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D edicated to My Parents, Son, Daughter and My beloved wife

In his teaching career since 1992 Ashish Arora personally mentored more than 10000 IITians and students who reached global heights in various career and profession chosen. It is his helping attitude toward students with which all his students remember him in life for his contribution in their success and keep connections with him live. Below is the list of some of the successful students in International Olympiad personally taught by him. NAVNEET LOIWAL

International GOLD Medal in IPhO-2000 at LONDON , Also secured AIR-4 in IIT JEE 2000 PROUD FOR INDIA : Navneet Loiwal was the first Indian Student who won first International GOLD Medal for our country in International Physics Olympiad.

DUNGRA RAM CHOUDHARY HARSHIT CHOPRA KUNTAL LOYA

AIR-1 in IIT JEE 2002

National Gold Medal in INPhO-2002 and got AIR-2 in IIT JEE-2002 A Girl Student got position AIR-8 in IIT JEE 2002

LUV KUMAR

National Gold Medal in INPhO-2003 and got AIR-3 in IIT JEE-2003

RAJHANS SAMDANI

National Gold Medal in INPhO-2003 and got AIR-5 in IIT JEE-2003

SHANTANU BHARDWAJ SHALEEN HARLALKA

International SILVER Medal in IPhO-2002 at INDONESIA International GOLD Medal in IPhO-2003 at CHINA and got AIR-46 in IIT JEE-2003

TARUN GUPTA

National GOLD Medal in INPhO-2005

APEKSHA KHANDELWAL

National GOLD Medal in INPhO-2005

ABHINAV SINHA

Hon’ble Mension Award in APhO-2006 at KAZAKHSTAN

RAMAN SHARMA

International GOLD Medal in IPhO-2007 at IRAN and got AIR-20 in IIT JEE-2007

PRATYUSH PANDEY

International SILVER Medal in IPhO-2007 at IRAN and got AIR-85 in IIT JEE-2007

GARVIT JUNIWAL

International GOLD Medal in IPhO-2008 at VIETNAM and got AIR-10 in IIT JEE-2008

ANKIT PARASHAR

National GOLD Medal in INPhO-2008

HEMANT NOVAL

National GOLD Medal in INPhO-2008 and got AIR-25 in IIT JEE-2008

ABHISHEK MITRUKA

National GOLD Medal in INPhO-2009

SARTHAK KALANI

National GOLD Medal in INPhO-2009

ASTHA AGARWAL

International SILVER Medal in IJSO-2009 at AZERBAIJAN

RAHUL GURNANI

International SILVER Medal in IJSO-2009 at AZERBAIJAN

AYUSH SINGHAL

International SILVER Medal in IJSO-2009 at AZERBAIJAN

MEHUL KUMAR ABHIROOP BHATNAGAR AYUSH SHARMA AASTHA AGRAWAL

International SILVER Medal in IPhO-2010 at CROATIA and got AIR-19 in IIT JEE-2010 National GOLD Medal in INPhO-2010 International Double GOLD Medal in IJSO-2010 at NIGERIA Hon’ble Mension Award in APhO-2011 at ISRAEL and got AIR-93 in IIT JEE 2011

ABHISHEK BANSAL

National GOLD Medal in INPhO-2011

SAMYAK DAGA

National GOLD Medal in INPhO-2011

SHREY GOYAL

National GOLD Medal in INPhO-2012 and secured AIR-24 in IIT JEE 2012

RAHUL GURNANI

National GOLD Medal in INPhO-2012

JASPREET SINGH JHEETA

National GOLD Medal in INPhO-2012

DIVYANSHU MUND

National GOLD Medal in INPhO-2012

SHESHANSH AGARWAL

International SILVER Medal in IAO-2012 at KOREA

SWATI GUPTA

International SILVER Medal in IJSO-2012 at IRAN

PRATYUSH RAJPUT

International SILVER Medal in IJSO-2012 at IRAN

SHESHANSH AGARWAL

International BRONZE Medal in IOAA-2013 at GREECE

SHESHANSH AGARWAL

International GOLD Medal in IOAA-2014 at ROMANIA

SHESHANSH AGARWAL

International SILVER Medal in IPhO-2015 at INDIA and secured AIR-58 in JEE(Advanced)-2015

