SSC CGL TIER I & II COMBINED GRADUATE LEVEL

2019-2021

51 SETS O O O O O

SOLVED PAPERS WITH DETAILED EXPLANATIONS

22 SETS of SSC CGL Tier-I EXAM Held in 2019 06 SETS of SSC CGL Tier-II EXAM Held in 2019 18 SETS of SSC CGL Tier-I EXAM Held in 2020 02 SETS of SSC CGL Tier-II EXAM Held in 2020 03 SETS of SSC CGL Tier-I EXAM Held in 2021

FOR FRANCHISEE CONTACT :

RU-67, PITAMPURA, DELHI-110034, Ph : 9821874015, 9821643815 SGE/2019/ 1

Delhi : RU-67, Opposite Power House,

For the books & magazines of Kiran Prakashan contact your nearest booksellers. For detailed information log on our website :

Pitampura, Delhi-110034, Ph. : 9821874015, 9821643815 www.kiranprakashan.com

www.kiranprakashan.com

© KIRAN INSTITUTE OF CAREER EXCELLENCE PVT. LTD. (KICX) NEW EDITION The copyright of this book is entirely with the Kiran Institute of Career Excellence Pvt. Ltd. The reproduction of this book or a part of this will be punishable under the Copyright Act. All disputes subject to Delhi jurisdiction. Every possible effort has been made to ensure that the information contained in this book is accurate at the time of going to press, and the publishers and authors cannot accept responsibility for any errors or omissions, however caused. No responsibility for loss or damage occasioned to any person acting, or refraining from action, as a result of the material in this publication can be accepted by the editor, the publisher or any of the authors.

Price : Rs. 555.00 (Rupees Five Hundred and Fifty Five Only) Reviewed by : Think Tank of PRATIYOGITA KIRAN & KIRAN PRAKASHAN Assistance : O Govind Pd. Singh O Rakesh Kumar O Satyendra Singh O Auranjeb Khan O Sanket Sah Design & Layout by : KIRAN COMPUTER SECTION, New Delhi. Printed at :

Must Read

Price :

625

USEFUL FOR ALL COMPETITIVE EXAMS

Price :

299

SGE/2019/ 2

Buy Today

Price :

295

Contents Solved Papers–2019 SET – 01 SET – 02 SET – 03 SET – 04 SET – 05 SET – 06 SET – 07 SET – 08 SET – 09 SET – 10 SET – 11 SET – 12 SET – 13 SET – 14 SET – 15 SET – 16 SET – 17 SET – 18 SET – 19 SET – 20 SET – 21 SET – 22 SET – 23

: : : : : : : : : : : : : : : : : : : : : : :

SET – 24

:

SET – 25

:

SET – 26

:

SET – 27

:

SET – 28

:

SSC CGL Tier-I (CBE) EXAM, Held on : 04.06.2019 (Shift-I) ............. SGE/2019/ 5 SSC CGL Tier-I (CBE) EXAM, Held on : 04.06.2019 (Shift-II) .......... SGE/2019/ 18 SSC CGL Tier-I (CBE) EXAM, Held on : 04.06.2019 (Shift-III) ......... SGE/2019/ 30 SSC CGL Tier-I (CBE) EXAM, Held on : 06.06.2019 (Shift-I) ........... SGE/2019/ 42 SSC CGL Tier-I (CBE) EXAM, Held on : 06.06.2019 (Shift-II) .......... SGE/2019/ 55 SSC CGL Tier-I (CBE) EXAM, Held on : 06.06.2019 (Shift-III) ......... SGE/2019/ 68 SSC CGL Tier-I (CBE) EXAM, Held on : 07.06.2019 (Shift-I) ........... SGE/2019/ 80 SSC CGL Tier-I (CBE) EXAM, Held on : 07.06.2019 (Shift-II) .......... SGE/2019/ 92 SSC CGL Tier-I (CBE) EXAM, Held on : 07.06.2019 (Shift-III) ...... SGE/2019/ 105 SSC CGL Tier-I (CBE) EXAM, Held on : 10.06.2019 (Shift-I) ........ SGE/2019/ 118 SSC CGL Tier-I (CBE) EXAM, Held on : 10.06.2019 (Shift-II) ....... SGE/2019/ 130 SSC CGL Tier-I (CBE) EXAM, Held on : 10.06.2019 (Shift-III) ...... SGE/2019/ 142 SSC CGL Tier-I (CBE) EXAM, Held on : 11.06.2019 (Shift-I) ........ SGE/2019/ 154 SSC CGL Tier-I (CBE) EXAM, Held on : 11.06.2019 (Shift-II) ....... SGE/2019/ 165 SSC CGL Tier-I (CBE) EXAM, Held on : 11.06.2019 (Shift-III) ...... SGE/2019/ 177 SSC CGL Tier-I (CBE) EXAM, Held on : 12.06.2019 (Shift-I) ........ SGE/2019/ 188 SSC CGL Tier-I (CBE) EXAM, Held on : 12.06.2019 (Shift-II) ....... SGE/2019/ 200 SSC CGL Tier-I (CBE) EXAM, Held on : 12.06.2019 (Shift-III) ...... SGE/2019/ 211 SSC CGL Tier-I (CBE) EXAM, Held on : 13.06.2019 (Shift-I) ........ SGE/2019/ 222 SSC CGL Tier-I (CBE) EXAM, Held on : 13.06.2019 (Shift-II) ....... SGE/2019/ 234 SSC CGL Tier-I (CBE) EXAM, Held on : 13.06.2019 (Shift-III) ...... SGE/2019/ 245 SSC CGL Tier-I (CBE) EXAM, Held on : 16.06.2019 (Shift-III) ...... SGE/2019/ 256 SSC CGL Tier-II (CBE) EXAM-2018, Held on : 11.09.2019 Quantitative abilities. ........................................................................................SGE/2019/ 267 SSC CGL Tier-II (CBE) EXAM-2018, Held on : 11.09.2019 English Language & Comprehension .........................................................SGE/2019/ 284 SSC CGL Tier-II (CBE) EXAM-2018, Held on : 12.09.2019 Quantitative Abilities ........................................................................................SGE/2019/ 306 SSC CGL Tier-II (CBE) EXAM-2018, Held on : 12.09.2019 English Language & Comprehension .........................................................SGE/2019/ 323 SSC CGL Tier-II (CBE) EXAM-2018, Held on : 13.09.2019 Quantitative Abilities ........................................................................................SGE/2019/ 344 SSC CGL Tier-II (CBE) EXAM, 2018, Held on : 13.09.2019 English Language & Comprehension .........................................................SGE/2019/ 361 SGE/2019/ 3

Solved Papers–2020 SET – 29

: SSC CGL Tier-I (CBE) EXAM, Held on : 03.03.2020 (Shift-I) ........ SGE/2020/ 385

