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Content Student's Corner

Page No.

 Agrawal Examcart Help Centre

v

 Best Strategy ijh{kk dh rS;kjh djus dk lgh rjhdk!

vi

 Current Affairs! dh 100% lVhd rS;kjh dSls djsa \

vii

 Student Corner!

viii

 SSC CGL (Tier-II) Analytical Chart

ix

 SSC CGL (Tier-II) Syllabus and Exam Pattern

xii

Mathematics 1. Number System

1-388 1-9

2. LCM & HCF

10-13

3. Square Root and Cube Root

14-19

4. Surds and Indices

20-25

5. Fractions and Decimal Numbers

26-31

6. Simplification

32-40

7. Average

41-51

8. Ratio and Proportion

52-65

9. Questions Related to Age

66-68

10. Percentage

69-82

11. Profit-Loss and Discount

83-108

12. Partnership

109-114

13. Mixture and Alligation

115-121

14. Time and Work

122-138

15. Pipe and Cistern

139-142

16. Simple Interest

143-147

17. Compound Interest

148-159

18. Speed, Distance and Time

160-168

19. Questions Related to Trains, Bus and Car

169-172

20. Questions Related to Boat and Stream

173-175

21. Data Interpretation & Statistics

176-198

22. Area of Plane Figures

199-209

23. Surface Area and Volume

210-245

24. Algebraic Expressions

246-266

25. Linear Equation

267-272

26. Quadratic Equation

273-275 ( iii )

Page No. 27. Triangle

276-302

28. Quadrilateral

303-308

29. Polygon

309-313

30. Circles

314-337

31. Trigonometry

338-367

32. Height and Distance

368-379

33. Sequence and Series

380-382

34. Coordinate Geometry

383-387

35. Permutations & Combinations

388

English

1-288

1. Noun

1-4

2. Pronoun

5-7

3. Verb & Modals

8-12

4. Adjective

13-16

5. Adverb

17-18

6. Preposition

19-23

7. Conjunction

24-25

8. Non-Finite Verb (Infinitive, Gerund & Participle)

26-28

9. Syntax

29-31

10. Article

32-33

11. Time & Tense

34-37

12. Voice

38-69

13. Narration

70-114

14. Sentence Improvement

115-143

15. Synonyms

144-149

16. Antonyms

150-154

17. Idioms & Phrases/Proverbs

155-167

18. One Word Substitution

168-182

19. Spelling Test

183-186

20. Re-Arrangement of Words/Sentences

187-215

21. Cloze Test

216-237

22. Comprehension

238-288

( iv )

(v)

(( vi v ))

( vii )

( viii )

SSC CGL (Tier-II) Analytical Chart Mathematics S. Chapter's Name No.

03-02- 29-01- 18-11- 16-11- 15-11- 13-9- 12-9- 11-9- 9-3- 21-2- 20-2- 19-2- 18-2- 17-22022 2022 2020 2020 2020 2019 2019 2019 2018 2018 2018 2018 2018 2018

1.

Number System

4

5

3

3

4

3

4

4

5

2

1

5

1

4

2.

HCF/LCM

1

1

2

1



2

2

2





1



1

1

3.

Square and Square Roots

3

2

1

2

2

1

1



3

3



2



1

4.

Cube and Cube Roots





















2







5.

Surds and Indices







1









1



2



3

2

6.

Fraction and Decimals

3

2

3

4

3

2

3

2

3

3

5

3

3

1

7.

Simplifications

5

5

5

3

6

5

5

6

2

1



2

2

3

8.

Average

2

2

1

2

2

1

2

2

3

4

3

4

4

4

9.

Ratio and Proportion

3

4

3

4

2

4

4

3

7

7

5

6

5

6

10.

Questions Related to Ages

1



2



1

1

1

1



1

2



1

1

11.