VIDUSHI VARSHNEY

International SILVER Medal in IJSO-2015 to be held at SOUTH KOREA

AMAN BANSAL

AIR-1 in JEE Advanced 2016

KUNAL GOYAL

AIR-3 in JEE Advanced 2016

GOURAV DIDWANIA

AIR-9 in JEE Advanced 2016

DIVYANSH GARG

International SILVER Medal in IPhO-2016 at SWITZERLAND

ABOUT THE AUTHOR

The complexities of Physics have given nightmares to many, but the homegrown genius of JaipurAshish Arora has helped several students to live their dreams by decoding it. Newton Law of Gravitation and Faraday’s Magnetic force of attraction apply perfectly well with this unassuming genius. A Pied Piper of students, his webportal https://www.physicsgalaxy.com, The world's largest encyclopedia of video lectures on high school Physics possesses strong gravitational pull and magnetic attraction for students who want to make it big in life. Ashish Arora, gifted with rare ability to train masterminds, has mentored over 10,000 IITians in his past 24 years of teaching sojourn including lots of students made it to Top 100 in IIT-JEE/JEE(Advance) including AIR-1 and many in Top-10. Apart from that, he has also groomed hundreds of students for cracking International Physics Olympiad. No wonder his student Navneet Loiwal brought laurel to the country by becoming the first Indian to win a Gold medal at the 2000 - International Physics Olympiad in London (UK). His special ability to simplify the toughest of the Physics theorems and applications rates him as one among the best Physics teachers in the world. With this, Arora simply defies the logic that perfection comes with age. Even at 18 when he started teaching Physics while pursuing engineering, he was as engaging as he is now. Experience, besides graying his hair, has just widened his horizon. Now after encountering all tribes of students - some brilliant and some not-so-intelligent - this celebrated teacher has embarked upon a noble mission to make the entire galaxy of Physics inform of his webportal PHYSICSGALAXY.COM to serve and help global students in the subject. Today students from 221 countries are connected with this webportal. On any topic of physics students can post their queries in INTERACT tab of the webportal on which many global experts with Ashish Arora reply to several queries posted online by students. Dedicated to global students of middle and high school level, his website www.physicsgalaxy.com also has teaching sessions dubbed in American accent and subtitles in 87 languages. For students in India preparing for JEE & NEET, his online courses will be available soon on PHYSICSGALAXY.COM.

FOREWORD New generation students need to acquire more of outcome based approach with abilities to solve problems. It is well known that case or design based studies are more impactful in delivering such attributes to students. The book titled “Step by Step Approach to Mental Ability for NTSE” contributed by very seasoned expert Er. Ashish Arora is a well thought of masterwork in this direction. It is interesting to note that this book covers more than 1800 questions with specified hints and solutions of Mental Ability divided in 21 chapters with required illustrations. The chapters in the book cover all aspects of the subject asked in MAT paper of NTSE with fundamental knowledge to understand the examination edge of National Talent Search Exam. The chapters in the book are categories in step wise manner to build logical, analytical and manipulative skills in cases of verbal and non-verbal reasoning to a level which is not only useful for MAT paper of NTSE but it will also enhance the abilities required for a student to improve grasping at root level in all higher classes for all the subjects. I am confident that potential aspirants will find this book most suitable to enhance understanding of the subject as well as improve their performance in all competitive examinations.