SET – 30

: SSC CGL Tier-I (CBE) EXAM, Held on : 03.03.2020 (Shift-II) ....... SGE/2020/ 397

SET – 31

: SSC CGL Tier-I (CBE) EXAM, Held on : 03.03.2020 (Shift-III) ...... SGE/2020/ 410

SET – 32

: SSC CGL Tier-I (CBE) EXAM, Held on : 04.03.2020 (Shift-I) ........ SGE/2020/ 423

SET – 33

: SSC CGL Tier-I (CBE) EXAM, Held on : 04.03.2020 (Shift-II) ....... SGE/2020/ 437

SET – 34

: SSC CGL Tier-I (CBE) EXAM, Held on : 04.03.2020 (Shift-III) ...... SGE/2020/ 451

SET – 35

: SSC CGL Tier-I (CBE) EXAM, Held on : 05.03.2020 (Shift-I) ........ SGE/2020/ 465

SET – 36

: SSC CGL Tier-I (CBE) EXAM, Held on : 05.03.2020 (Shift-II) ....... SGE/2020/ 480

SET – 37

: SSC CGL Tier-I (CBE) EXAM, Held on : 05.03.2020 (Shift-III) ...... SGE/2020/ 495

SET – 38

: SSC CGL Tier-I (CBE) EXAM, Held on : 06.03.2020 (Shift-I) ........ SGE/2020/ 510

SET – 39

: SSC CGL Tier-I (CBE) EXAM, Held on : 06.03.2020 (Shift-II) ....... SGE/2020/ 525

SET – 40

: SSC CGL Tier-I (CBE) EXAM, Held on : 06.03.2020 (Shift-III) ...... SGE/2020/ 538

SET – 41

: SSC CGL Tier-I (CBE) EXAM, Held on : 07.03.2020 (Shift-I) ........ SGE/2020/ 552

SET – 42

: SSC CGL Tier-I (CBE) EXAM, Held on : 07.03.2020 (Shift-II) ....... SGE/2020/ 565

SET – 43

: SSC CGL Tier-I (CBE) EXAM, Held on : 07.03.2020 (Shift-III) ...... SGE/2020/ 579

SET – 44

: SSC CGL Tier-I (CBE) EXAM, Held on : 09.03.2020 (Shift-I) ........ SGE/2020/ 593

SET – 45

: SSC CGL Tier-I (CBE) EXAM, Held on : 09.03.2020 (Shift-II) ....... SGE/2020/ 606

SET – 46

: SSC CGL Tier-I (CBE) EXAM, Held on : 09.03.2020 (Shift-III) ...... SGE/2020/ 620

SET – 47

: SSC CGL Tier-II (CBE) EXAM-2018, Held on : 18.11.2020 Quantitative Abilities ........................................................................................SGE/2020/ 633

SET – 48

: SSC CGL Tier-II (CBE) EXAM, 2018, Held on : 11.11.2020 English Language & Comprehension .........................................................SGE/2020/ 653

Solved Papers–2021 SET – 49

: SSC CGL Tier-I (CBE) EXAM, Held on : 13.08.2021 (Shift-I) ........ SGE/2021/ 677

SET – 50

: SSC CGL Tier-I (CBE) EXAM, Held on : 17.08.2021 (Shift-I) ........ SGE/2021/ 692

SET – 51

: SSC CGL Tier-I (CBE) EXAM, Held on : 20.08.2021 (Shift-I) ........ SGE/2021/ 706 SGE/2019/ 4

SOLVED PAPER–01

S E T

SOLVED PAPER–01

SOLVED PAPER

1

SSC CGL TIER-I (CBE) EXAM Held on : 04.06.2019 (Shift-I)

GENERAL INTELLIGENCE & REASONING 1. If DIG is coded as 25 and CUT is coded as 49, then how will KICK be coded as? (1) 43 (2) 39 (3) 41 (4) 34 2. Select the option in which the given figure is embedded. Question Figure :

4. Select the figure that will come next in the following figure series : Question Figures : ?

Answer Figures :

(1)

(2)

(3)

(4)

5. Select the set in which the numbers are related in the same way as are the numbers of the following set. (9, 35, 16) (1) (16, 50, 64) (2) (25, 30, 4)

Rotation not allowed Answer Figures :

(3) (36, 55, 25) (4) (81, 65, 36) (1)

(2)

(3)

(4)

6. Select the set in which the numbers are related in the same way as are the numbers of the following set. (3, 24, 4) (1) (6, 35, 11)

3. A paper is folded and cut as shown below. How will it appear when unfolded? Question Figures :

Answer Figures :

(1)

(2)

(3)

(4)

(2) (2, 30, 8) (3) (12, 84, 4) (4) (4, 72, 9) 7. Three of the following four letter–clusters are alike in a certain way and one is different. Pick the odd one out. (1) CFIL (2) GHIJ (3) MOQS (4) PSUX 8. Three of the following four numbers are alike in a certain way and one is different. Pick the number that is different from the rest. (1) 126 (2) 189 (3) 254

(4) 217

SGE/2019/ 5

9. In a family of eight persons, there are two couples, each having two children. B and D are brothers and each has two children. E is the aunt of A, who is the cousin brother of C. C is the sister of H, who is the cousin brother of G. F is the wife of B. How is H related to F? (1) Nephew (2) Son-in-law (3) Son (4) Brother-in-law 10. Arrange the following words in a logical and meaningful order. 1. Buy 2. Dinner 3. Market 4. Vegetables 5. Cook (1) 1, 4, 5, 3, 2 (2) 3, 5, 4, 1, 2 (3) 4, 5, 3, 1, 2 (4) 3, 4, 1, 5, 2 11. Select the Venn diagram that best illustrates the relationship among the following classes. Uncle, Relatives, Rich

(1)

(2)

(3)

(4)

SOLVED PAPER–01

SOLVED PAPER–01

12. Two different positions of the same dice are shown. Which number will be at the top if 6 is at the bottom? 5 1

CEGI : AGEK : : DFHJ : ?

2 6

(1) 4

3

16. Select the option that is related to the third letter–cluster in the same way as the second letter–cluster is related to the first letter–cluster.

