CHAPTER-WISE MARKS DISTRIBUTION
I-5 S. No. Chapter 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 J D J D J D J D J D J D J D J D D Jan July D J D 1 Ratio & Proportions 1 1 2 1 2 1 2 2 1 1 1 2 1 2 1 1 3 3 3 3 2 1 2 Indices 1 1 2 1 1 3 1 1 1 1 2 2 1 1 1 4 2 1 3 Logarithms 1 1 2 4 2 2 1 3 1 2 2 1 2 2 2 1 1 2 2 2 4 Linear Equations 2 1 3 2 1 1 1 2 1 1 0 0 1 2 3 5 Quadratic Equations 3 2 1 2 1 1 2 1 1 2 3 3 2 1 3 4 3 4 2 1 2 6 Inequalities 1 1 1 1 1 2 1 1 1 1 2 1 1 3 1 1 1 1 2 1 1 7 Simple Interest 2 3 1 2 1 1 2 1 1 1 3 4 5 1 3 2 1 3 1 8 Compound Interest 2 1 1 1 1 2 2 1 2 2 11 3 7 6 7 5 4 3 8 9 AnnuityApplications 1 1 1 2 3 3 1 4 4 7 1 8 5 10 Basic Concepts of Permutations and Combinations 2 3 3 3 2 3 3 3 3 3 3 2 2 4 4 4 4 6 4 4 7 4 11 Sequence & SeriesArithmetic & Geometric Progression 3 3 4 2 3 4 3 3 3 3 3 1 4 4 4 4 3 3 3 3 4 2 12 Sets, Functions and Relations 3 3 3 3 3 4 1 3 3 3 3 2 3 4 5 2 4 3 4 3 3 3 13 Basic Concepts of Differential Calculus 2 3 2 1 1 1 2 2 1 2 2 4 1 2 2 3 2 1 3 3 1 3 14 Integral Calculus 1 1 2 1 1 1 2 1 2 1 1 2 3 2 3 3 3 1 1 1 2 3 15 Number and Letter Series & CodingDecoding 3 5 4 5 4 5 5 5 5 6
I-6
CHAPTER-WISE MARKS DISTRIBUTION
Note : J: June; D : December
S. No. Chapter 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 J D J D J D J D J D J D J D J D D Jan July D J D 16 Direction Test 6 5 4 6 4 3 4 8 5 5 17 Seating Arrangement 5 3 4 2 5 4 4 3 4 2 18 Blood Relations 4 4 4 4 3 4 4 5 5 7 19 Description of Data 3 1 1 3 4 4 5 4 1 4 3 2 4 7 5 4 7 10 8 5 8 4 20 Central Tendency 2 5 3 1 1 4 1 1 1 5 5 3 5 7 5 7 11 4 4 10 6 8 21 Dispersion 2 2 4 2 2 3 5 3 1 1 2 4 8 8 1 5 7 1 5 8 22 Probability 5 4 5 4 3 3 4 4 5 4 3 4 7 6 5 3 4 6 6 4 6 7 23 Probability Distribution 3 4 5 1 3 5 3 3 3 4 3 3 6 5 4 7 7 4 5 8 5 4 24 Correlations 2 2 2 1 1 1 1 2 1 2 2 8 1 4 3 3 2 1 1 4 2 25 Regression Analysis 4 3 1 2 3 2 1 1 2 3 1 3 5 5 2 2 3 4 3 1 3 26 Index Number 2 2 3 3 4 2 3 1 4 3 3 4 8 3 4 3 3 3 4 5 5 5
CHAPTER-WISE COMPARISON WITH STUDY
I-7 No. Name of Chapter Study Material Chapter 1 Ratio & Proportions 1 2 Indices 1 3 Logarithms 1 4 Linear Equations 2 5 Quadratic Equations 2 6 Inequalities 3 7 Simple Interest 4 8 Compound Interest 4 9 Annuity - Applications 4 10 Basic Concepts of Permutations and Combinations 5 11 Sequence & Series - Arithmetic & Geometric Progression 6 12 Sets, Functions and Relations 7 13 Basic Concepts of Differential Calculus 8 14 Integral Calculus 8 15 Number and Letter Series & Coding-Decoding 9 16 Direction Test 10 17 Seating Arrangement 11 18 Blood Relations 12 19 Description of Data 14 20 Central Tendency 15 21 Dispersion 15 22 Probability 16 23 Probability Distribution 17 24 Correlations 18
