CHAPTER-WISE COMPARISON WITH STUDY MATERIAL
I-7 No.NameofChapterStudyMaterialChapter 1Ratio&Proportions1 2Indices1 3Logarithms1 4LinearEquations2 5QuadraticEquations2 6Inequalities3 7SimpleInterest4 8CompoundInterest4 9Annuity-Applications4 10BasicConceptsofPermutationsand Combinations 5 11Sequence&Series-Arithmetic&Geometric Progression 6 12Sets,FunctionsandRelations7 13BasicConceptsofDifferentialCalculus8 14IntegralCalculus8 15NumberSeries,Coding&Decoding9 16DirectionTests10 17SeatingArrangement11 18BloodRelations12 19DescriptionofData14 20CentralTendency15 21MeasuresofDispersion15 22Probability16 23ProbabilityDistribution17 24Correlation18
I-8 CHAPTER-WISECOMPARISONWITHSTUDYMATERIAL No.NameofChapterStudyMaterialChapter 25RegressionAnalysis18 26IndexNumber19
I-9 Contents Chapter-wise Marks Distribution I-5 Chapter-wise Comparison with Study Material I-7 CHAPTER 1 RATIO & PROPORTION 1.1 CHAPTER 2 INDICES 2.1 CHAPTER 3 LOGARITHM 3.1 CHAPTER 4 LINEAR EQUATION 4.1 CHAPTER 5 QUADRATIC EQUATION 5.1 CHAPTER 6 INEQUALITIES 6.1 CHAPTER 7 SIMPLE INTEREST 7.1 CHAPTER 8 COMPOUND INTEREST 8.1
I-10 CONTENTS CHAPTER 9 ANNUITY 9.1 CHAPTER 10 PERMUTATIONS AND COMBINATIONS 10.1 CHAPTER 11 SEQUENCE & SERIES 11.1 CHAPTER 12 SETS, FUNCTION AND RELATION 12.1 CHAPTER 13 DIFFERENTIAL CALCULUS 13.1 CHAPTER 14 INTEGRATION 14.1 CHAPTER 15 NUMBER SERIES, CODING & DECODING 15.1 CHAPTER 16 DIRECTION TESTS 16.1 CHAPTER 17 SEATING ARRANGEMENT 17.1 CHAPTER 18 BLOOD RELATIONS 18.1 CHAPTER 19 DESCRIPTION OF DATA 19.1 CHAPTER 20 CENTRAL TENDENCY 20.1 CHAPTER 21 MEASURES OF DISPERSION 21.1 CHAPTER 22 PROBABILITY 22.1 CHAPTER 23 PROBABILITY (THEORETICAL) DISTRIBUTION 23.1
CONTENTS I-11 CHAPTER 24 CORRELATION 24.1 CHAPTER 25 REGRESSION ANALYSIS 25.1 CHAPTER 26 INDEX NUMBERS 26.1 Solved Paper : June 2023 (Memory Based) P.1
)(CT ∪ ∴ )(CT ∩ )(CT ∪ ∴ )(EH ∪ ′ ⇒ ∪ ∴ )(EH ∪ )(EH ∪ ∴
→ → 2 x 1 3) 2 3( 3) 2 ( 2 + + x x 2 4 x 2 4 x ∴ ∩ ∩ ∩ ∩ ∩ ) ( T R N n ∪ ∪ ) ( R N ∩ ) ( ) ( ) ( T R N n T R n T N n ∩ ∩ + ∩ ∩ ) T R N ( n 300 ∪ ∪ = ∴ →
2 1) ( ) ( + = x x f ∵ } 1) {( 2 + x 2 2 1} 1) {( + + x ∴ → 2 7 = y x 2 7 ) ( 1 = ∴ x x f 4% ) ( 5%; ) ( = ∩ = ∩ C B n B A n 2% ) ( 4%; ) ( = ∩ ∩ = ∩ C B A n A C n ) ( ) ( ) ( ) ( C B A n C A n B A n A n ∩ ∩ + ∩ ∩ = × ∴ → ÷ x x f 2 ) ( = y x y x y x f .2 2 2 ) ( = = + + ∴
32 ) ( 30; ) ( = ∩ = ∩ E M n M A n 25 ) ( 35; ) ( = ∩ ∩ = ∩ M E M n M A n ) ( M E A n ∪ ∪ ∴ ∴ : ) ( , 2 2 ) ( 1 x f x x x f + = 1 1) 2( + x x 1 1) 2( + x x 1 1 + x x 1 1 + x x ) ( 2 2 ) ( let y x x x f = + = ∵ y y x + = 1 1) 2( 1 1) 2( ) ( 1 + = ∴ x x x f →