1

(2) 3

(3) 5 (4) 2 13. ‘Lawyer’ is related to ‘Justice’ in the same way as ‘Arbitrator’ is related to ‘______’. (1) Judgement (2) Injustice (3) Settlement (4) Communication 14. Three of the following four words are alike in a certain way and one is different. Pick the odd word out. (1) Groundnut (2) Mustard (3) Cumin (4) Fennel 15. Two statements are given followed by three Conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the Conclusions logically follow(s) from the statements. Statements : All rulers are machines. Some machines are costly items. Conclusions : I. Some rulers are costly items. II. Some costly items are machines. III. All costly items are machines. (1) Both Conclusions II and III follow (2) Both Conclusions I and II follow (3) Only Conclusion II follows (4) Only Conclusion I follows

(1) CHFI

(2) CGIK

(3) BHFL

(4) BDJK

17. Select the combination of letters that when sequentially placed in the gaps of the given letter series will complete the series. b_bab_bc_abbb_ba_b (1) cbbac

(2) cbabc

(3) cbbcb

(4) bcbab

(1) Tree : Forest (2) Reptile : Python (3) Furniture : Wood (4) Tennis : Ball 23. Which two signs should be interchanged in the following equation to make it correct? 12 – 8 + 12 × 9 ÷ 3 = 9 (1) + and ÷

(2) + and ×

(3) – and ÷

(4) + and –

24. How many squares are there in the following figure?

18. Which number will replace the question mark (?) in the following series? 3, 7, 16, 35, ?, 153 (1) 84

(2) 74

(3) 78

(4) 63

19. In a code language, VICTORY is written as CIVSYRO. How will TRAITOR be written as in that language? (1) RATHORT(2) RTAJOR T (3) AR TJOTR (4) ARTHROT 20. Select the number–pair in which the two numbers are related in the same way as are the two numbers of the following number–pair. 36 : 84 (1) 27 : 63

(2) 21 : 51

(3) 57 : 135

(4) 45 : 95

21. Rs. 1,875 is divided among A, B and C in such a way that A’s share is half of the combined share of B and C and B’s share is one–fourth of the combined share of A and C. By what amount is C’s share more than that of A? (1) Rs. 500

(2) Rs. 225

(3) Rs. 250

(4) Rs. 200

22. Select the word–pair in which the two words are related in the same way as are the two words in the following wordpair. Book : Thesaurus

SGE/2019/ 6

(1) 12

(2) 16

(3) 13

(4) 14

25. Select the correct mirror image of the given figure when the mirror is placed to the right of the figure. Question Figure :

Answer Figures :

(1)

(2)

(3)

(4)

SOLVED PAPER–01

SOLVED PAPER–01

GENERAL AWARENESS 26. ______ dance, performed by Buddhists to ward off evil spirits, is a dance form of Himachal Pradesh. (1) Chham (2) Natya (3) Dham (4) Gogra 27. The Musi and Bhima are tributaries of the river ______. (1) Mahanadi (2) Krishna (3) Kaveri (4) Brahmaputra 28. The Malimath Committee Report deals with : (1) judicial delays (2) textile sector reforms (3) criminal justice system reforms (4) stock market reforms 29. Who attacked and looted the famous Somnath temple in 1026 AD? (1) Muhammad Ghori (2) Mahmud of Ghazni (3) Nadir Shah (4) Genghis Khan 30. Which country was the first to implement Goods and Services Tax (GST)? (1) France (2) USA (3) Germany (4) Canada 31. Which of the following is mined in the Badampahar mines of Odisha? (1) Azurite (2) Dolomite (3) Bauxite (4) Hematite 32. Sundari, a well known species of trees, is found in : (1) tropical rainforests (2) Himalayan mountains (3) tropical deciduous forests (4) mangrove forests 33. The Tata Iron and Steel company (TISCO) was established by Dorabji Tata in : (1) 1919 (2) 1913 (3) 1907 (4) 1911 34. Who was the first female Director General of Police in Puducherry? (1) Aswathy Tonge (2) Kanchan Choudhary

35.

36.

37.

38.

39.

40.

41.

42.

(3) Kiran Bedi (4) Sundari Nanda Which of the following elements is a metalloid? (1) Tin (2) Bismuth (3) Silicon (4) Phosphorus Methyl propane is an isomer of : (1) n–hexane (2) n–butane (3) n–propane (4) n–pentane According to The Economist Intelligence Unit report ‘Worldwide Cost of Living Survey 2019’, which of the following is NOT one of the three cheapest cities in India? (1) Mumbai (2) Bengaluru (3) New Delhi (4) Chennai Which of the following places was ruled by the Wadiyar dynasty? (1) Mysore (2) Guwahati (3) Jabalpur (4) Patna Name the first ever judge of the Supreme Court against whom the motion of impeachment was introduced into Parliament in Independent India. (1) Justice Viraswami (2) Justice Ramaswami (3) Justice Mahajan (4) Justice Subba Rao In March 2019, _______ was sworn in as the new chief minister of Goa, following the demise of Manohar Parrikar. (1) Vasundhara Raje (2) H D Kumaraswamy (3) Ashok Gehlot (4) Pramod Sawant JJ Thomson received the Nobel Prize in Physics for the discovery of _____. (1) protons (2) electrons (3) neutrons (4) positrons Which queen died fighting Mughal armies while defending Garha Katanga in 1564? (1) Rani Avantibai (2) Rani Rudrambara (3) Rani Durgavati (4) Rani Ahilyabai

SGE/2019/ 7

43. Which gas in its solid state is also known as dry ice? (1) Nitrogen (2) Carbon dioxide (3) Oxygen (4) Hydrogen 44. The Olympic Council of Asia (OCA) has decided to reintroduce _____ in the 2022 Asian Games to be held at Hangzhou, China after it was dropped in 2018. (1) fencing (2) cricket (3) soccer (4) volleyball 45. The property of catenation is predominant in ______. (1) sulphur (2) nitrogen (3) silicon (4) carbon 46. ‘Thoda’ a sport dance belongs to which of the following states? (1) Sikkim (2) Andhra Pradesh (3) Haryana (4) Himachal Pradesh 47. The lone gold medal for India was won by _______ at the 38th GeeBee Boxing Tournament held at Helsinki, Finland. (1) Kavinder Singh Bisht (2) Naveen Kumar (3) Mohammed Hussamuddin (4) Shiva Thapa 48. The ______ edition of the India–Indonesia coordinated patrol (IND–INDO CORPAT) held from 19 March to 14th April, 2019 was inaugurated at Port Blair, Andaman and Nicobar Islands. (1) 23rd (2) 42nd (3) 45th (4) 33rd 49. _____ is the founder of Facebook. (1) Mark Zuckerberg (2) Brian Acton (3) Jimmy Wales (4) Larry Page 50. The Indian National Association was established in 1876 by _____ in Calcutta. (1) Badruddin Tyabji (2) V K Chiplunkar (3) Anand Mohan Bose (4) Sisir Kumar Ghosh