Percentage

5

6

6

4

4

6

6

6

4

4

4

4

4

2

12. Profit and Loss

7

7

7

7

7

5

7

7

8

8

8

8

8

9

13. Partnership

2

1

2

2

2

2

2

2

2

2

2

2

2

2

14. Mixture and Allegation

2

2

1

2

2

3



1

1



2

2

2

2

15. Time and Work

2

2

4

4

3

3

3

3

4

4

4

4

4

4

16. Pipe and Cistern

2

3





1

1

1

1













17. Simple Interest

4

1

2

2

2

2

2

2













18. Compound Interest

3



2

2

2

2

2

2

4

4

4

4

4

4

2

3

4

2

3

3

2

3

2

3

2

3

4

3

2





1

1



1

1



1

1



1

–-





1

1

1

1

1

1

1



1



22. Data Intrepretation

7

7

7

7

7

7

7

7

5

5

5

5

5

5

23. Area of Plane Figures

12

11









1





2

1

4

5

6

24. Surface Area and Volume





12

12

11

12

11

12

8

8

9

8

7

8

25. Algebra

5

6

5

6

6

5

5

5

7

3

4

5

8

6

19.

Time, Speed and Distance

20.

Question Related Train, Bus and Car

21.

Question Related to Boat and Stream

to

( ix )

S. Chapter's Name No.

03-02- 29-01- 18-11- 16-11- 15-11- 13-9- 12-9- 11-9- 9-3- 21-2- 20-2- 19-2- 18-2- 17-22022 2022 2020 2020 2020 2019 2019 2019 2018 2018 2018 2018 2018 2018

26. Linear Equations





1

2

1

2

2

1

2

2

2

27. Quadratic Equation













28. lines and Angles





1



1

29. Triangles

9

9

8

9

30. Quadrilateral

2

2

1

31. Polygon

1

1

32. Circles

2

33. Trigonometry





1

6

4

2

2

1



1

1













8

8

7

6

4

2

3

5

5

3

1

1

1

1

2

3

4

2

1

1

1

2

1

1

1

2

1

2

1

1

1

3

3

3

4

4

4

8

8

8

6

6

7

10

10

10

10

11

10

10

10

7

7

7

7

7

7

34. Height and Distance

1

1

1

1

1

1

1

1

3

3

3

3

3

3

35. Logarithm





























36. AP





1













1



1

1



37. GP



















1









38. HP & Special Series





















1





1

39. Coordinate Geometry

2

2

1

1

1

2

2

1





































1



100

100

100

100

100

100

100

100

100

100

100

100

100

100

40.

Permutation and Combination Total Number of Questions

2

1

English S. Chapter's Name No.

03-02- 29-01- 18-11- 16-11- 15-11- 13-9- 12-9- 11-9- 21-2- 20-2- 19-2- 18-2- 17-22022 2022 2020 2020 2020 2019 2019 2019 2018 2018 2018 2018 2018

1.

Cloze Test

25

25

25

25

25

25

25

25

25

25

25

25

25

2.

Reading Comprehension

30

30

30

30

30

30

30

30

30

30

30

30

30

3.

Voice

20

20

20

20

20

20

20

20

20

20

20

20

20

4.

Improvement of Sentences

22

22

20

20

22

22

22

21

22

21

22

22

22

5.

Idioms & Phrases

9

9

10

10

10

10

10

10

10

10

10

10

10

6.

PQRS

22

22

20

20

20

20

20

20

20

20

20

20

20

7.

Common Errors

22

22

20

20

20

20

20

20

20

20

20

20

20

8.

Narration

26

26

27

26

26

26

26

26

27

26

27

27

27

9.

One words substitution

11

11

14

15

13

13

13

14

12

14

12

12

12

(x)

S. Chapter's Name No.

03-02- 29-01- 18-11- 16-11- 15-11- 13-9- 12-9- 11-9- 21-2- 20-2- 19-2- 18-2- 17-22022 2022 2020 2020 2020 2019 2019 2019 2018 2018 2018 2018 2018

10.

Synonyms

3

3

3

3

3

3

3

3

3

3

3

3

3

11.

Antonyms

3

3

3

3

3

3

3

3

3

3

3

3

3

12.

Spelling Test

2

2

3

3

3

3

3

3

3

3

3

3

3

13.