March, 2019

Prof. Sandeep Sancheti Ph. D. (U.K.), B.Tech. FIETE, MIEEE VC, SRMIST, Chennai & President, AIU, New Delhi

PREFACE Class X is the milestone when a student studies all the subject in school academics for the last time. Right after class X students need to choose the stream in which they wish to opt their career in life. It is the time when the overall aptitude of a student must be judged at National level for right decision toward their career. During this year along with school academics students have one and only opportunity to appear in one of the most prestigious scholarship competition - National Talent Search Examination (NTSE). This exam judges the academic, language and mental ability of a student and on the basis of merit in two stages about 1000 students in India are selected for this prestigious scholarship. The exam consist of three sections-Scholastic Aptitude Test (SAT), Language Test (LT) and Mental Ability Test (MAT). First section SAT (100 marks) is based on the academics of classes IX and X, which includes the subjects Physics, Chemistry, Biology, Maths and Social Studies. Student can prepare for this section along with their school studies. The second section LT(50 marks) is based on the basic verbal part of the languages Hindi and English. Students can also prepare for this section along with their routine studies. The third section MAT which is also of same weightage (50 marks) is based on mental ability and IQ of student. There is only one way of getting good knowledge in this section is by systematic practice. This book is designed in such a way that a student can excel in Mental Ability, by self preparation at home. At the end of book six actual Mental Ability Stage I, 2013 Tests of various states and NTSE Mental Ability stage II, 2013 National paper are included for final practice. Students are advised to attempt these tests only after finishing all the practice exercises in each step of the book. I am very much thankful to my best friend, my wife Anuja for helping me in preparation of the book, without her I could not think to make this book in a proper format. I am very grateful to my father and mother for their inspiration and encouragement to complete the book in the best possible way. I am also thankful for the EDP editor of this book Mr. Dayashankar Prajapati for completing the type setting of this book in a new style and format. In this new edition I have tried my best to make this book error free but owing to the nature of work, inadvertently, there is possibility of errors left untouched. I shall be grateful to the readers, if they point out me regarding errors and oblige me by giving their valuable and constructive suggestions for further improvement of the book on my mail ID.

Date : March, 2019

Ashish Arora PHYSICSGALAXY.COM B-80, Model Town, Malviya Nagar, Jaipur-302017 e-mails: [email protected] [email protected]

CONTENTS Step-1

Number Series

… 01-12

Step-2

Odd-one out (Numbers)

… 13-16

Step-3

Missing Number

… 17-32

Step-4

Letter Series

… 33-40

Step-5

Coding and Decoding

… 41-54

Step-6

Time Sequence

… 55-60

Step-7

Direction Sense

… 61-68

Step-8

Directory

… 69-72

Step-9

Ranking and Ordering

… 73-90

Step-10 Counting of Figures

… 91-96

Step-11 Mirror Images

… 97-102

Step-12 Water Images

… 103-106

Step-13 Analogy

… 107-119

Step-14 Odd One Out Words

… 120-124

Step-15 Cubes and Dices

… 125-140

Step-16 Venn Diagram

… 141-166

Step-17 Relationship

… 167-176

Step-18 Coding of Arithmetic signs

… 177-182

Step-19 Non Verbal Reasoning Ability

… 183-273

Step-20 Logical Reasoning

… 274-288

Step-21 Miscellaneous

… 289-306

Hints and Answers

… 307-374

______

S t e p

NUMBER SERIES Number series consist of sequence of some numbers which follow a set pattern. You are required to observe the specific order in which number of figure would fill the blank space, if they continue to change in the same order or sometimes you have to find the wrong term in the series.

5.

6.

Example 1 Find the next number of the given sequence = 3, 9, 27, 81, (.......) (a) 96 (b) 143 (c) 243 (d) 162

7.

Answer : (c) Clearly, the series is of pattern = x, x × 3 and so on.

8.

Example 2 9. Which number will replace the ‘?’ 7, 13, ?, 25, 31. (a) 19 (b) 20 (c) 21 (d) 22 Answer : (a) Clearly, the series is of pattern x, x + 6 and so on. ? 7, 7 + 6 = 13, 13 + 6 = 19, 19 + 6 = 25, 25 + 6 = 31.

Practice Exercise 1

Time Limit : 30 Min.

Directions : Find the missing term.

1.

2.

3.

4.

