Held on : 26-10-2014 (First Sitting) SSC Combined Graduate ... · PDF fileSSC Combined...

Part–A : General Intelligenceand Reasoning

Directions (Q. 1–6) : In each of the followingquestions, select the related word/letters/numberfrom the given alternatives.1. 23 : 13 : : 54 : ?

A) 40 B) 41C) 44 D) 39

2. Seismometer : Earthquakes : : Thermometer : ?A) Mercury B) TemperatureC) Fever D) Doctor

3. Play : Actor : : Concert : ?A) Percussion B) SymphonyC) Musician D) Piano

4. DLIP : FNKR : : JROV : ?A) MURY B) LTQXC) NVSZ D) KSPW

5. YAWC : UESG : : QIOK : ?A) MMKO B) ROMEC) MINC D) MIKE

6. 17 : 24 : : 153 : ?A) 213 B) 216C) 118 D) 198Directions (Q. 7–11) : In each of the following

questions, select the one which is different fromthe other three alternatives.7. A) Duck B) Avoid

C) Dodge D) Flee8. A) 36 B) 96

C) 16 D) 809. A) 41, 4 B) 83, 6

C) 74, 7 D) 97, 910. A) LNOR B) TRPS

C) CEFI D) GIJM11. A) Emu B) Penguin

C) Kiwi D) Eagle12. Which one of the given responses would be a

meaningful order of the following colours ?1. Indigo 2. Red 3. Violet4. Blue 5. Green 6. Yellow7. OrangeA) 3, 1, 4, 5, 2, 6, 7 B) 3, 1, 4, 5, 6, 2, 7C) 1, 5, 6, 7, 3, 4, 2 D) 3, 1, 4, 5, 6, 7, 2

13. Arrange the following words as per order in theEnglish dictionary :1. Caricature 2. Cardinal 3. Carnivore4. Cartoon 5. CategoryA) 2, 1, 3, 4, 5 B) 4, 5, 1, 3, 2C) 1, 2, 3, 4, 5 D) 2, 1,3, 5,4

14. Which one set of letters when sequentially placedat the gaps in the given letter series shallcomplete it ?

Held on : 26-10-2014 (First Sitting)

SSC Combined Graduate Level Tier–I ExamR_S_ PM_KSB_MRK_A) KRKSP B) KBRPSC) RKSPM D) BPSMP

15. In the following series, how many HIG occur insuch a way that ‘I’ is in the middle and ‘H’ and‘G’ are adjacent to it on both sides ?GGHIHIIGGJKLMGIHIGA) 3 B) 2C) 5 D) 4Directions (Q. 16–18) : In each of the following

questions, a series is given with one term missing.Choose the correct alternative from the given onesthat will complete the series.16. 2, 2, 4, 6, ?, 10, 8, 14, 10

A) 6 B) 5C) 8 D) 7

17. ELFA, GLHA, ILJA, ?, MLNAA) ILMA B) KLLAC) QLPA D) KLMA

18. 3, 8, 18, 35, ?, 98A) 61 B) 71C) 41 D) 51

19. L, M, N and O are brothers. L is darker than O, Nis the fairest of all. M is fairer than O. Who isthe darkest of all ?A) N B) OC) L D) M

20. Anjali says, “He is the only son of the father ofmy sister’s brother.” How is that person relatedto Anjali?A) Uncle B) CousinC) Brother D) Father

21. From the given alternative words, select the wordwhich can be formed using the letters of the givenword.FUNDAMENTALA) TAME B) FUNDSC) DETRIMENTAL D) NOSE

22. From the given alternative words, select the wordwhich cannot be formed using the letters of thegiven word.THERMODYNAMICSA) MATHEMATICS B) MOTHERC) MODERN D) DYNAMO

23. Joan’s age is 42 years and Kelvin’s age is 26 years.How many years ago was Kelvin’s age half of Joan’sage?A) 6 years B) 4 yearsC) 10 years D) 8 years