Fill in the Blanks

5

5

5

5

5

5

5

5

5

5

5

5

5

200

200

200

200

200

200

200

200

200

200

200

200

200

Total Number of Questions

( xi )

SSC CGL (Tier-II) Syllabus Quantitative Ability 1. Computation of Whole Numbers 2. Decimals 3. Fractions 4. Relationships Between Numbers 5. Percentage 6. Ratio & Proportion 7. Square Roots 8. Averages 9. Interest 10. Profit and Loss 11. Discount 12. Partnership Business 13. Mixture and Alligation 14. Time and Distance 15. Time & Work 16. Basic Algebraic Identities of School Algebra & Elementary Surds 17. Graphs of Linear Equations 18. Triangle and Its Various Kinds of Centres 19. Congruence and Similarity of Triangles 20. Circle and Its Chords, Tangents, Angles Subtended by Chords of a Circle, Common Tangents to Two or More Circles

21. Triangle 22. Quadrilaterals 23. Regular Polygons 24. Right Prism 25. Right Circular Cone 26. Right Circular Cylinder 27. Sphere 28. Hemispheres 29. Rectangular Parallelepiped 30. Regular Right Pyramid with Triangular or Square Base 31. Trigonometric Ratio 32. Degree and Radian Measures 33. Standard Identities 34. Complementary Angles 35. Heights and Distances 36. Histogram 37. Frequency Polygon 38. Bar Diagram 39. Pie Chart

English Language and Comprehensive 1. Spot the Error 2. Fill in the Blanks 3. Synonyms 4. Antonyms 5. Spelling/Detecting Misspelt Words 6. Idioms & Phrases 7. One Word Substitution

8. Improvement of Sentences 9. Active/Passive Voice of Verbs 10. Conversion into Direct/Indirect Narration 11. Shuffling of Sentence Parts 12. Shuffling of Sentences in a Passage 13. Cloze Passage 14. Comprehension Passage

SSC CGL (Tier-II) Exam Pattern S. No. Sections No. of Questions Quantitative Ability 100 1. English Language and Comprehension 200 2. Total

500

( xii )

Total Marks

Time Allotted

200

2 hours

200

2 hours

600

8 hours

Mathematics

Chapter

Number System

1

1. 571 + 572 + 573 + 574 + 575 is divisible by which of the following number ? (A) 71

(B) 69

(C) 89 (D) 73 [SSC CGL TIER-II CBE EXAM 03-02-2022 (I-Shift)] 1. (A) 571 + 572 + 573 + 574 + 575 ⇒ 571 (1 + 5 + 52 + 53 + 54) ⇒ 571 (6 + 25 + 125 + 625) ⇒ 571 × 781 ⇒ 571 × 71 × 11 Thus, from the given option, the given expression will be divisible by 71. 2. Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers and r > s and both are one-digit numbers, then the value of p-q-1 the expression r - s is : (A) – s – 1

(B) s – 1

(C) 1 – s (D) s + 1 [SSC CGL TIER-II CBE EXAM 03-02-2022 (I-Shift)] 2. (A) Two digits natural numbers with only 3 exact factors are = 25 and 49 As, q>p Then p = 25 q = 49 One digit natural numbers with only 3 exact factors are = 4 and 9 As, r>s Then r=9 s=4 p-q-1 25 - 49 - 1 Now, = r-s 9-4 25 = - 5 =–5 ⇒ –5=–4–1 =–s–1 3. If a nine-digit number 789x6378y is divisible by 72, then the value of xy is : (A) 10

(B) 12

(C) 8 (D) 15 [SSC CGL TIER-II CBE EXAM 03-02-2022 (I-Shift)]

3. (C) Number 789x6378y is given For divisibility by 72, the number must be divisible by 9 and 8 both : as 72 = 9 × 8. For divisibility by 8, the last 3 digits of number must be divisible by 8. Here last 3 digits = 78y The possible value for y = 4, as 784 is divisble by 8. Now, for divisibility by 9, the sum of digits of numbers must be divisible by 9. Sum of digits = 7 + 8 + 9 + x + 6 +3+7+8+y = 48 + x + 4 = 52 + x Possible value for x = 2, as 54 is divisible by 9. So, we have, x = 2 and y = 4 Then, xy = 2 × 4 = 8 4. If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is : 7 5 (A) 52 (B) 52 1 3 (C) 52 (D) 52 [SSC CGL TIER-II CBE EXAM 29-01-2022 (I-Shift)] 4. (B) Let the two positive numbers x and y \ x + y = 65