4, 9, 16, 25, (.......) (a) 32 (c) 55

(b) 42 (d) 36

4, 9, 19, 34, 54, (.......), 109 (a) 89 (b) 84 (c) 74 (d) 79 1, 4, 9, 16, 25, (.......) (a) 35 (c) 48

(b) 36 (d) 49

4, 11, 7, 14, 10, 17, (.......) (a) 24 (b) 13 (c) 20 (d) 21

5, 15, 25, (.......) (a) 30 (c) 35

(b) 20 (d) 125

2, 5, 8, 11, 14, (.......) (a) 18 (c) 19

(b) 17 (d) 16

1, 6, 13, 22, 33, (.......) (a) 44 (c) 46

(b) 45 (d) 47

3, 15, 35, 63, 99, (.......) (a) 144 (c) 121

(b) 143 (d) 169

3, 6, 15, (.......), 123, 366, (a) 34 (b) 59 (c) 42 (d) 60

10. 96, 90, 78, (.......), 36, 6 (a) 60 (c) 72 11.

(b) 54 (d) 48

80, 64, 48, 32, 16, (.......) (a) 4 (b) 0 (c) 8 (d) 1

12. 1, 9, 17, 33, 49, 73, (.......) (a) 97 (b) 98 (c) 99 (d) 100 13. –1, 0, 3, 8, (.......) (a) 13 (c) 11

(b) 12 (d) 15

14. 121, 225, 361, (.......) (a) 441 (c) 529

(b) 484 (d) 729

15. 9, 81, 90, 810, 819, (.......) (a) 7371 (b) 900 (c) 8100 (d) 1638 16. 5, 3, 6, 2, 7, 1, (.......) (a) 0 (c) 8

(b) 2 (d) 4

2

Step-1 Number Series

17. 2, 7, 14, 23, (.......), 47 (a) 30 (c) 39

(b) 34 (d) 44

18. 1, 1, 6, 6, 11, 11, (.......) (a) 11 (c) 16

(b) 13 (d) 17

19. 3, 12, 48, 192, (.......) (a) 202 (c) 768

(b) 301 (d) 689

20. 12, 32, 72, 152, (.......) (a) 312 (c) 515

(b) 325 (d) 613

21. 2, 3, 5, 6, 7, 9, 10, 11, 13, (.......) (a) 12 (b) 15 (c) 14 (d) 16 22. 5, 8, 12, 17, 23, (.......), 38 (a) 26 (b) 28 (c) 30 (d) 29 23. 4, 32, 128, (.......) (a) 128 (c) 192

(b) 144 (d) 256

Practice Exercise 2

Time Limit : 30 Min.

Directions : Find the missing term.

6.

2, 4, 8, 3, 9, 27, 4, 16, (.......) (a) 64 (b) 32 (c) 48 (d) 24

7.

D-23, F-21, H-19, J-17, (.......) (a) K-18 (b) M-18 (c) O-21 (d) L-15

8.

19200, 1920, 240, 40, 10, (.......) (a) 1 (b) 0 (c) 5 (d) 10

9.

C3, F6, I9, L12, (.......) (a) O13 (c) P15

(b) Q17 (d) O15

10. 5, 16, 49, 104, (.......) (a) 115 (c) 170

(b) 148 (d) 181

11.

55, 45, 36, 28, 21, (.......) (a) 11 (b) 16 (c) 15 (d) 17

12. 97, 86, 73, 58, 45, (.......) (a) 34 (b) 54 (c) 55 (d) 56 13. 128, 64, 32, 16, (.......), 4 (a) 10 (b) 8 (c) 6 (d) 12

1.

4, 10, (.......) 82, 244, 730 (a) 24 (b) 28 (c) 77 (d) 218

2.

5, 9, 16, 29, 54, 103, (.......) (a) 102 (b) 94 (c) 103 (d) 200

3.

C-2, E-3, G-4, I-5, (.......) (a) H-6 (b) J-8 (c) K-6 (d) L-7

16. 30, 23, 17, 12, (.......), 5 (a) 6 (c) 8

4, 9, 20, 43, 90, (.......) (a) 180 (c) 179

17. 17, 27, 37, 56, 66, (.......) (a) 67 (b) 76 (c) 82 (d) 97

4.