24. In a certain code, ‘RATIONAL’ is written as‘RTANIOLA’. How would ‘TRIBAL’ be written inthe same code ?A) TIRLBA B) TIRABLC) TRIALB D) TIRALB

DESIZN CIRCLE

GAT Mock Test KK0160916

Previous Papers SSC Combined Graduate Level Exam (Tier–I)

25. If ‘INDUS’ is coded as ‘03865’ and ‘TENNIS’ iscoded as ‘243305’, then what will be the code for‘STUDENT’ ?A) 5628342 B) 5648324C) 5268432 D) 5642832

26. Given below are capital letters in the first lineand symbols in the second line. Symbols andletters are codes for each other. Choose thecorrect code for the given letters.

A C E G H I O N P R T S B D M

+ – ÷ × = ( ) [ ] ≠ || # | > <

A) = ÷ (× = || B) = × (× = ||C) = ÷ (× ||= D) = × (÷ = ||

27. In a school, the bell is rung once after each halfan hour. The school starts at 8 : 00 am and closesat 1 : 30 pm. The bell is rung 3 timescontinuously, at the time of beginning, at thetime of lunch break, at 10 : 00 am, at 10 : 30 amand at the end. How many times is the bell rungevery day ?A) 21 B) 22C) 19 D) 20

28. Some letters are given with numbers from 2 to 9.Select the sequence of numbers which arrangesthe letters into a meaningful word.N A E X I M O T N A I9 2 3 4 5 6 7 8 9 2 5A) 3, 4, 6, 2, 9, 5, 8, 5, 2, 9, 7B) 3, 6, 2, 4, 2, 9, 5, 7, 5, 9, 8C) 3, 4, 2, 2, 6, 5, 9, 7, 8, 9, 5D) 3, 4, 2, 6, 5, 9, 2, 8, 5, 7, 9

29. Select the correct combination of mathematicalsigns to replace * signs and to balance thefollowing equation :

( 121 * 9) * 5 * 4 * 1A) – + × = B) + ÷ × =C) = + × ÷ D) – × + =

30. If ‘– ’ stands for ‘division’, ‘+’ stands for‘multiplication’, ‘÷’ stands for ‘subtraction’, ‘×’stands for ‘addition’, then which one of thefollowing equations is correct ?A) 36 × 4 – 12 + 5 ÷ 3 = 420B) 52 ÷ 4 + 5 × 8 – 2 = 36C) 36 – 12 × 6 ÷ 3 + 4 = 60D) 43 × 7 ÷ 5 + 4 – 8 = 25

31. Some equations are solved on the basis of acertain system. Find the correct answer for theunsolved equation on that basis.5 3= –7; 3 7= –11; 7 11= ?A) –59 B) 77C) –15 D) 18Directions (Q. 32–34) : In each of the following

questions, select the missing number from thegiven responses.

32. 8 4 76 9 948 36 ?16 12 21A) 24 B) 16C) 42 D) 63

33. 3 8 79 6 32 ? 12A) 4 B) 3C) 7 D) 6

34. 2 4 3 29 7 6 5? 33 27 21A) 77 B) 35C) 69 D) 80

35. Some statements are given followed by threeconclusions I, II and III. You have to considerthe statements to be true, even if they seem tobe at variance from commonly known facts. Youhave to decide which of the given conclusions ifany, follow from the given statements. Indicateyour answer.Statements:All chickens are birds.Some chickens are hens.Female birds lay eggs.Conclusions:I. All birds lay eggs.II. Some hens are birds.III. Some chickens are not hens.A) Conclusions II and III both followB) All conclusions I, II and III followC) Only conclusion I followsD) Only conclusion II follows

36. A man is facing South. He turns 135° in theanticlockwise direction and then 180° in theclockwise direction. Which direction is he facingnow ?A) South - East B) South - WestC) North - East D) North - West

37. Raju cycled 10 km South from his house, turnedright and went 5 km and again turned right andcycled 10 km and then turned left and cycled10 km. How many kilometres will he have to cycleback to reach his house ?A) 10 km B) 5 kmC) 20 km D) 15 km

38. “If a person is rich, he has a lot of influence.”What inference can you draw from the abovestatement ?A) Kamala is rich, so she has a lot of influence.B) Poor people cannot have influence.C) Ram has a lot of influence, so he is rich.D) Govind is not rich, so he does not have a lot

of influence.