...(i)

xy = 26 xy = 676

...(ii)

x+ y 1 1 Required sum = x + y = xy 65 5 = 676 = 52 5. Let x = (433)24 – (377)38 + (166)54. What is the units digits of x ? (A) 8

(B) 9

(C) 7 (D) 6 [SSC CGL TIER-II CBE EXAM 29-01-2022 (I-Shift)] 5. (A) x = Unit digit of [(433)24 – (377)38 + (166)54]

= Unit digit of [{(433)4}6 – {(377)4}9 × (377)2 + {(166)4}13 × (166)2] = Unit digit of [1 – 1 × 9 + 6 × 6] = –2 = 10 – 2 = 8 6. If a 10-digit number 75462A97B6 is divisible by 72, then the value of 8A – 4B is : (A) (C)

30

(B)

27

(D) 28 21 [SSC CGL TIER-II CBE EXAM 29-01-2022 (I-Shift)]

6. (D) Given that 10 digit number 75462A97B6 To be divisible by 72 number should be divisible by 8 and 9 To divisible by 8, last 3 digits should be divisible by 8 So 7B6 should be divisible by 8 it is possible when B = 3 To be divisible by 9, sum of digits should be divisible by 9 \ sum of digits = 7 + 5 + 4 + 6 + 2 +A+ 9 + 7 + B + 6 = 46 + A + B = 46 + A + 3 = 49 + A To be divisible of (49 + A) by 9 A=5 \ 8A – 4B = 8 × 5 – 4 × 3 = 40 – 12 = 28 7. A divisor is 15 times the quotient and 3 times the remainder. If the remainder is 40, find the dividend. (A) 900

(B) 750

(C) 1000 (D) 600 [SSC CGL TIER-II CBE EXAM 18-11-2020] 7. (C) Given that divisor = 15 × quotient and divisor = 3 × remainder divisor = 3 × 40 divisor = 120 120 \ Quotient = 15 = 8 Mathematics | 1

We know that dividend = divisor × quotient + remainder = 120 × 8 + 40 = 1,000 8. Let ab, a ≠ b, is a 2-digit prime number such that ba is also a prime number. The sum of all such numbers is : (A) 407

(B) 418

(C) 396 (D) 374 [SSC CGL TIER-II CBE EXAM 16-11-2020] 8. (B) Possible cases of such prime number : (1) For prime number starting from 1, there are only two valid = 13, 17 (2) Similarly for 3, 7, 9, there are 31, 37, 71, 73, 79, 97 prime No. repsectively. So, total prime numbers are : 8 i.e., (13, 17, 31, 37, 71, 73, 79, 97) Total sum = [13 + 17 + 31 + 37 + 71 + 73 + 79 + 97] = 418 9. When positive numbers a, b and c are divided by 13, the remainders are 9, 7 and 10, respectively. What will be the remainder when (a + 2b + 5c) is divided by 13? (A) 8

(B) 9

(C) 5 (D) 10 [SSC CGL TIER-II CBE EXAM 16-11-2020] 9. (A) Given, a 13 ⇒ Remainder = 9 b 13 ⇒ Remainder = 7 c 13 ⇒ Remainder = 10 So, b a + 2b + 5c l ⇒ Remainder = ? 13 Taking sum of total remainder, as per given condition,



9 + 2 × 7 + 5 × 10 13 =

9 + 14 + 50 13

73 8 = 13 = 5 13 So, Remainder = 8 10. If the five-digit number 235xy is divisible by 3, 7 and 11, then what is the value of (3x – 4y) ? 2 |