SOLVED PAPER–01

SOLVED PAPER–01

QUANTITATIVE APTITUDE 61. If sinθ = 51. A circle is inscribed in a triangle ABC. It touches the sides AB, BC and AC at the points R, P and Q respectively. If AQ = 4.5 cm, PC = 5.5 cm and BR = 6 cm, then the perimeter of the triangle ABC is : (1) 30.5 cm. (2) 28 cm. (3) 32 cm. (4) 26.5 cm. Directions (52–55) : The table shows the production of different types of cars (in thousands). Study the table carefully and answer the questions Years 2012 2013 2014 2015 2016 Cars A 30 35 48 45 56 B 42 48 40 38 56 C 48 36 38 35 44 D 51 24 30 46 54 E 20 42 40 35 43 52. If the data related to the production of cars of type E is represented by a pie chart, then the central angle of the sector representing the data of production of cars in 2013 will be : (1) 102° (2) 84° (3) 70° (4) 80° 53. What is the ratio of the total production of cars of type A in 2014 and type C in 2013 taken together to the total production of cars of type B in 2016 and type E in 2015 taken together? (1) 12 : 13 (2) 11 : 12 (3) 10 : 11 (4) 12 : 11 54. The total production of type B cars in 2012, 2014 and 2015 taken together is approximately what per cent more than the total production of type A cars in 2013 and 2016 taken together? (1) 31.9 (2) 33.2 (3) 36.3 (4) 34.4 55. The number of years, in which the production of cars of type B is less than the average production of type D cars over the years is : (1) 4 (2) 1 (3) 3 (4) 2 56. If 4 – 2 sin2θ – 5 cosθ = 0, 0° < θ < 90°, then the value of (sinθ + tanθ) is :

3 2 (1) 2

(3) 3 2

(3) 16

2 3

(4) 20

e

j e

59. If 5 5 x 3 – 81 3y 3 ÷

j

j

15C is :

(1) 10 (2) 9 (3) 15 (4) 12 60. If a nine–digit number 985x3678y is divisible by 72, then the value of (4x – 3y) is : (1) 5 (2) 4 (3) 6 (4) 3

SGE/2019/ 8

p (3) 1 + p 2

2p (4) p 2 – 1

(3) 17

= (Ax2 + By2 + Cxy), then the value of

e6A + B –

p (2) p 2 – 1

together can complete

4 th 9

1 days 7

(4) 24 days

63. The average of twelve numbers is 42. The average of the last five numbers is 40 and that of the first four numbers is 44. The 6th number is 6 less than the fifth and 5 less than the 7th number. The average of the 5th and the 7th number is : (1) 44 (2) 44.5 (3) 43 (4) 43.5 64. If x + y + z = 19, x2 + y2 + z2 = 133 and xz = y2, then the difference between z and x is : (1) 5 (2) 3 (3) 6 (4) 4 65.

5 x – 3 3y

2p (1) 1 + p 2

part of that work in : (1) 27 days (2) 15 days

57. A truck covers a distance of 384 km at a certain speed. If the speed is decreased by 16 km/h., it will take 2 hours more to cover the same distance. 75% of its original speed (in km/h.) is : (1) 45 (2) 54 (3) 48 (4) 42 58. If decreasing 120 by x% gives the same result as increasing 40 by x%, then x% of 210 is what per cent less than (x + 20)% of 180? (2) 18

, the cosθ is

62. The ratio of the efficiencies of A, B and C is 2 : 5 : 3. Working together, they can complete a work in 27 days. B and C

(4) 2 3

1 3

p2 + 1

equal to :

3 3 (2) 2

(1) 33

p2 – 1

2 + tan 2 θ + cot 2 θ is equal to : sec θ cosecθ

(1) cotθ (2) cosθ sinθ (3) secθ cosecθ (4) tanθ 66. In a circle of radius 10 cm., with centre O, PQ and PR are two chords each of length 12 cm. PO intersects chord QR at the points S. The length of OS is : (1) 2.8 cm. (2) 2.5 cm. (3) 3.2 cm. (4) 3 cm. 67. A sum amounts to Rs. 8,028 in 3 years and to Rs. 12.042 in 6 years at a certain rate per cent per annum, when the interest is compound yearly. The sum is :

SOLVED PAPER–01

68.

69.

70.

71.

72.

SOLVED PAPER–01

(1) Rs. 5,352 (2) Rs. 5,235 (3) Rs. 5,325 (4) Rs. 5,253 The value of 2 × 3 ÷ 2 of 3 × 2 ÷ (4 + 4 × 4 ÷ 4 of 4 – 4 ÷ 4 × 4) is : (1) 8 (2) 1 (3) 4 (4) 2 After giving two successive discounts, each of x%, on the marked price of an article, total discount is Rs. 259.20. If the marked price of the article is Rs. 720, then the value of x is : (1) 18 (2) 24 (3) 20 (4) 25 A solid cube of valume 13824 cm 3 is cut into 8 cubes of equal volumes. The ratio of the surface area of the original cube to the sum of the surface areas of three of the smaller cubes is : (1) 2 : 3 (2) 4 : 3 (3) 8 : 3 (4) 2 : 1 The ratio of the ages of A and B, four years ago, was 4 : 5. Eight years from now, the ratio of the ages of A and B will be 11 : 13. What is the sum of their present ages? (1) 80 years (2) 96 years (3) 72 years (4) 76 years In ∆ABC, F and E are the points on sides AB and AC, respectively, such that FE||BC and FE divides the triangle in two parts of equal area. If AD ⊥ BC and AD intersects FE at G, then GD : AG = ? (1)

2 :1

(3) 2 2 : 1

e (4) e (2)

j 2 + 1j : 1 2 –1 : 1

73. A person sold an article at a loss of 15%. Had he sold it for Rs. 30.60 more, he would have gained 9%. To gain 10%, he should have sold it for : (1) Rs. 140.25 (2) Rs. 132 (3) Rs. 130 (4) Rs. 128.40 74. In a ∆ABC, the bisectors of ∠B and ∠C meet at point O, inside the traingle. If ∠BOC = 122°, then the measure of ∠A is :

(1) 64° (2) 62° (3) 72° (4) 68° 75. If x4 + x–4 = 194, x > 0, then the value of (x – 2)2 is : (1) 1 (2) 6 (3) 2 (4) 3

ENGLISH COMPREHENSION Directions (76–80) : In the following passage some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank. Seoul’s city government is asking people for help to correct poorly translated street signs -with prizes on offer for (76) who spot the most errors. It’s running (77) twoweek campaign calling on Koreans and foreigners (78) to keep their eyes peeled for (79) in English, Japanese and Chinese text, the Korea Times reports. There’s a (80) focus on public transport signs, maps and information signs at historic sites, as part of a drive to improve the experience of foreign tourists in the South Korean capital. 76. (1) this (2) those (3) that (4) these 77. (1) one (2) the (3) an (4) a 78. (1) same (2) similarly (3) alike (4) likely 79. (1) guffaws (2) blunder (3) oversight (4) mistakes 80. (1) particular (2) important (3) signifying (4) meticulous 81. Select the synonym of the given word. COERCE (1) enchant (2) pressurize (3) cajole (4) leave 82. In the sentence identify the segment which contains the grammatical error. We had to decline several orders in case that the production was held up due to labour strike. (1) in case that (2) the production was held up (3) due to labour strike (4) We had to decline

