Table of Contents
Table of Contents 1
Contributors 5
1 Discrete Mathematics: Combinatory (50) 6
1.1 Balls In Bins (4) 6
1.2 Combinatory (22) 6
1.3 Counting (4) 10
1.4 Generating Functions (6) 11
1.5 Modular Arithmetic (2) 12
1.6 Pigeonhole Principle (2) 12
1.7 Recurrence Relation (7) 12
1.8 Summation (3) 14
Answer Keys 14
2 Discrete Mathematics: Graph Theory (83) 15
2.1 Counting (3) 15
2.2 Degree of Graph (12) 15
2.3 Graph Coloring (11) 17
2.4 Graph Connectivity (40) 19
2.5 Graph Isomorphism (3) 26
2.6 Graph Matching (1) 27
2.7 Graph Planarity (13) 28
Answer Keys 30
3 Discrete Mathematics: Mathematical Logic (77) 31
3.1 First Order Logic (34) 31
3.2 Logical Reasoning (3) 39
3.3 Propositional Logic (40) 39
Answer Keys 47
4 Discrete Mathematics: Set Theory & Algebra (171) 48
4.1 Binary Operation (8) 48
4.2 Countable Uncountable Set (2) 49
4.3 Functions (29) 50
4.4 Group Theory (33) 55
4.5 Identify Function (1) 61
4.6 Lattice (10) 61
4.7 Mathematical Induction (2) 63
4.8 Number Theory (7) 64
4.9 Onto (1) 65
4.10 Partial Order (10) 65
4.11 Polynomials (4) 67
4.12 Relations (37) 68
4.13 Set Theory (27) 74
Answer Keys 79
5 Engineering Mathematics: Calculus (63) 81
5.1 Continuity (9) 81
5.2 Definite Integral (3) 83
5.3 Differentiation (10) 83
5.4 Integration (11) 85
5.5 Limits (15) 87
5.6 Maxima Minima (13) 89
5.7 Polynomials (2) 92
Answer Keys 92
6 Engineering Mathematics: Linear Algebra (102) 93
6.1 Cartesian Coordinates (1) 93
6.2 Determinant (11) 93
6.3 Eigen Value (33) 96
6.4 Gaussian Elimination (1) 103
6.5 Lu Decomposition (1) 103
, 6.6 Matrix (22) 103
6.7 Orthonormality (2) 107
6.8 Rank of Matrix (6) 107
6.9 Singular Value Decomposition (1) 109
6.10 Subspace (1) 109
6.11 System of Equations (17) 109
6.12 Vector Space (6) 113
Answer Keys 114
7 Engineering Mathematics: Probability (107) 116
7.1 Bayes Theorem (1) 116
7.2 Bayesian Network (2) 116
7.3 Bernoulli Distribution (1) 117
7.4 Binomial Distribution (6) 117
7.5 Conditional Probability (14) 118
7.6 Continuous Distribution (1) 121
7.7 Expectation (13) 121
7.8 Exponential Distribution (5) 124
7.9 Independent Events (6) 125
7.10 Normal Distribution (2) 126
7.11 Poisson Distribution (4) 126
7.12 Probability (28) 127
7.13 Probability Density Function (1) 132
7.14 Probability Distribution (1) 132
7.15 Random Variable (8) 132
7.16 Square Invariant (1) 134
7.17 Statistics (2) 134
7.18 Uniform Distribution (10) 134
7.19 Variance (1) 136
Answer Keys 136
8 General Aptitude: Analytical Aptitude (139) 138
8.1 Age Relation (2) 138
8.2 Code Words (5) 138
8.3 Coding Decoding (1) 139
8.4 Counting Figure (1) 139
8.5 Direction Sense (12) 139
8.6 Family Relationship (7) 143
8.7 Inequality (1) 144
8.8 Logical Inference (1) 144
8.9 Logical Reasoning (39) 145
8.10 Number Relations (3) 155
8.11 Odd One (6) 155
8.12 Passage Reading (6) 156
8.13 Round Table Arrangement (6) 158
8.14 Seating Arrangement (4) 159
8.15 Sequence Series (12) 160
8.16 Statements Follow (33) 162