MATERIAL
I-8 CHAPTER-WISE COMPARISON WITH STUDY MATERIAL No. Name of Chapter Study Material Chapter 25 Regression Analysis 18 26 Index Number 19
Contents
I-9
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
) ( C T ∪ ∴ ) ( C T ∩ ) ( C T ∪ ∴ ) ( E H ∪ ′ ⇒ ∪ ∴ ) ( E H ∪ ) ( E H ∪ ∴
→ → 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 ∩ ∴ { } { }4,9 1, , 3 2, = ± ± B ( ) ( ) ( ) ( ) { } 4 3, , 3,9 , 4 2, , 4 2, ∴ () 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, , 2 5, , 4 4, , 2 4, , 4 2, , 2 2, ( ) ( ) ( ) ( ) ( ) ( ) { } 4 5, , 2 5, , 4 3, , 2 3, , 4 1, , 2 1, ( ) ( ) ( ) ( ) { } 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=− { }4,5,6,7 3, 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
1 x x y x x y y x y x y x y x y x f = = = 1 () () y x y x y y x x x y f y x f y x y x x y x y x y x y x y f = = = = = : 1 → N x ∈ ∨
x )} ( { ) ( x g f x fog = 2 2 ) ( 2 2 + = = x x f 34 2 4 2 4) ( 2 = + × = fog
35% ) ( ) ( ) ( = ∩ = T C n C n T C n
% 45 ) ( ) ( ) ( = ∩ = T C n T n C T n
100 ) ( ) ( ) ( ) ( = ∩ + = T C n T n C n CUT n 100 ) ( ) ( 45 ) ( 35 = ∩ ∩ + + ∩ + T C n T C n T C n
100 ) ( 80 = ∩ + T C n
20% ) ( = ∩ T C n
% 55 20 35 ) ( 35 ) ( = + = ∩ + = ∴ T C n C n
44 55% 80 = × =
→
2
≤ ≤ ∈ = 10 x Z,0 2 x : x A { }and number prime digit one is x : x B = ≤ ∈ = 12 x , N 3 x : x C = ∩ ∩ C) (B A φ { } {} {} 12 9, 6, 3, C 7 5, 3, 2, B 10 8, 6, 4, 2, A = = = ( )C B A ∩ ∩ ( ) ϕ = ∩ ∩ = C B A 1 2 + x ∞ ∞ ∞ ∞ 1 2 ) ( + = = x x f y ) ( x f ∴ 1 + x ∴ 2 0 2 = = ∴ 2 ≤ < ∞ = y 2] ; ( ∞ =
A y A, x ∈ ∈ A y x ∈ + ∈ A ∈ y x ∈ { }Nos. natural of squares the is / A x x = { }25,.......... 16, 9, 4, 1, A. 4 1; ∈ = = y x ∴ A. 5 4 1 ∉ = + = + y x A. 3 4 1 ∉ = = y x A. 4 1 ∉ = y x A. 4 4 1 ∈ = × = xy ∴ ( ) x x f 100 = ( ) = x f 1 100 x x 100 1 100 1 100 y x = 100 ) ( 1 x x f =
R R : f → ( ) x x 2 f = ( ) HE40 n ∩= ( ) ( ) ( ) ( ) HEHEHE nnnn∪=+−∩ ∴ () x x x f 1 = () x x g = 1 1 ∪ ( ) fogx {()}fgx ()1 () gx gx () 1 1 1 11 1 1 11 1 x x x x x −+ =× ∴ () 2 2 + = x x x f