SGE/2019/ 9

83. Select the most appropriate word to fill in the blank. His company has the ____ of producing the best cricket balls in the country. (1) opinion (2) brand (3) reputation (4) position 84. Select the antonym of the given word. EXPANSION (1) inflation (2) augmentation (3) extension (4) compression 85. Select the antonym of the given word. SCARCE (1) scanty (2) few (3) seldom (4) plentiful 86. Select the wrongly spelt word. (1) calender (2) career (3) callous (4) carriage 87. Select the most appropriate word to fill in the blank. Around sixty bands in colourful ____ took part in the Notting Hill Carnival. (1) clothings (2) costumes (3) apparels (4) dressing 88. Select the word which means the same as the group of words given. A person, animal or plant much below the usual height (1) wizard (2) dwarf (3) creature (4) witch Directions (89–90) : Select the most appropriate option to substitute the bold segment in the given sentence. If no substitution is required, select No improvement. 89. The workers of this textile factory demand higher wages for a long time. (1) have beens demanding higher wages (2) demanded higher wages (3) No improvement (4) has demanded higher wages 90. If you park your car here, the traffic police has fined you.

SOLVED PAPER–01 (1) will fine you (2) No improvement (3) fine you (4) fined you Directions (91–92) : Given below are four jumbled sentences. Select the option that gives their correct order. 91. A. The cafe’s owner says he’s interested in conservation, and hopes customers will realise the animals are worth saving, even though they often have a bad reputation. B. None of them are venomous, meaning customers can get up close and personal with the reptiles. C. Here you sip your drink in the company of 35 snakes. D. This cafe, which has just opened in Tokyo, is not for the faint-hearted. (1) DBCA (2) DCBA (3) ABCD (4) ABDC 92. A. An environmental group performed a necropsy on the animal and found about 40 kilograms of plastic, including grocery bags and rice sacks. B. A 4.7-metre long whale died on Saturday in Phillipines where it was stranded a day earlier. C. “It’s very disgusting and heartbreaking,” he said. “We’ve done necropsies on 61 dolphins and whales in the last 10 years and this is one of the biggest amounts of plastic we’ve seen.” D. “The animal died from starvation and was unable to eat because of the trash filling its stomach,” said Darrell Blatchley, Director of D’ Bone Collector Museum Inc.. (1) ABCD (2) DABC (3) BADC (4) BACD 93. Select the most appropriate meaning of the given idiom. To play ducks and drakes

SOLVED PAPER–01

94.

95.

96.

97.

98.

99.

(1) to use recklessly (2) to change places (3) to be friendly (4) to act cleverly In the sentence identify the segment which contains the grammatical error. Cyclone Idai killed at least 157 people in Zimbabwe and Mozambique although it tore across Southern Africa. (1) Cyclone Idai killed (2) it tore across (3) although (4) at least 157 people Select the correct active form of the given sentence. Every passing vehicle was being thoroughly checked by the guards. (1) The guards were thoroughly checking every passing vehicle. (2) The guards have thoroughly checked every passing vehicle. (3) Every passing vehicle were thoroughly checking the guards. (4) The guards have been thoroughly checking every passing vehicle. Select the wrongly spelt word. (1) exploite (2) explicit (3) expire (4) explode Select the synonym of the given word. CHRONIC (1) ordinary (2) persistent (3) common (4) temporary Select the most appropriate meaning of the given idiom. At daggers drawn (1) deceiving somebody (2) without hope (3) friendly with each other (4) bitterly hostile Select the word which means the same as the group of words given. A student who idly or without excuse absents himself/herself from school (1) truant (2) vagrant (3) itinerant (4) migrant

SGE/2019/ 10

100. Select the correct passive form of the given sentence. Do not buy medicines without the doctor’s prescription. (1) Medicines should not be bought without the doctor’s prescription. (2) Medicines need not be bought without the doctor’s prescription (3) Medicines might not be bought without the doctor’s prescription (4) Medicines could not be bought without the doctor’s prescription

1. (2)

2. (4)

3. (4)

4. (4)

5. (3)

6. (4)

7. (4)

8. (3)

9. (1)

10. (4)

11. (4)

12. (4)

13. (3)

14. (1)

15. (3)

16. (3)

17. (3)

18. (2)

19. (4)

20. (1)

21. (3)

22. (2)

23. (1)

24. (4)

25. (4)

26. (1)

27. (2)

28. (3)

29. (2)

30. (1)

31. (4)

32. (4)

33. (3)

34. (4)

35. (3)

36. (2)

37. (1)

38. (1)

39. (2)

40. (4)

41. (2)

42. (3)

43. (2)

44. (2)

45. (4)

46. (4)

47. (1)

48. (4)

49. (1)

50. (3)

51. (3)

52. (2)

53. (1)

54. (1)

55. (4)

56. (2)

57. (3)

58. (3)

59. (4)

60. (2)

61. (1)

62. (2)

63. (2)

64. (1)

65. (3)

66. (1)

67. (1)

68. (4)

69. (3)

70. (2)

71. (1)

72. (2)

73. (1)

74. (1)

75. (3)

76. (2)

77. (4)

78. (3)

79. (4)

80. (1)

81. (2)

82. (1)

83. (3)

84. (4)

85. (4)

86. (1)

87. (2)

88. (2)

89. (1)

90. (1)

91. (2)

92. (3) 96. (1)

93. (1)

94. (3)

95. (1)

97. (2)

98. (4)

99. (1) 100. (1)

SOLVED PAPER–01

1. (2) D

I

4 + 9 + ⇒ 20 + 5 = 25 C U

SOLVED PAPER–01

G

7 = 20

6. (4) (3, 24, 4) ⇒ 3 × 4 × 2 = 24 Similarly, (4, 72, 9) ⇒ 4 × 9 × 2 = 72 7. (4) C

T G

3 + 21 + ⇒ 44 + 5 = 49 Therefore, K I C

20 = 44

K

11 + 9 + 3 + 11 = 34 ⇒ 34 + 5 = 39

2. (4)

3. (4) 4. (4) From First Figure to Third Figure one vertical but tilted and one horizontal line segments are added. Similarly, from second figure to fourth figure one vertical but tilted and one horizontal line segments are added. Therefore, similar changes would occur from third figure to fifth figure. Alternatively, after every two figures one vertical but tilted and one horizontal line segments are added and vertical line segment(s) change(s) direction in each subsequent figure. 5. (3) (9, 35, 16)

M

+3 +1 +2

F H O

+3 +1 +2

iv lat Re

Uncle

I I Q

+3 +1 +2

L J S

Uniform gap between adjacent letters. But, +3

+2

+3

P S U X 8. (3) Except the number 254, in all other numbers, the number formed by the first and the second digits is multiple of the third digit. 126 ⇒ 6 × 2 = 12 189 ⇒ 9 × 2 = 18 217 ⇒ 7 × 3 = 21 But, 254 ⇒ 4 × 6 + 1 = 25 9. (1) A is cousin brother of C and H. F is the wife of B. Therefore, E is the wife of D. E is mother of C and H. F is mother of A and G. H is nephew of F. 10. (4) Logical and meaningful order of words : 3. Market

4. Vegetables

Rich

12. (4) The numbers 2, 3, 5 and 6 lie on the faces adjacent to the number 1. Therefore, 4 lies opposite 1. Thus, it is not a standard dice. From the two views of the same dice, it is clear that 2 lies opposite 6. 13. (3) Lawyer pleads in the court for justice to his/her client. Similarly, Arbitrator tries to settle the matter between the two parties. 14. (1) Except Groundnut, all others are spices. Groundnut is an edible nut grows in a thin crisp shell. 15. (3) First Premise is Universal Affirmative (A–type). Second Premise is Particular Affirmative (I–type). All rulers are machines.