Answer Keys 170
9 General Aptitude: Quantitative Aptitude (494) 172
9.1 Absolute Value (7) 172
9.2 Age Relation (1) 174
9.3 Algebra (6) 174
9.4 Alligation Mixture (3) 175
9.5 Area (2) 175
9.6 Arithmetic Series (9) 176
9.7 Average (3) 178
9.8 Bar Graph (18) 179
9.9 Calendar (2) 186
9.10 Cartesian Coordinates (10) 186
9.11 Circle (7) 188
9.12 Clock Time (10) 190
, 9.13 Combinatory (12) 191
9.14 Compound Interest (5) 193
9.15 Conditional Probability (6) 194
9.16 Cones (1) 195
9.17 Contour Plots (4) 195
9.18 Cost Market Price (6) 197
9.19 Counting (6) 198
9.20 Cube (2) 199
9.21 Currency Notes (1) 199
9.22 Curves (2) 199
9.23 Data Interpretation (5) 200
9.24 Digital Image Processing (1) 202
9.25 Factors (4) 202
9.26 Fractions (4) 203
9.27 Functions (18) 203
9.28 Geometry (29) 208
9.29 Graph Coloring (1) 215
9.30 Inequality (4) 215
9.31 LCM HCF (1) 216
9.32 Line Graph (12) 217
9.33 Lines (1) 221
9.34 Logarithms (14) 222
9.35 Maps (1) 224
9.36 Maxima Minima (4) 224
9.37 Mensuration (1) 225
9.38 Modular Arithmetic (2) 225
9.39 Number Series (10) 225
9.40 Number System (7) 227
9.41 Number Theory (6) 228
9.42 Numerical Computation (14) 229
9.43 Percentage (21) 231
9.44 Permutation and Combination (4) 235
9.45 Pie Chart (16) 236
9.46 Polynomials (4) 242
9.47 Powers (1) 243
9.48 Prime Numbers (1) 243
9.49 Probability (29) 243
9.50 Probability Density Function (1) 249
9.51 Profit Loss (6) 249
9.52 Quadratic Equations (11) 250
9.53 Radar Chart (1) 252
9.54 Ratio Proportion (26) 252
9.55 Scatter Plot (1) 256
9.56 Seating Arrangement (4) 257
9.57 Sequence Series (10) 257
9.58 Set Theory (1) 259
9.59 Speed Time Distance (19) 259
9.60 Squares (4) 262
9.61 Statistics (9) 263
9.62 System of Equations (1) 265
9.63 Tables (1) 266
9.64 Tabular Data (10) 266
9.65 Triangles (11) 269
9.66 Trigonometry (1) 272
9.67 Unit Digit (2) 272
9.68 Venn Diagram (16) 273
9.69 Volume (2) 276
9.70 Work Time (17) 276
Answer Keys 279
10 General Aptitude: Spatial Aptitude (49) 282
, 10.1 Assembling Pieces (4) 282
10.2 Counting Figure (1) 283
10.3 Grouping (1) 284
10.4 Image Rotation (7) 284
10.5 Mirror Image (7) 287
10.6 Paper Folding (12) 290
10.7 Patterns In Three Dimensions (8) 296
10.8 Patterns In Two Dimensions (9) 298
Answer Keys 300
11 General Aptitude: Verbal Aptitude (376) 302
11.1 Articles (2) 302
11.2 Comparative Forms (7) 302
11.3 English Grammar (12) 303
11.4 Grammatical Error (9) 305
11.5 Incorrect Sentence Part (5) 307
11.6 Most Appropriate Word (113) 308
11.7 Narrative Sequencing (1) 325
11.8 Noun Verb Adjective (3) 326
11.9 Opposite (5) 326
11.10 Passage Reading (57) 327
11.11 Phrasal Verb (2) 342
11.12 Phrase Meaning (8) 342
11.13 Prepositions (8) 343
11.14 Pronouns (4) 344
11.15 Sentence Ordering (5) 345
11.16 Statement Sufficiency (2) 346
11.17 Statements Follow (2) 347
11.18 Synonyms (19) 347
11.19 Tenses (25) 350
11.20 Verbal Reasoning (40) 354
11.21 Word Meaning (17) 363
11.22 Word Pairs (30) 366