SSC Combined Graduate Level Tier–I Exam, 26-10-2014 (First Sitting)

39. How many triangles are there in the given figure ?

A) 11 B) 12 or moreC) 9 D) 10

40. Among the four answer figures, which one can beformed from the cut out pieces given below inthe question figure ?Question Figure

Answer Figures

A) B) C) D)41. Choose the cube which will be formed on folding

the given question figure.Question Figure

Answer Figures

A) B) C) D)42. In the given figure, which letter represents those

Nurses who are Doctors as well as Pharmacists ?

A) R B) SC) P D) Q

Directions (Q. 43–44) : In the followingquestions, identify the diagram that bestrepresents the relationship among the classesgiven below:43. Duck, Penguin, Bird

A) B) C) D)44. Profit, Dividend, Bonus

A) B) C) D)Directions (Q. 45–46) : In each of the following

questions, which answer figure will complete thepattern in the question figure ?45. Question Figure

Answer Figures

A) B) C) D)46. Question Figure

Answer Figures

A) B) C) D)47. A piece of paper is folded and cut as shown below

in the question figures. From the given answerfigures, indicate how it will appear when opened.Question Figures

Answer Figures

A) B) C) D)48. From the given answer figures, select the one in

which the question figure is hidden/embedded.



Question Figure

Answer Figures

A) B) C) D)49. A word is represented by only one set of

numbers as given in any one of thealternatives. The sets of numbers given inthe alternatives are represented by twoclasses of alphabets as in two matrices givenbelow. The columns and rows of Matrix–I arenumbered from 0 to 4 and that of Matrix–IIare numbered from 5 to 9. A letter from thesematrices can be represented first by its rowand next by its column, eg ‘A’ can berepresented by 03, 34, 86, etc and ‘N’ can berepresented by 12, 65, 79, etc. Similarly, youhave to identify the set for the given word.REST

Matrix-I

0 1 2 3 4

0 G V E A C

1 R O N G S

2 M N E S I

3 O T I T A

4 N S N E P

Matrix–II

5 6 7 8 9

5 R E O N G

6 N P V E S

7 M T I O N

8 E A I C O

9 N T A R S

A) 55, 43, 23, 69 B) 98, 56, 31, 77C) 10, 02, 69, 88 D) 55, 22, 99, 33

50. If a mirror is placed on the line MN, then whichof the answer figures is the right image of thegiven question figure ?

Question Figure

Answers Figures

A) B) C) D)

Part–B : General Awareness51. A unit price elastic demand curve will touch

A) both price and quantity axisB) neither price axis nor quantity axisC) only price axisD) only quantity axis

52. India follows the policy of non-alignment whichimpliesA) being a third world powerB) choosing its own policiesC) neutrality towards power blocsD) bringing peace and amity to the world

53. If the supply curve is a straight line passingthrough the origin, then the price elasticity ofsupply will beA) less than unity B) infinitely largeC) greater than unity D) equal to unity

54. According to Modern Theory of Rent, rent accrues toA) capital only B) any factorC) labour only D) land only

55. The book which is at the centrepiece of the studyof Macro - Economics was written byA) Prof Samuelson B) Prof JM KeynesC) Prof Benham D) Prof Baumol

56. The basic problem studied in Macro - EconomicsisA) production of incomeB) usage of incomeC) flow of incomeD) distribution of income

57. The number of subjects incorporated in the UnionList isA) 97 B) 102C) 82 D) 89

58. Who was the French Governor of Pondicherry.Who tried to make the French Company as apowerful company ?A) Thomas Arthur, Comte de LallyB) GodeheuC) La BourdonnaisD) Joseph Francois Duplcix