5.

(b) 182 (d) 185

165, 195, 255, 285, 345, (.......) (a) 375 (b) 420 (c) 435 (d) 390

14. 6, 11, 18, 27, 38, (.......), 66 (a) 58 (b) 54 (c) 51 (d) 59 15. 6.25, 9, 12.25, 16, 20.25, 25, 30.25, (.......) (a) 36 (b) 32 (c) 28.25 (d) 40.25

18. 4, 5, 7, (.......), 19 (a) 8 (c) 10

(b) 7 (d) 9

(b) 9 (d) 11

Step-1 Number Series

19.

3

1 1 2 2 11 , 12 , 14 , 16 , (.......) 9 2 7 3 1 1 (a) 8 (b) 9 11 3 (c) 10 (d) 20

20. 1, 4, 5, 11, 9, 18, (.......), 25 (a) 12 (b) 13 (c) 19 (d) 23 21. 68, 81, 96, (.......), 132 (a) 105 (c) 130

(b) 110 (d) 113

22. 2, 7, 11, 8, 13, 17, 14, 19, 23, (.......) (a) 22 (b) 20 (c) 18 (d) 25 23. 11, 10, (......), 100, 1001, 1000, 10001 (a) 101 (b) 110 (c) 111 (d) None of these

Practice Exercise 3

Time Limit : 30 Min.

Directions (Q. 1-5) : In each of the following questions, one term in the number series is wrong. Find out the wrong term. 1.

2.

3.

4.

5.

49, 48, 45, 42, 33, 24, 13 (a) 48 (b) 45 (c) 42 (d) 33 (e) 24 1, 4, 7, 11, 16, 22, 29 (a) 1 (c) 22 (e) 29

(b) 7 (d) 11

2, 5, 10, 18, 26, 37, 50 (a) 2 (c) 37 (e) 50

(b) 5 (d) 18

3, 10, 19, 31, 43, 58, 75 (a) 31 (c) 58 (e) 19

(b) 43 (d) 10

720, 120, 24, 8, 2, 1, 1 (a) 1 (c) 24 (e) 120

(b) 2 (d) 8

Directions (Q. 6-8) : Find the missing term. 6.

13, 32, 24, 43, 35, (.......), 46, 65, 57, 76 (a) 45 (b) 52 (c) 54 (d) 55

7.

9, 17, 19, 27, 29, (.......), 39 (a) 38.5 (b) 38 (c) 37 (d) 37.5

8.

840, 168, 42, 14, 7, (.......) (a) 1 (b) 7 (c) 9 (d) 12

Directions (Q. 9-17) : In each of the following series, one term is wrong. Select the answer from the given options. 9.

10, 100, 1100, 11000, 111000, 1210000 (a) 1210000 (b) 11000 (c) 100 (d) 111000

10. 24576, 6144, 1536, 386, 96, 24 (a) 386 (b) 6144 (c) 96 (d) 1536 11.

36, 43, 49, 54, 60, 61, 63, 64 (a) 60 (b) 63 (c) 54 (d) 43

12. 3, 10, 41, 206, 1236, 8660 (a) 10 (b) 41 (c) 206 (d) 1236 13. 17, 25, 37, 50, 65, 82, 101 (a) 25 (b) 17 (c) 101 (d) 65 14. 8, 13, 21, 32, 47, 63, 83 (a) 47 (c) 32

(b) 13 (d) 83

15. 7, 14, 56, 168, 336, 1344, 2688, 8064 (a) 1344 (b) 56 (c) 2688 (d) 8064 16. 36, 49, 100, 144, 196, 256, 324 (a) 100 (b) 49 (c) 256 (d) 144 17. 105, 85, 60, 30, 0, –45, –90 (a) 0 (b) 30 (c) 85 (d) – 45

4

Step-1 Number Series

Directions (Q. 18-20) : Find the missing term. 18.