Some machines are costly items.

A + I ⇒ No Conclusion Conclusion II is the Converse of the second Premise. 16. (3) C

E

G

I

A

G

E

K

–2 +2 –2

1. Buy

+2

Similarly, 5. Cook

⇒ 9 = 3 × 3; 16 = 4 × 4 First and third numbers are perfect squares. (16 – 9) × 5 = Middle Number ⇒ 7 × 5 = 35 Similarly, (36, 55, 25) ⇒ 36 = 6 × 6; 25 = 5 × 5 (36 – 25) × 5 ⇒ 11 × 5 = 55

es

D

F

H

J

B

H

F

L

–2

2. Dinner One goes to market, where vegetables are bought. Then it is cooked for dinner. 11. (4) Uncle comes under the class Relatives. Some uncles and some relatives may be rich.

SGE/2019/ 11

+2 –2 +2

17. (3) b c b b/b

bab b /bc b

c

ba b

b

a

SOLVED PAPER–01

SOLVED PAPER–01 ⇒ 12 – 6 + 3 = 9 ⇒ 15 – 6 = 9 ⇒ 9=9

18. (2) 3 + 4 = 7 7 + 9 (= 4 + 5) = 16 16 + 19 (= 9 + 10) = 35 35 + 39 (= 19 + 20) = 74 74 + 79 (= 39 + 40) = 153 19. (4) V I C T O R

A

24. (4) L

Y

B

C

Q

K

O

P R

T

I V S Therefore, R A I

Y

R

T

O

–1

A

R

T

H

20. (1) 36

:

12 × 3 Similarly, 27

R

O

T

84

12 × 7 :

S

O J

R

29.

N

M

–1

C

D

I

H

E F G

The squares are : ABML; BCNM; LMOK; MNPO; ACPK; KPIJ; CDEP; PQSR; QEFS; RSHI; SFHG; PEGI; KCEI; ADGJ Thus, there are altogether 14 squares in the given figure.

30.

63 25. (4)

9×3 9×7 21. (3) A + B + C = 1875 B+C ⇒ 2A = B + C 2 A + 2A = 1875

A=

⇒ A=

1875 = Rs. 625 3

A +C = 4B = A + C 4 4B + B = 1875

B=

1875 = Rs. 375 5 ∴ Share of C = Rs. (1875 – 1000) = Rs. 875 C – A = Rs. (875 – 625) = Rs. 250 22. (2) The second belongs to the first. Thesaurus is a book containing words and phrases arranged according to their meanings. Similarly, Python is a large reptile. 23. (1) 12 – 8 + 12 × 9 ÷ 3 = 9 ⇒ 12 – 8 ÷ 12 × 9 + 3 = 9

⇒ B=

⇒ 12 –

8 ×9+3=9 12

26. (1) Chham is a folk dance of Himachal Pradesh, performed by the Buddhist monks (Lamas,) in the courtyard of monasteries during religious and other festivals, as a part of the celebrations. It is performed to exorcise evil spirits and demons. The theme rotates around killing the ‘Evil King’, symbolic of evil tendencies in humans, natural calamities, diseases and epidemics. 27. (2) Musi and Bhima are tributaries of Krishna River. Bhima originates near Bhima Shankar Temple on the western side of the Western Ghats in Pune District, Maharashtra and merges into the Krishna along the border between Karnataka and Telangana. Similarly, Musi River or Musinuru is a tributary of the Krishna River in the Deccan Plateau flowing through Telangana. 28. (3) The Malimath Committee was set up by the Home Ministry in 2000 for examining the fundamental principles of criminal law so as to restore confidence in the criminal justice system.This involved re-

SGE/2019/ 12

31.

32.

33.

viewing the Code of Criminal Procedure (CrPC), 1973, the Indian Evidence Act, 1872, and the Indian Penal Code (IPC), 1860. It submitted its report in 2003. (2) In 1024, during the reign of Bhima I, the prominent Turkic ruler Mahmud of Ghazni raided Gujarat, plundering the Somnath temple and breaking its jyotirlinga.He took away a booty of 20 million dinars. Later it was destroyed during 1299 invasion of Gujarat by Alauddin Khalji’s army, led by Ulugh Khan. (1) The Goods and Service Tax or GST was first introduced in France in the year 1954. It was consequently after France that countries like Japan, South Korea, UK and Australia implemented the GST law. GST is an indirect tax which was introduced in India on 1 July, 2017. Nearly 160 countries up till now, have opted this mode for bringing individually tax rates into a single tax. (4) Badampahar mines, located in Mayurbhanj, Odisha, are famous for the mining of gold and iron ore.In Badampahar, high grade hematite ores of iron are found. To the east in Mayurbhanj, the banded hematite quartzite forms a series of hills from Badampahar to Gorumahisani. An enormous amount of iron ore is present in this Iron Ore Range. (4) Sundari tree is one of the most extensively found mangrove species in the Sundarbans. a mangrove area in the delta formed by the confluence of Ganges, Brahmaputra and Meghna Rivers in the Bay of Bengal. The Sundari tree (Heritiera fomes) comprises about 70% of the trees in the area. (3) Tata Iron and Steel Company was founded by Jamsetji Tata and established by Dorabji Tata at Jamshedpur on 26 August, 1907. It began producing steel in 1912 as a branch of Jamsetji’s Tata Group. The company changed its name

SOLVED PAPER–01

34.

35.

36.

37.