59. The most powerful Peshwa wasA) Balaji Baji Rao B) Baji RaoC) Madhava Rao D) Balaji Vishwanath



60. Democratic Socialism aims atA) bringing about Socialism through peaceful

meansB) bringing about Socialism through violent and

peaceful meansC) bringing about Socialism through violent

meansD) bringing about Socialism through democratic

means61. Two-Party System is found in

A) Russia B) USAC) India D) France

62. Chief Justice of the Supreme Court is appointedby theA) Speaker of the Lok SabhaB) Chairman of the Rajya SabhaC) Prime MinisterD) President

63. What are the folds found in the mucous lining ofthe empty stomach ?A) Typhlosole B) AreolaeC) Rugae D) Villi

64. The first Mysore War fought between the Britishand Hyder Ali in 1767-69 AD, came to an end bytheA) Treaty of PondicherryB) Treaty of MadrasC) Treaty of MysoreD) Treaty of Aix - la - Chapelle

65. The British Government intervened in the affairsof the Company and passed an Act in 1773 AD,known as theA) Regulating Act B) Pit’s India ActC) Charter Act D) Company Act

66. Sher Shah defeated Humayun and captured Gaurin the battle ofA) Ghaghra in 1529 ADB) Chausa in 1539 ADC) Panipat in 1526 ADD) Khanwa in 1527 AD

67. Identify the most infertile amongst the followingsoils.A) Black cotton soil B) Alluvial soilC) Laterite soil D) Peaty soil

68. Spot the odd item of the following :A) Shale B) MarbleC) Limestone D) Sandstone

69. Which of the following reasons is responsible forlack of vegetation in the deserts ?A) Heavy volume of sandsB) Absence of B-horizon in the soilC) High temperatureD) Lack of rainfall

70. Which one of the following pairs is not correctlymatched ?A) Khadar - Zonal soilB) Podzol - Zonal soilC) Chestnut - Zonal soilD) Bhangar - Azonal soil

71. Select the correct direction of Sirocco storm.A) Sahara to Mediterranean SeaB) North from USAC) West from SaharaD) Adriatic Sea to Italy

72. Which among the following is an abiotic factor ?A) Mites B) MoistureC) Insects D) Rodents

73. Leaves of many grasses are capable of folding andunfolding becauseA) their mesophyll is not differentiated into

palisade and spongy parenchymaB) they have stomata on both sides of the leafC) they have high levels of silicaD) they have specialised bulliform cells

74. Pleura is the covering ofA) Lung B) LiverC) Kidney D) Heart

75. Which one of the following is an egg-layingmammal ?A) Sloth B) Duck - billed platypusC) Kangaroo D) Bandicoot

76. The moderator used in a nuclear reactor isA) Uranium B) RadiumC) Ordinary water D) Graphite

77. Solar eclipse occurs whenA) the Moon does not lie on the line joining the

Sun and the EarthB) the Moon comes between the Sun and the

EarthC) the Sun comes between the Moon and the

EarthD) the Earth comes between the Moon and the

Sun78. An aspect of Input/Output controller of data logic

is calledA) General Buffering B) Zero BufferingC) Buffering D) Data Buffering

79. What does BIOS stand for ?A) Basic Internal Output SystemB) Basic Intra Operating SystemC) Basic Internal Organ SystemD) Basic Input Output System

80. The device used to convert solar energy intoelectricity isA) Photovoltaic cellB) Daniell cellC) Electrochemical cellD) Galvanic cell

81. The type of kidneys present in frog areA) Mesonephros B) MetanephrosC) Archinephros D) Pronephros

82. A spinning neutron star is known asA) White dwarf B) Black holeC) Pulsar D) Quasar

83. Light year is a unit ofA) Light B) CurrentC) Distance D) Time

84. The chemical name of “Plaster of Paris” commonly



used for setting broken bones isA) Calcium nitrate B) Calcium sulphateC) Calcium carbonate D) Calcium chloride