1 f ∴ 1 2 + x x 1 2 ) 2 ( 1) 4( 2 2 + = + x x x x 2 4 x 2 4 x ∴ ∴ ∩ ⊂ ) ( B A ∩ ∩ ∴ { } { }4 2,3, 1, , , , , = = y z w y x X → → → →
∴ ∵ ∴ ∵ ∴ ∴ { }0 2 3 : 2 = + = X X X A { }0 12 4 : 2 = + = X X X B { }6 {} 1 { }2 1, { }6 2, ∵ 0 2 3 2 = + x x 0 2 2 2 = + x x x ∵ ∵ 2 x
2 x ∴ ∴ ∴ ∴ → x 1 { }1 R { }0 R x 1 ∈ ∴ ∴ ( )AAB ∩∪ ′ B A ∩ B A ∪ B A ∪’
1 1 1 {4;5} {4,5}{2,3,4,5} {2,3,4,5} () {0,1,2,3}{2,3,4,5} {2,3} AA AB AAB AB ∴=∪− = ∪=∪ = ∴∩∪ =∩ = =∩ ∴ ∩ ′ ∪ ∩ { }∪ ∩ ∩ R R f → : ( ) 1, + = x x f ( ) 1 x g : 2 + = → x R R g ∵ 5 1 2) ( 2) ( 1. 2 2 = + = ⇒ + g x ∴ ⊂ ∩ ∪ ∩ ∩ 8, 4 2 + x x 8 2 + x 7 2 + x 4 2 + x x x 4 2 8 4 2 + x x 2 1) 1 ( + x ∴ 2 1) 1 ( + + x 2 2) ( + x 2 x 2 x ∴
) ( M E ∩ ) ( M E ∩ ∴ { } { }1,4,9 , 3 2, = ± ± B ( ) ( ) ( ) ( ) { } 3,4 , 3,9 , 2,4 , 2,4 ∴ () 2 2 1 x g 1 x x and x x = + x 1 2 1 x x 2 1 x x → →
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 1 x x f 2 2 2 1 1 1 x x x x + 2 2 2 2 1 1 1 x x x x x + 1 1 1 2 2 x x x × = ∴ 0 3 < < x × ∴ × ( ) ( ) ( ) ( ) ( ) ( ) { } 4 5, , 5,2 , 4 4, , 4,2 , 4 2, , 2,2 ( ) ( ) ( ) ( ) ( ) ( ) { } 4 5, , 5,2 , 3,4 , 3,2 , 1,4 , 1,2 ( ) ( ) ( ) ( ) { } 4,5 , 4 4, , 2 4, , 2,2 ( ) ( ) ( ) ( ) { } 4 4, , 2 4, , 4 2, , 2,2 × ×
( )’ ’ B A ∪ = ∪ = B B 1 1 B A ∪ {3} ) ( ) ( 1 1 1 = ∪ ∪ = ∪ B A B A {3} ) ( ) ( 1 1 1 = ∪ ∪ = ∪ B A B A (AB) ∪ ′′ A(B) =∩′′′ AB=∩ ′ BAB=−∩ BA=− { }3,4,5,6,7 1 2 n 31 1 2 5 =
→ ( ) 1 1 x { }1 0, { }1 1, { }1,0 { }1 1,0, 1 1) ( ) ( = ∴ x x f ∴ 30; ) C A ( n 40; B) A ( n = ∩ = ∩ 10 ) C B A ( n 20; ) C B ( n = ∩ ∩ = ∩ 11
n(BAC)n(B)n(BA)n(BC)n(ABC) ∴∩∩=−∩−∩+∩∩
R R f → : ( ), 1 x f 7 10 1 x 7 10 1 + x 10 7 + x 10 7 x 10 7 + = ∴ y x 10 7 ) ( 1 + = ∴ x x f 10 7 ) ( + = ∴ x x g ∈ x 7 x x x 7 2 7 + 2 7 + x 2 ) (7 + x x 7 ∴ →
2 12 1 1 + ⎛⎞⎛⎞ ⎝⎠⎝⎠ + xx thenf x x 2 2 2 2 1 2 1 log 2 1 1 1 x x x f x x x ⎛⎞ + ⎛⎞ ⎜⎟ + = ⎜⎟ ⎝⎠ + ⎜⎟ ⎝⎠ + 2 2 12 log 12 xx xx ⎛⎞ ++ ⎜⎟ ⎝⎠ +− 2 2 2 (1) 1 loglog 1 (1) x x x x + + ⎛⎞ = ⎝⎠ 1 2log2() 1 x fx x + ⎛⎞ = ⎝⎠ ∴ ∈ ∈
()40;()30;()60()10. nABnBCnCAnABC ∩=∩=∩=∩∩= 190 10 60 30 40 140 70 100 ) ( = + + + = ∪ ∪ ∴ C B A n 5 25 2 x x 0 0 5 5 25 5 5 25 (5) 2 2 = = = x x f ∴ n 1 n ) x (a ) x ( f = n x / 1 n a / 1 { } { } n n n a f x f f / 1 ) ( ) ( = n n n n x a a 1 1 ) ( ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ [ ] [ ] x x x a a n n n n = = 1 1 ) ( ) ( C M ∪ () MC ∩
) C B ( A ∩ × {5} {5,6} {4,5} = ∩ = ∩ C B (){2,3}{5} {(2,5);(3,5)} ABC ∴×∩=× = = ) x / y ( f ) y / x ( f then , 1 x x