38.

from TISCO to Tata Steel Ltd. in 2005. (4) IPS officer Sundari Nanda in July 2018 assumed charge as Puducherry Director General of Police, becoming the first woman to head the force in the Union Territory. A 1988 batch officer, she was transferred to Puducherry from the National Capital Territory of Delhi. (3) Silicon is neither metal nor non-metal; it’s a metalloid, an element that falls somewhere between the two.It is a hard and brittle crystalline solid with a blue-grey metallic lustre; and it is a tetravalent metalloid and semiconductor. It is the second most abundant element in the Earth’s crust (about 28% by mass) after oxygen. (2) Isobutane, also known as ibutane, 2-methylpropane or methylpropane, is a chemical compound with molecular formula HC(CH?)?. It is an isomer of butane. It is the simplest alkane with a tertiary carbon. Isobutane is used as a precursor molecule in the petrochemical industry, for example in the synthesis of isooctane. (1) Cities of Bengaluru—India’s technology capital, the southern city of Chennai, and the country’s capital city New Delhi ranked among the world’s ten cheapest cities in a ranking released by the Economist Intelligence Unit in its bi-annual survey on March 19, 2019. These three cities joined the ranks of Caracas, Buenos Aires, Lagos and Karachi among others that remain highly affordable when compared to other cities globally. (1) The Wadiyar dynasty was a Hindu dynasty in Indian subcontinent that ruled the Kingdom of Mysore from 1399 to 1950, with a brief interruption in the late 1700s. From 1760 to 1799, the rule of the dynasty was essentially nominal, with real power in the hands of Hyder Ali and his son Tipu

SOLVED PAPER–01

39.

40.

41.

42.

43.

Sultan, who expanded the kingdom aggressively. (2) Veeraswami Ramaswami was the first judge against whom removal proceedings were initiated in 1991. However, his impeachment motion failed because of the abstention of Congress party. Another judge to face removal proceedings is Soumitra Sen of Calcutta High Court, proceedings against whom were initiated in Rajya Sabha on 17 August, 2011. (4) Pramod Sawant, former Speaker of the Goa legislative Assembly and BJP MLA from Sankhelim in north Goa, was in March 2019 sworn in as the 11th Chief Minister of Goa, succeeding Manohar Parrikar, who died due to pancreatic cancer. Sawant was administered the oath of office and secrecy at the Raj Bhavan by Governor Mridula Sinha. (2) J. J. Thomsonwas an English physicist who was awarded the 1906 Nobel Prize in Physics for his work on the conduction of electricity in gases. He credited with the discovery and identification of the electron, the first subatomic particle to be discovered. (3) Rani Durgavati Madavi was a ruling Queen of Gondwana from 1550 until 1564 who killed herself in the battlefield on June 24, 1564 while fighting against the Mughals. Her courage for defending Garha Kingdom, also called Garha Mandla or Garha Katanga, is remembered even today. Her martyrdom is even today commemorated as “Balidan Diwas”. (2) Dry ice, sometimes referred to as “cardice,” is the solid form of carbon dioxide. It is used primarily as a cooling agent. Its advantages include lower temperature than that of water ice and not leaving any residue. It is useful for preserving frozen foods, ice cream, etc., where mechanical cooling is unavailable.

SGE/2019/ 13

44. (2) The Olympic Council of Asia (OCA) in March 2019 decided to reintroduce Cricket in the 2022 Asian Games to be held at Hangzhou, China. Earlier Cricket had featured in 2010 and 2014 Asian Games but was dropped from the 2018 Asian Games. 45. (4) In chemistry, catenation is the bonding of atoms of the same element into a series, called a chain. Catenation occurs most readily with carbon, which forms covalent bonds with other carbon atoms to form longer chains and structures. This is the reason for the presence of the vast number of organic compounds in nature. 46. (4) Thoda is the impressive martial art cum dance form of Himachal Pradesh. It revolves around game of archery where the target is a dancing human, is played between two teams called pasha and saatha who identify themselves as descendants of Pandavas and Kauravas. 47. (1) At the 38th GeeBee Boxing Tournament, held at Helsinki in Finland in March 2019, the lone gold medal for India was won by Kavinder Singh Bisht. He won against Indian counterpart Mohammed Hussamuddin in summit clash in the 56kg category. 48. (4) The 33rd edition of IndiaIndonesia coordinated patrol (IND-INDO CORPAT) was inaugurated at Port Blair, Andaman & Nicobar Islands, on 19 March 2019. It coincided with 70 years of India-Indonesia diplomatic ties and aimed to contribute towards the Indian Navy’s efforts to consolidate inter -operability and forge strong bonds of friendship across the seas. 49. (1) Mark Zuckerberg is cofounder and CEO of the socialnetworking website Facebook. Zuckerberg attended Harvard University, where he launched Facebook from his dormitory room on February 4, 2004, with college roommates Edu-

SOLVED PAPER–01

SOLVED PAPER–01

ardo Saverin, Andrew McCollum, Dustin Moskovitz, and Chris Hughes. 50. (3) The Indian National Association also known as Indian Association was the first avowed nationalist organization founded in British India by Surendranath Banerjee and Ananda Mohan Bose in 1876. It became an important forum for India’s aspirations for independence. It later merged with the Indian National Congress. A

51. (3) R

Q

B P C The tangents drawn from an exterior point to a circle are equal. ∴ AQ = AR = 4.5 cm. CP = CQ = 5.5 cm. BR = BP = 6 cm. ∴ AB + BC + CA = (AR + RB) + (BP + PC) + (CQ + QA) = [(4.5 + 6) + (6 + 5.5) + (5.5 + 4.5)] cm. = (10.5 + 11.5 + 10) cm. = 32 cm. 52. (2) Total production of type–E cars = (20 + 42 + 40 + 35 + 43) thousands = 180 thousands Production of type–E cars in 2013 = 42 thousands Q 180 ≡ 360° 360 × 42 = 84° ∴ 42 ≡ 180 53. (1) Required ratio = (48 + 36) : (56 + 35) = 84 : 91 = 12 : 13 54. (1) Total production of B–type cars in 2012, 2014 and 2015 = (42 + 40 + 38) thousands = 120 thousands Total production of type–A cars in 2013 and 2016 = (35 + 56) thousands = 91 thousands Required per cent

120 – 91 2900 × 100 = 91 91 = 31.86 ≈ 31.9% 55. (4) Average production of type–D cars

=

F 51 + 24 + 30 + 46 + 56 IJ = GH K 5

F 207 IJ = GH 5 K

=

thousands

⇒

120x 40 x + = 120 – 40 100 100

⇒

160x = 80 100

thousands

3 =

3+2 3 2

210 2 = 105 and (x + 20)% of 180

∴ x% of 210 =

70 × 180 = 126 100 ∴ Required per cent

=

=

FG 126 – 105 IJ H 126 K

=

21 50 2 × 100 = = 16 % 126 3 3

59. (4)

3 3 2 57. (3) Let the original speed of truck be x kmph.

∴

384 384 – =2 x – 16 x

FG 1 – 1 IJ = 2 H x – 16 x K F x – x + 16 I ⇒ 384 G x b x – 16g J = 2 H K ⇒ 384

⇒

384 × 16 =2 x x – 16

b

g

⇒ x (x – 16) = 384 × 8 = 64 × 48 ⇒ x (x – 16) = 64 (64 – 16) ⇒ x = 64 kmph. ∴ 75% of 64 kmph.