4.

2 3 4 5 , , , , (......) 5 25 5 5 5

(a)

6 5 5

(b)

6 25 5

(c)

6 125

(d)

7 25

19. 1, 3, 7, 15, 31, (.......) (a) 38 (c) 63

5.

6. (b) 49 (c) 42

20. 48, 24, 72, 36, 108, (.......) (a) 110 (b) 115 (c) 121 (d) 54 This section consists of questions as choosing a similarly related pair as the given pair on basis of the relationship, between the numbers in the each pair or sometimes to choose another group of numbers on basis of certain characteristics.

7.

8.

3 : 11 : : 7 : ? (a) 22 (c) 18 (e) 21

(b) 29 (d) 51

6 : 18 : : 4 : ? (a) 2 (c) 8 (e) 4

(b) 6 (d) 16

7 : 11 : : 31 : ? (a) 36 (c) 37 (e) 45

(b) 39 (d) 43

121 : 12 : : 25 : ? (a) 1 (c) 6 (e) 4

(b) 2 (d) 7

01 : 08 : : 16 : ? (a) 25 (c) 64 (e) 81

(b) 125 (d) 27

7528 : 5306 : : 4673 : ? (a) 2367 (c) 2531 (e) None of these

(b) 2451 (d) 2617

Example 3 9. Find the pair which have same relationship as the given pair = 5 : 35 (a) 7 : 77 (b) 9 : 45 (c) 11 : 55 (d) 3 : 24 Answer : (a) Clearly, 5 : 35 (based on relation as x × next prime no.) so, 7 × next prime no. i.e. 11 = 7 × 11 = 77 = 7 : 77 is the correct answer.

10. 01 : 04 : : 08 : ? (a) 96 (c) 72 (e) 49 11.

Practice Exercise 4

Time Limit : 30 Min.

Directions : Find the missing term of the pair. 1.

2.

3.

6:9::8:? (a) 14 (c) 25 (e) 20

(b) 81 (d) 64

(b) 64 (d) 27

(b) 1/3 (d) 1/7

12. 25 : 37 : : 49 : ? (a) 41 (c) 60 (e) 50

(b) 56 (d) 65

09 : 25 : : 49 : ? (a) 63 (c) 64 (e) 100

(b) 36 (d) 81

13. 6 : 24 : : 5 : ? (a) 23 (c) 25 (e) 20

(b) 22 (d) 27

12 : 35 : : 16 : ? (a) 32 (c) 49 (e) 45

(b) 48 (d) 63

14. 25 : 125 : : 36 : ? (a) 180 (c) 216 (e) 72

(b) 206 (d) 318

1/4 : 1/8 : : 2/3 : ? (a) 1/4 (c) 1/2 (e) 1/7

Step-1 Number Series

5

15. 17 : 52 : : 1 : ? (a) 3 (c) 5 (e) 10

(b) 4 (d) 51

16. 3 : 7 : : 08 : ? (a) 10 (c) 17 (e) 16

(b) 13 (d) 14

17. 7 : 56 : : 9 : ? (a) 63 (c) 90 (e) 80

(b) 81 (d) 99

8.

Given set : (246, 257, 358) choose the number which is similar to given set : (a) (145, 235, 325) (b) (143, 253, 246) (c) (273, 365, 367) (d) (233, 343, 345)

18. 8 : 81 : : 64 : ? (a) 125 (c) 525 (e) 136

(b) 137 (d) 625

9.

6 : 35 : 11 : ? (a) 120 (c) 122 (e) 124

Practice Exercise 5

6.

Time Limit : 30 Min.

1.

Given set : 363, 489, 579, choose the number which is similar to the given set : (a) 562 (b) 471 (c) 382 (d) 281 (e) All of the above

2.

5 : 8 : : 15 : ? (a) 19 (c) 18 (e) 17

3.

4.

5.

