 |
Exercise 97
| 775 |
Chapter Test
| 779 |
Answers
| 780 |
DIFFERENTIAL EQUATIONS HINTS AND SOLUTIONS
| 435 |
VECTOR ALGEBRA
| 491 |
102 Vector Algebra
| 789 |
Exercise 101
| 807 |
10 Scalar or Dot Product of Two Vectors
| 813 |
Exercise 102
| 830 |
104 Vector Or Cross Product of Two Vectors
| 833 |
Exercise 103
| 849 |
105 Scalar Triple Product
| 851 |
Exercise 104
| 859 |
Typical Illustrative Examples
| 860 |
Exercise 105 Typical Problems
| 867 |
Chapter Test
| 869 |
Answers
| 872 |
VECTOR ALGEBRA HINTS AND SOLUTIONS
| 491 |
THREE DIMENSIONAL GEOMETRY
| 876 |
Exercise 111
| 886 |
112 Straight Line In Space
| 888 |
Exercise 112
| 895 |
113 Angle Between Two Lines
| 897 |
Exercise 113
| 902 |
114 Shortest Distance Between Two Lines
| 904 |
Exercise 114
| 911 |
115 Plane
| 912 |
Exercise 115
| 924 |
Exercise 116
| 941 |
116 Angle Between Two Planes
| 943 |
Exercise 117
| 952 |
117 Distance of a Point From a Plane
| 954 |
Exercise 118
| 960 |
Chapter Test
| 962 |
Answers
| 964 |
THREE DIMENSIONAL GEOMETRY HINTS AND SOLUTIONS
| 538 |
LINEAR PROGRAMMING
| 611 |
122 Formulation of an LPP in Two Variables x and y
| 972 |
Exercise 121
| 975 |
Exercise 122
| 989 |
Chapter Test
| 995 |
Answers
| 996 |
LINEAR PROGRAMMING HINTS AND SOLUTIONS
| 611 |
PROBABILITY
| 634 |
Exercise 131
| 1005 |
132 Multiplication Theorem on Probability
| 1007 |
Exercise 132
| 1025 |
133 The Law of Total Probability
| 1030 |
Exercise 133
| 1035 |
Exercise 134
| 1046 |
135 Random Variables
| 1050 |
136 Probability Distribution of Random Variables
| 1051 |
Exercise 135
| 1056 |
137 Mean and Variance of Probability Distribution
| 1057 |
Exercise 136
| 1063 |
138 Binomial Experiment
| 1065 |
Exercise 137
| 1074 |
139 Mean and Variance of Binomial Distribution
| 1077 |
Exercise 138
| 1083 |
Typical Illustrative Examples
| 1084 |
Exercise 139 Typical Problems
| 1093 |
Chapter Test
| 1096 |
Answers
| 1100 |
PROBABILITY HINTS AND SOLUTIONS
| 634 |
Veelvoorkomende woorden en zinsdelen
2x dx bijective binary operation C.B.S.E. Sample Paper cm/sec codomain commutative continuous function cosec decreasing defined by f(x derivable df df diff w.r.t. Differentiating w.r.t. domain of f dx dx dx NCERT equivalence relation Evaluate the following Example 11 exists f is continuous f is one-one f is strictly find the value following functions following integrals given curve Given f(x given function given operation given system Hence Hint identity element inverse inverse trigonometric functions JC JC log x Lt f(x matrix of order maxima maximum mean value theorem metres minima minimum value NCERT Examplar Problems Operate R2 prove radius range of f real number reflexive Rolle’s theorem Show skew-symmetric skew-symmetric matrix Slope of tangent square matrix strictly increasing symmetric symmetric matrix system of equations tan-l triangle