(A) 10 (B) 8 (C) 9 (D) 5 [SSC CGL TIER-II CBE EXAM 16-11-2020] 10. (A) Given, No. 235xy is divisible by 3, 7, 11 Value of (3x – 4y) = ? Q Divisible rule for 3 = Sum of its digit is divisible by 3. Divisible rule for 7 and 11 are : (1) Make pair of 3 from unit digit and subtract left and the remainder should be divisible by 7 (2) in case to (11) : The difference of the sum of the digits at odd places and even places are 0 or divisible by 11. So, for, 3, x + y = 2 , 5, 8, 11 For 11, (y + 7) – (x + 3) = 0 or 11 y = 2, then, x = 6 x+y =8 For 7, 562 – 023 = 539 It is divisible by 7, then x = 6, y = 2 Now, 3x – 4y = 3 × 6 – 4 × 2 = 18 – 8 = 10 11. If the 5-digit number 535 ab is divisible by 3, 7 and 11, then what is the value of (a2 – b2 + ab) ? (A) 77 (B) 89 (C) 95 (D) 83 [SSC CGL TIER-II CBE EXAM 15-11-2020] 11. (C) If 5 digits number 535 ab is divisible by 3, 7 and 11, then we can say number also divisible by 231 because 3 × 7 × 11 = 231 Let, assume the largest number by 53599 Now on dividing 53599 by 231 We get approx 232.03 So, the actual number = 231 × 232 = 53592 \ a = 9 and b = 2 So, value of a2 – b2 + ab = 92 – 22 + 9 × 2 = 81 – 4 + 18 = 95 12. When positive numbers x, y and z are divided by 31, the remainders are 17, 24 and 27, respectively. When (4x – 2y + 3z) is divided by 31, the remainder will be : (A) 9 (B) 16 (C) 8 (D) 19 [SSC CGL TIER-II CBE EXAM 15-11-2020]

12. (C) If a number (x) is divided by (a) leaves ramainder (b), then x=a×n+b [where n in an integer] Let the number n = 1 x = 31 × 1 + 17 = 48 y = 31 × 1 + 24 = 55 z = 31 × 1 + 27 = 58 \ 4x – 2y + 3z = 4 × 48 – 2 × 55 + 3 × 58 = 256 = 31 × 8 + 8 So, when (4x – 2y + 3z) is divided by 31, the remainder will be 8. 13. Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is : (A) 1558 (B) 1458 (C) 1585 (D) 1485 [SSC CGL TIER-II CBE EXAM 15-11-2020] 13. (D) Let, the smaller number = x and the greater number = x + 1280 According to the question, Dividend = Quotient × Divisor + Remainder x + 1280 = 7 × x + 50 6x = 1280 – 50 6x = 1230 x = 205 \ Greater number = 205 + 1280 = 1485 14. If x is the remainder when 361284 is divided by 5 and y is the remainder when 496 is divided by 6. then what is the value of (2x –y) ? (A) –4 (B) 4 (C) –2 (D) 2 [SSC CGL TIER-II CBE EXAM 13-09-2019] 14. (C) (3) 61284 = (3 4 ) 15321 = (81) 15321 Dividing (81)15321 by 5, remainder =1=x [Using property (ax)y = ax × y] And Now, Dividing 41 by 6, remainder = 4 Dividing 42 by 6, remainder = 4 Dividing 43 by 6, remainder = 4 i.e., we can observe that, any power of 4 divide by 6 leaves a remainder of 4. \ Dividing 496 by 6, remainder =4=y \ 2x – y = 2 × 1 – 4 = – 2

15. If a 10-digit number 5432y1749x is divisible by 72, then what is the value of (5x –4y) ? (A) 14

(B) 15

(A) 6

(C) 10 (D) 9 [SSC CGL TIER-II CBE EXAM 13-09-2019] 15. (A) As we know, by the divisibility rule of 72, a number is divisible by 72 if it is divisible by 8 and 9 both. For divisibility by 8, Number 49x must be divisible by 8. For x = 6, 496 ÷ 8 = 62 Also for, divisibility by 9, Sum of digits = 41 + y must be divisible by 9. For y = 4, 45 ÷ 9 = 5 \ 5x – 4y = 5 × 6 – 4 × 4 = 30 – 16 = 14 16. What is the remainder when (12797 + 9797) is divided by 32 ? (A) 4 (B) 2 (C) 7 (D) 0 [SSC CGL TIER-II CBE EXAM 13-09-2019] 16. (D) By divisibility rule, (a + b) is a factor of (an + bn) if n is odd. \ One factor of (12797 + 9797) = 127 + 97 = 224 and 224 ÷ 32 = 7 \ Remainder = 0 17. Two positive numbers differ by 2001. When the larger number is divided by the smaller number, the quotient is 9 and the remainder is 41. The sum of the digits of the larger number is : (A) 15