85. In our country the ‘Van Mahotsav Day’ isobserved onA) 10th August B) 1st JulyC) 2nd October D) 1st December

86. Medicine of Quinine is provided byA) Cinchona plant B) Money plantC) Eucalyptus plants D) Aconite plants

87. The apparatus used to test acidity of aqueoussolution isA) pH meter B) AmmeterC) Hygrometer D) Acidmeter

88. The Hutti Gold mines are located in the State ofA) Karnataka B) Tamil NaduC) Andhra Pradesh D) Maharashtra

89. Who was the first recipient of ‘Mahathir Award’for Global Peace in August 2013 ?A) Malala Yousafzai B) John BoehnerC) Howard Stern D) Nelson Mandela

90. Process through which plants reproduceA) Pollination B) CondensationC) Eating D) Evaporation

91. Which river serves the largest cultivable area ?A) Ganga B) SaryuC) Godavari D) Krishna

92. In August 2013, who won the InternationalChildren’s Peace Prize?A) Malala Yousafzai B) Angela MerkelC) APJ Abdul Kalam D) Silvio Berlusconi

93. Who is the present President of Pakistan ?A) Asif Ali Zardari B) Nawaz SharifC) Raza Rabbani D) Mamnoon Hussain

94. Who had been selected for the Rajiv GandhiNational Sadbhavana Award 2013 ?A) Amjad Ali Khan B) Gautam GhoshC) Aashish Khan D) Muzaffar Ali

95. Who was elected as the Ninth President ofInternational Olympic Committee (IOC) on 10thSeptember, 2013 ?A) Thomas Bach B) Ching - Kuo - WuC) Sergei Bubka D) Richard Carrion

96. The Indian Grandmaster who won theCommonwealth Chess Championship in 2013 isA) Koneru Humpy B) Magnus CarlsenC) Abhijeet Gupta D) Vishwanathan Anand

97. Who had been selected for the Tagore Award forCultural Harmony in 2013 ?A) Kiran Bedi B) Chetan AnandC) Zubin Mehta D) Anita Desai

98. Who won the US Open Men’s Singles in 2013 inLawn Tennis ?A) Andy Murray B) Roger FedererC) Rafael Nadal D) Novak Djokovic

99. On which date did the Rajya Sabha pass “ TheMarriage Laws” (Amendment) Bill 2012 ?A) 18th August, 2013 B) 5th August, 2013C) 26th August, 2013 D) 23rd August, 2013

100. Which of the following was the first Indianexclusive defence satellite which wassuccessfully launched on 29th August, 2013?A) GSAT-7 B) MIG-47C) GSET-4 D) GSAT-6

Part–C : Quantitative Aptitude101. Solve for x :

3x – 3x–1 = 486.A) 7 B) 9C) 5 D) 6

102. A can do a piece of work in 4 days and B can do itIn 12 days. In how many days will they finish thework, both working together ?A) 4 days B) 6 daysC) 2 days D) 3 days

103. A can do 14

of a work in 10 days. B can do 13 of

the work in 20 days. In how many days can bothA and B together do the work ?A) 30 days B) 32 daysC) 24 days D) 25 days

104. A and B can together finish a work in 30 days.They worked at it for 20 days and then B left. Theremaining work was done by A alone in 20 moredays. A alone can finish the work inA) 60 days B) 54 daysC) 48 days D) 50 days

105. A circular wire of diameter 112 cm is cut and bentin the form of a rectangle whose sides are in theratio of 9 : 7. The smaller side of the rectangle isA) 77 cm B) 97 cmC) 67 cm D) 87 cm

106. A piece of cloth measured with a metre stick,one cm short, is 100 metres long. Reckoning themetre stick as being right, the actual length ofthe cloth (in cm) isA) 3,900 B) 9,900C) 8,000 D) 6,100