(b) 20 (d) 21

Given set : 538, 725, 813, find the member of given set : (a) 814 (b) 712 (c) 328 (d) 219 (e) 217 3:3

3 (b) 6 8 5 (d) 2 8

(b) 9 (d) 13

3 : 27 : : 4 : ? (a) 140 (c) 100 (e) 64

(b) 75 (d) 80

(b) 115 (d) 121

Directions (Q. 10-11) : Each of the following questions consists of a pair of numbers that have a certain relationship to each other, followed by four other pairs of numbers given as alternatives. Select the pair in which the numbers are similarly related as in the given pair. 10. 27 : 9 (a) 64 : 8 (c) 135 : 15 11.

Given set : 992, 733, 845, 632, find the next member of group: (a) 114 (b) 326 (c) 425 (d) 947 (e) 131

3 :: 5:? 8 5 (a) 5 8 1 (c) 5 8 5 (e) 6 8

7.

1:5::7:? (a) 8 (c) 15 (e) 11

11 : 1210 (a) 6 : 216 (c) 8 : 448

(b) 125 : 5 (d) 729 : 81

(b) 7 : 1029 (d) 9 : 729

12. Find a group similar to (3, 7, 11) (a) 2, 9, 21 (b) 2, 17, 23 (c) 4, 6, 14 (d) 7, 9, 16 13. Given set : (49, 25, 9) (a) (36, 16, 4) (c) (39, 26, 13)

(b) (36, 25, 16) (d) (64, 27, 8)

14. Given set : (21, 51, 15) (a) (21, 30, 51) (c) (21, 51, 42)

(b) (21, 35, 41) (d) (21, 91, 35)

15. Given set : (9, 15, 21) (a) (10, 14, 16) (c) (5, 10, 25)

(b) (7, 21, 28) (d) (4, 8, 12)

6

Step-1 Number Series

16. 11 : 17 : : 19 : ? (a) 23 (c) 33

7. (b) 27 (d) 21

17. Which number is like the given set of numbers ? Given set : (3, 17, 31) (a) 5 (b) 15 (c) 45 (d) 49

8.

Practice Exercise 6 (Previous Years Questions)

9.

1.

2.

3.

4.

5.

5, 9, 16, 29, 54, 103, ? (a) 94 (c) 103 (e) 202

(b) 102 (d) 200

4, 5, 7, 10, 11, 13, 16, ? (a) 48 (c) 20 (e) 18

(b) 38 (d) 19

2, 5, 10, 17, ?, 37, 50 (a) 21 (c) 26 (e) 50

(b) 23 (d) 37

3, 9, 17, 27, ? (a) 33 (c) 39 (e) 41

(b) 37 (d) 40

47, 53, 59, ?, 67, 71 (a) 61 (c) 64 (e) 66

(b) 63 (d) 65

Directions (Q. 6-7) : Find the wrong number in the series : [Mizoram 2012-13] 6.

2, 3, 4, 4, 6, 8, 9, 12, 16 (a) 3 (c) 6 (e) 9

(b) 4 (d) 8

(b) 52 (d) 8

Directions (Q. 8-12) : In each question there is a number series with one term missing shown by question mark (?). This term is one of the alternatives among the four numbers given under it. That number is : [Rajasthan 2012-13]

18. As 425 is related to 2, in the same way 613 is related to : (a) 1 (b) 2 (c) 3 (d) 4

Directions (Q. 1-5) : In each of the following questions, the numbers are arranged in a particular order or pattern. Choose the missing number from the given alternatives. [Mizoram 2012-13]

2, 8, 18, 32, 52, 72 (a) 32 (c) 72 (e) 18

2, 30, 6, 20, 12, 12, (?) (a) 26 (c) 20

(b) 22 (d) 24

6, 20, 36, 48, 50, (?), 0 (a) 36 (c) 46

(b) 40 (d) 56

10. 7, 15, 28, 59, 114, (?) (a) 243 (c) 213 11.