18. If the 11-digit number of 5678x43267y is divisible by 72, then the value of 5x + 8y is :

18. (A) Divisibility rule of 72 : A number is exactly divisible by 72, if it is divisible by 8 and 9 both. Now, for divisibility by 8, The number formed by last three digits i.e., 67y must be divisible by 8. For y=2 ...(i) 672 ÷ 8 = 84 For divisibility by 9, Sum of digits = 5 + 6 + 7 + 8 + x + 4 + 3 + 2 + 6 + 7 + 2 = 50 + x. must be divisible by 9. For x = 4, ...(ii) 54 ÷ 9 = 6 by question, 5x + 8y = 5 × 4 + 8 × 2 =

19. If x = + (333)337 – (727)726, then what is the unit digit of x ? (A) 5



Unit digit in (333)337 = Unit’s digit of 333 = 3 



= 72 = 49 =9  Remainder of 726 ÷ 4 = 2  Required unit digit = 10 + 4 + 3 – 9 =8

...(i)

x = 9y + 41 x – 9y = 41 2001 + y – 9y = 41

From equation (i) 8y = 2001 – 41 = 1960 1960 ⇒ y = 8 = 245 \ x = 2001 + 245 = 2246 ⇒

\ Sum of digits = 2 + 2 + 4 + 6 = 14

Remainder of 337 ÷ 4 = 1

Unit digit of (727)726 will be

Again, ⇒

Remainder of 169 ÷ 4 = 1

Unit digit of 164 will be 41 = 4

17. (D) Let, the number be x and y where x > y.

\

(B) 7

(C) 8 (D) 9 [SSC CGL TIER-II CBE EXAM 12-09-2019] 19. (C) Unit digit in (164)169 = Unit digit of 164 = 4

(C) 10 (D) 14 [SSC CGL TIER-II CBE EXAM 13-09-2019]

x – y = 2001

36 = 6

(164)169

(B) 11

\

(B) 4

(C) 7 (D) 8 [SSC CGL TIER-II CBE EXAM 12-09-2019]

20. If a nine-digit number 389x6378y is divisible by 72, then the value of 6x + 7y will be : (A) 6 (C)

(B)

13

(D) 8 46 [SSC CGL TIER-II CBE EXAM 11-09-2019]

20. (D) We know that, by the divisibility rule of 72. A number is divisible by 72 if it is divisible by 8 and 9 both and, For divisibility by 8, 78y must be divisible by 8 which is true for y = 4. Again, for divisibility by 9. Sum of digits = 3 + 8 + 9 + x + 6 + 3 + 7 + 8 + 4 = 48 + x must be divisible by 9. When x = 6, then 48 + 6 = 54 which is divisible by 9. \ 6x + 7y = 6 × 6 + 7 × 4 = 36 + 28 = 64 = 8 21. When 12, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 4 but x is divisible by 7. What is the digit at the thousand's place in x ? (A) 5

(B) 8

(C) 4 (D) 3 [SSC CGL TIER-II CBE EXAM 11-09-2019] 21. (B) First, we find the LCM of 12, 16, 18, 20 and 25 \ L.C.M = 2 × 2 × 3 × 3 × 4 × 5 × 5 = 3600 \ Required number = 3600N + 4, which is divisible by 7. 3600N + 4 = 514x × 7 +2N + 4 Here, 2N + 4 is divisible by 7 for N = 5. \ x = 3600 × 5 + 4 = 18000 + 4 = 18004 \ Thousandth digit = 8 22. One of the factors of (82k + 52k), where k is an odd number, is : (A) 86

(B) 88

(C) 84 (D) 89 [SSC CGL TIER-II CBE EXAM 11-09-2019] 22. (D) We know that, When n = odd number, (an + bn) has a factor as (a + b). \ 82k + 52k = 64k + 25k \ Required factor = 64 + 25 = 89 23. Let x = (633)24 – (277)38 + (266)54. What is the unit's digit of x ? (A) 7

(B) 6

(C) 4 (D) 8 [SSC CGL TIER-II CBE EXAM 11-09-2019] Mathematics | 3

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