Answer Keys 371
Table of Contents 1
Contributors 5
1 Discrete Mathematics: Combinatory (50) 6
1.1 Balls In Bins (4) 6
1.2 Combinatory (22) 6
1.3 Counting (4) 10
1.4 Generating Functions (6) 11
1.5 Modular Arithmetic (2) 12
1.6 Pigeonhole Principle (2) 12
1.7 Recurrence Relation (7) 12
1.8 Summation (3) 14
Answer Keys 14
2 Discrete Mathematics: Graph Theory (83) 15
2.1 Counting (3) 15
2.2 Degree of Graph (12) 15
2.3 Graph Coloring (11) 17
2.4 Graph Connectivity (40) 19
2.5 Graph Isomorphism (3) 26
2.6 Graph Matching (1) 27
2.7 Graph Planarity (13) 28
Answer Keys 30
3 Discrete Mathematics: Mathematical Logic (77) 31
3.1 First Order Logic (34) 31
3.2 Logical Reasoning (3) 39
3.3 Propositional Logic (40) 39
Answer Keys 47
4 Discrete Mathematics: Set Theory & Algebra (171) 48
4.1 Binary Operation (8) 48
4.2 Countable Uncountable Set (2) 49
4.3 Functions (29) 50
4.4 Group Theory (33) 55
4.5 Identify Function (1) 61
4.6 Lattice (10) 61
4.7 Mathematical Induction (2) 63
4.8 Number Theory (7) 64
4.9 Onto (1) 65
4.10 Partial Order (10) 65
4.11 Polynomials (4) 67
4.12 Relations (37) 68
4.13 Set Theory (27) 74
Answer Keys 79
5 Engineering Mathematics: Calculus (63) 81
5.1 Continuity (9) 81
5.2 Definite Integral (3) 83
5.3 Differentiation (10) 83
5.4 Integration (11) 85
5.5 Limits (15) 87
5.6 Maxima Minima (13) 89
5.7 Polynomials (2) 92
Answer Keys 92
6 Engineering Mathematics: Linear Algebra (102) 93
6.1 Cartesian Coordinates (1) 93
6.2 Determinant (11) 93
6.3 Eigen Value (33) 96
6.4 Gaussian Elimination (1) 103
6.5 Lu Decomposition (1) 103
, 6.6 Matrix (22) 103
6.7 Orthonormality (2) 107
6.8 Rank of Matrix (6) 107
6.9 Singular Value Decomposition (1) 109
6.10 Subspace (1) 109
6.11 System of Equations (17) 109
6.12 Vector Space (6) 113
Answer Keys 114
7 Engineering Mathematics: Probability (107) 116
7.1 Bayes Theorem (1) 116
7.2 Bayesian Network (2) 116
7.3 Bernoulli Distribution (1) 117
7.4 Binomial Distribution (6) 117
7.5 Conditional Probability (14) 118
7.6 Continuous Distribution (1) 121
7.7 Expectation (13) 121
7.8 Exponential Distribution (5) 124
7.9 Independent Events (6) 125
7.10 Normal Distribution (2) 126
7.11 Poisson Distribution (4) 126
7.12 Probability (28) 127
7.13 Probability Density Function (1) 132
7.14 Probability Distribution (1) 132
7.15 Random Variable (8) 132
7.16 Square Invariant (1) 134
7.17 Statistics (2) 134
7.18 Uniform Distribution (10) 134
7.19 Variance (1) 136
Answer Keys 136
8 General Aptitude: Analytical Aptitude (139) 138
8.1 Age Relation (2) 138
8.2 Code Words (5) 138
8.3 Coding Decoding (1) 139
8.4 Counting Figure (1) 139
8.5 Direction Sense (12) 139
8.6 Family Relationship (7) 143
8.7 Inequality (1) 144
8.8 Logical Inference (1) 144
8.9 Logical Reasoning (39) 145
8.10 Number Relations (3) 155
8.11 Odd One (6) 155
8.12 Passage Reading (6) 156
8.13 Round Table Arrangement (6) 158
8.14 Seating Arrangement (4) 159
8.15 Sequence Series (12) 160
8.16 Statements Follow (33) 162