SGE/2019/ 14

80 × 100 = 50 160

⇒ x=

=

Distance Q Time = Speed

120 × x 40 x = 40 + 100 100

120 –

1 ⇒ cosθ = = cos 60° 2 ⇒ θ = 60° and cosθ ≠ 2 ∴ sinθ + tanθ = sin 60° + tan 60° 3 + 2

kmph.

= 48 kmph. 58. (3) According to the question,

= 41.4 thousands Required years ⇒ 2014 and 2015 56. (2) 4 – 2 sin2θ – 5 cosθ = 0 ⇒ 4 – 2 (1 – cos2θ ) – 5 cosθ = 0 ⇒ 4 – 2 + 2 cos2θ – 5 cosθ = 0 ⇒ 2 cos2θ – 5 cosθ + 2 = 0 ⇒ 2 cos2θ – 4 cosθ – cosθ + 2 =0 ⇒ 2 cosθ (cosθ – 2) – 1 (cosθ – 2) = 0 ⇒ (2 cosθ – 1) (cosθ – 2) = 0 ⇒ 2 cosθ – 1 = 0

=

FG 3 × 64IJ H4 K

=

=

e

e

× 100

5 5 x 3 – 81 3y 3 5 x – 3 3y 5x

5 x – 3 3y

3

3

j – e3 3y j

5 x – 3 3y

jRSTe

5x

j

2

e

+ 5 x × 3 3y + 3 3y

j UVW 2

5 x – 3 3y

[ Q a3 – b3 = (a – b) (a2 + ab + b2)] = 5x2 + 3 15 xy + 27y2 ∴ Ax2 + By2 + Cxy = 5x2 + 27y2 + 3 15 xy ⇒ A = 5, B = 27, C = 3 15 ∴ 6A + B – 15 C = 6 × 5 + 27 –

15 × 3 15 = 30 + 27 – 45 = 12 60. (2) The given number is exactly divisible by 72 if it is divisible by 8 and 9. The given number is divisible by 8 if 78y is divisible by 8. For y = 4, 784 ÷ 8 = 98

SOLVED PAPER–01

SOLVED PAPER–01

The given number is divisible by 9 if sum of its digits is divisible by 9 For 985x36784, Sum of digits = 50 + x which is divisible by 9 for x = 4 ∴ 4x – 3y = 4 × 4 – 3 × 4 = 16 – 12 = 4 p2 – 1

61. (1) sin θ =

p2 + 1

∴ cos θ =

e ep

2

1 – sin θ

j + 1j

p2 – 1

=

1–

ep

2

+1

2

4p

ep

2

2

j – ep ep + 1j

2

=

=

2

2

2

j

–1

2

2

j

+1

2

2p p2 +1

62. (2) The ratio of efficiencies of A, B and C = 2 : 5 : 3 ∴ Respective ratio of time taken =

1 1 1 : : 2 5 3

1 1 1 × 30 : × 30 : × 30 2 5 3 = 15 : 6 : 10 According to the question,

=

1 1 1 1 + + = 15x 6x 10x 27 2+5+3 1 = 30x 27 ⇒ 30x = 27 × 10

⇒

27 × 10 ⇒ x= =9 30 ∴ Time taken by B = 6 × 9 = 54 days Time taken by C = 10 × 9 = 90 days ∴ (B + C)’s 1 day’s work

=

1 1 + 54 90

5+3 8 4 = = 270 270 135

4 ∴ Time taken in doing 9 4 135 work = × = 15 days 9 4 63. (2) Fifth number = x ∴ Sixth number = x – 6 Seventh number = x – 1 ∴ 5 × 40 + 4 × 44 + x + x – 6 + x – 1 = 12 × 42 ⇒ 200 + 176 + 3x – 7 = 504 ⇒ 369 + 3x = 504 ⇒ 3x = 504 – 369 = 135 135 = 45 3 ∴ Required average

⇒ x=

=

2

[ Q (a + b)2 – (a – b)2 = 4ab] =

=

x + x –1 2x – 1 = 2 2

2 × 45 – 1 89 = = 44.5 2 2 2 2 64. (1) (x + y + z) = x + y2 + z2 + 2xy + 2yz + 2zx ⇒ (19)2 = 133 + 2 (xy + yz + zx) ⇒ 361 – 133 = 2 (xy + yz + zx) ⇒ 2 (xy + yz + zx) = 228 ⇒ xy + yz + zx = 114 ⇒ xy + yz + y2 = 114 ( Q y2 = xz) ⇒ y (x + y + z) = 114 ⇒ y × 19 = 114

=

114 =6 19 ∴ x + y + z = 19 ⇒ x + z = 19 – 6 = 13 ∴ (x – z)2 = (x + z)2 – 4xz = (13)2 – 4 × y 2 = 169 – 4 × 36 = 169 – 144 = 25

⇒ y=

∴ x – z = 25 = 5 65. (3) Expression

[ Q sec2θ – tan2θ = 1; cosec2θ – cot2θ = 1] =

sec2 θ cosec2θ + sec θ. cosecθ sec θ. cosecθ

=

sec θ cosecθ + cosecθ sec θ

=

1 1 . sinθ + . cosθ cos θ sin θ

LMcosecθ = 1 ; sec θ = 1 OP sin θ cos θ Q N = =

sin 2 θ + cos 2 θ sin θ.cos θ 1 = secθ . cosecθ sin θ.cos θ R

66. (1) P

S

M

O

Q PS = y cm. RS = SQ = x cm. PQ = PR = 12 cm. PM = 20 cm. (diameter) ∠PQM = ∠PRM = 90° (Angle in the semi–circle) ∴ QM2 = PM2 – PQ 2 = 202 – 122 = 400 – 144 = 256

∴ QM =

256 = 16 cm. MS = 20 – y SQ2 = PQ2 – PS2 = 122 – y2 ∴ SQ2 + SM2 = QM2 ⇒ 144 – y2 + (20 – y)2 = 162 ⇒ 144 – y2 + 400 – 40y + y2 = 256 ⇒ 40y = 544 – 256 = 288 288 = 7.2 40 ∴ OS = OP – PS = 10 – 7.2 = 2.8 cm. 67. (1) Let the sum be Rs. P.

⇒ y=

FG H

=

2 + tan 2 θ + cot 2 θ sec θ. cosecθ

∴ A = P 1+

=

1 + tan 2 θ + 1 + cot 2 θ sec θ. cosecθ

⇒ 8028 = P 1 +

=

sec2 θ + cosec2θ sec θ. cosecθ

12042 = P 1 +

SGE/2019/ 15

R 100

FG H

FG H

IJ K

T

R 100

R 100

IJ K

IJ K

3

...(i)

6

...(ii)