25, 49, 89, 145, 217, (?) (a) 305 (c) 309

(b) 233 (d) 223

(b) 327 (d) 303

12. 0, 2, 2, 3, 3, 5, 8, 4, 10, (?), 5, 17 (a) 6 (b) 7 (c) 9 (d) 15 Directions (Q. 13-17) : These questions consists of a number series which contains a wrong term. This term is given as one of the four alternatives among the four numbers given below. The wrong term is : [Rajasthan 2012-13] 13. 89, 78, 86, 80, 85, 82, 83 (a) 83 (b) 82 (c) 86 (d) 78 14. 1, 1, 3, 9, 6, 36, 10, 100, 16, 225 (a) 225 (b) 16 (c) 10 (d) 9 15. 444, 300, 200, 136, 87, 84, 80 (a) 300 (b) 200 (c) 136 (d) 87 16. 8, 15, 31, 61, 123, 247, 491 (a) 247 (b) 491 (c) 121 (d) 61 17. 3, 6, 24, 30, 63, 72, 122, 132 (a) 132 (b) 30 (c) 122 (d) 72

Step-1 Number Series

7

Directions (Q. 18-27) : In the number series given below, one number is missing. Each series is followed by five alternatives (a), (b), (c), (d) and (e). One of them is the right answer. Identify and indicate it as per the “instructions”. [Andhra Pradesh 2012-13]

Directions (Q. 28-31) : Complete the given series in each questions: [Delhi 2012-13] 28. 50, 55, 61, 68, ................. (a) 81 (b) 80 (c) 75 (d) 76

18. 2, 7, 17, 32, …… (a) 42 (c) 47 (e) 62

(b) 52 (d) 27

19. 72, 63, 54, 45, …… (a) 36 (c) 27 (e) 18

(b) 81 (d) 90

20. 3, 8, 18, ……, 78 (a) 38 (c) 28 (e) 58

(b) 50 (d) 48

31. Complete the series: 5, 6, 10, 19, 35, ................. (a) 50 (b) 60 (c) 40 (d) 70

21. 3, 7, 14, 24, …… (a) 34 (c) 38 (e) 37

(b) 28 (d) 40

32. Find the next number in the sequence 0, 2, 24, 252 . ______ [National Level 2012-13] (a) 620 (b) 1040 (c) 3120 (d) 5430

22. 12, 15, 19, 24, …… (a) 29 (c) 30 (e) 31

(b) 32 (d) 34

33. Find the next number in the sequence 6, 24, 60, 120 ______ [National Level 2012-13] (a) 180 (b) 210 (c) 240 (d) 360

23. 150, 140, 125, 105, …… (a) 90 (b) 80 (c) 85 (d) 75 (e) 95 24. 231, 342, 453, 564, …… (a) 576 (b) 475 (c) 675 (d) 567 (e) 676 25. 796, 675, 554, 433, …… (a) 512 (b) 231 (c) 213 (d) 312 (e) 321 26. 243, 81, ……, 9, 3 (a) 28 (c) 23 (e) 45

(b) 27 (d) 29

27. 1, 5, 13, 29, …… (a) 60 (c) 59 (e) 45

(b) 61 (d) 42

29. 144, 121, 100, 81, ................. (a) 80 (b) 72 (c) 64 (d) 60 30. 2197, 2744, 3375, 4096, ................. (a) 4761 (b) 4232 (c) 4913 (d) 3291

34. Find the missing number in the series 2, 10, 26, _____, 242 [National Level 2012-13] (a) 80 (b) 81 (c) 82 (d) 84 Directions (Q. 35-38) : In each of the questions 35 to 38 some of the numbers are missing in the given series with one term missing shown by question mark (?). This term is one of the alternatives among the four numbers given under it. Find the right alternative. [Rajasthan 2013-14] 35. 5, 10, 17, 26, 37, 50, (?) (a) 70 (c) 65

(b) 66 (d) 64

36. 6, 25, 62, 123, (?), 341 (a) 216 (c) 215

(b) 214 (d) 217

37. 5, 3, 10, 8, 17, 15, (?), 24 (a) 26 (b) 27 (c) 29 (d) 36