Answer Keys 170
9 General Aptitude: Quantitative Aptitude (494) 172
9.1 Absolute Value (7) 172
9.2 Age Relation (1) 174
9.3 Algebra (6) 174
9.4 Alligation Mixture (3) 175
9.5 Area (2) 175
9.6 Arithmetic Series (9) 176
9.7 Average (3) 178
9.8 Bar Graph (18) 179
9.9 Calendar (2) 186
9.10 Cartesian Coordinates (10) 186
9.11 Circle (7) 188
9.12 Clock Time (10) 190
, 9.13 Combinatory (12) 191
9.14 Compound Interest (5) 193
9.15 Conditional Probability (6) 194
9.16 Cones (1) 195
9.17 Contour Plots (4) 195
9.18 Cost Market Price (6) 197
9.19 Counting (6) 198
9.20 Cube (2) 199
9.21 Currency Notes (1) 199
9.22 Curves (2) 199
9.23 Data Interpretation (5) 200
9.24 Digital Image Processing (1) 202
9.25 Factors (4) 202
9.26 Fractions (4) 203
9.27 Functions (18) 203
9.28 Geometry (29) 208
9.29 Graph Coloring (1) 215
9.30 Inequality (4) 215
9.31 LCM HCF (1) 216
9.32 Line Graph (12) 217
9.33 Lines (1) 221
9.34 Logarithms (14) 222
9.35 Maps (1) 224
9.36 Maxima Minima (4) 224
9.37 Mensuration (1) 225
9.38 Modular Arithmetic (2) 225
9.39 Number Series (10) 225
9.40 Number System (7) 227
9.41 Number Theory (6) 228
9.42 Numerical Computation (14) 229
9.43 Percentage (21) 231
9.44 Permutation and Combination (4) 235
9.45 Pie Chart (16) 236
9.46 Polynomials (4) 242
9.47 Powers (1) 243
9.48 Prime Numbers (1) 243
9.49 Probability (29) 243
9.50 Probability Density Function (1) 249
9.51 Profit Loss (6) 249
9.52 Quadratic Equations (11) 250
9.53 Radar Chart (1) 252
9.54 Ratio Proportion (26) 252
9.55 Scatter Plot (1) 256
9.56 Seating Arrangement (4) 257
9.57 Sequence Series (10) 257
9.58 Set Theory (1) 259
9.59 Speed Time Distance (19) 259
9.60 Squares (4) 262
9.61 Statistics (9) 263
9.62 System of Equations (1) 265
9.63 Tables (1) 266
9.64 Tabular Data (10) 266
9.65 Triangles (11) 269
9.66 Trigonometry (1) 272
9.67 Unit Digit (2) 272
9.68 Venn Diagram (16) 273
9.69 Volume (2) 276
9.70 Work Time (17) 276
Answer Keys 279
10 General Aptitude: Spatial Aptitude (49) 282
, 10.1 Assembling Pieces (4) 282
10.2 Counting Figure (1) 283
10.3 Grouping (1) 284
10.4 Image Rotation (7) 284
10.5 Mirror Image (7) 287
10.6 Paper Folding (12) 290
10.7 Patterns In Three Dimensions (8) 296
10.8 Patterns In Two Dimensions (9) 298
Answer Keys 300
11 General Aptitude: Verbal Aptitude (376) 302
11.1 Articles (2) 302
11.2 Comparative Forms (7) 302
11.3 English Grammar (12) 303
11.4 Grammatical Error (9) 305
11.5 Incorrect Sentence Part (5) 307
11.6 Most Appropriate Word (113) 308
11.7 Narrative Sequencing (1) 325
11.8 Noun Verb Adjective (3) 326
11.9 Opposite (5) 326
11.10 Passage Reading (57) 327
11.11 Phrasal Verb (2) 342
11.12 Phrase Meaning (8) 342
11.13 Prepositions (8) 343
11.14 Pronouns (4) 344
11.15 Sentence Ordering (5) 345
11.16 Statement Sufficiency (2) 346
11.17 Statements Follow (2) 347
11.18 Synonyms (19) 347
11.19 Tenses (25) 350
11.20 Verbal Reasoning (40) 354
11.21 Word Meaning (17) 363
11.22 Word Pairs (30) 366
Answer Keys 371