107. A parallelogram has sides 60 m and 40 m andone of its diagonals is 80 m long. Its area is

A) 500 15 m2 B) 600 15 m2

C) 400 15 m2 D) 450 15 m2

108. The cost price of a table is `3,200. A merchantwants to make 25 % profit by selling it. At thetime of sale he declares a discount of 20% on themarked price. The marked price (in `) isA) 5,000 B) 6,000C) 4,000 D) 4,500

109. A shopkeeper allows a discount of 12.5 % on themarked price of a certain article and makes aprofit of 20%. If the article costs the shopkeeper



`210, then the marked price of the article will beA) ̀ 387 B) ̀ 350C) `386 D) `288

110. A businessman allows a discount of 10% on themarked price. What per cent above the cost pricemust he mark his goods to make a profit of 17per cent ?A) 27% B) 18%C) 30% D) 20%

111. Some bricks are arranged in an area measuring20 cu m. If the length, breadth and height of eachbrick is 25 cm, 12.5 cm and 8 cm respectively,then in that pile the number of bricks are(suppose there is no gap in between two bricks)A) 6,000 B) 8,000C) 4,000 D) 10,000

112. The average salary per head of all the workers ofan institution is `60. The average salary of 12officers is `400; the average salary per head ofthe rest is `56. The total number of workers inthe institution isA) 1030 B) 1035C) 1020 D) 1032

113. Charging 30% above its production cost a radiomaker puts a label of `286 on a radio as its price.But at the time of selling it, he allows 10%discount on the labelled price. What will his gainbe ?A) ̀ 257.40 B) ̀ 254.40C) `198 D) `37.40

114. In an election, a candidate who gets 84 % of thevotes is elected by a majority of 476 votes. Whatis the total number of votes polled ?A) 900 B) 810C) 600 D) 700

115. A man having height 169 cm is standing near apole. He casts a shadow 130 cm long. What isthe length of the pole if it gives a shadow 420 cmlong?A) 550 cm B) 589 cmC) 323 cm D) 546 cm

116. `555 was to be divided among A, B and C in the

ratio of 1 1 1: :4 5 6 . But by mistake it was divided

in the ratio of 4 : 5 : 6. The amount in excessreceived by C wasA) `72 B) ̀ 75C) `22 D) `52

117. The average of 50 numbers is 38. If two numbers,namely 45 and 55 are discarded, the average ofthe remaining numbers isA) 37.5 B) 37.9C) 36.5 D) 37.0

118. In what time will `8,000, at 3% per annum,produce the same interest as `6,000 does in 5years at 4% simple interest ?A) 5 years B) 6 yearsC) 3 years D) 4 years

119. The reciprocal of x +1x is

A) 2 1x

x + B) 1x

x +

C) 1xx

− D) 1 xx

+

120. What is the value of2.75 2.75 2.75 2.25 2.25 2.252.75 2.75 2.75 2.25 2.25 2.25

× × − × ×× + × + × ?

A) 3 B) 32

C) 1 D) 12

121. The value of 1 111

1

a

aa

−−

+−

is

A) a B) 1 – aC) 1 D) 0

122. The value of 2 15

1

(243) 39 3

nn

n n

+

−

××

is

A) 3 B) 9C) 6 D) 12

123. A speed of 45 km per hour is the same asA) 12.5 metres/seccondB) 13 metres/seccondC) 15 metres/seccondD) 12 metres/seccond

124. A train travelling at a speed of 55 km/hr travelsfrom place X to place Y in 4 hours. If its speed isincreased by 5 km/hr, then the time of journeyis reduced byA) 25 minutes B) 35 minutesC) 20 minutes D) 30 minutes

125. If a, b, c are positive and a + b + c = 1, then the

least value of 1 1 1a b c

+ + is

A) 9 B) 5C) 3 D) 1

126. In a ∆ ABC, ∠A + ∠B = 118°, ∠A + ∠C = 96°. Findthe value of ∠A.A) 36° B) 40°C) 30° D) 34°

127. In ∆ ABC, if AD ⊥ BC, then AB2 + CD2 is equal toA) 2BD2 B) BD2 + AC2

C) 2 AC2 D) None of these128. ABC is an equilateral triangle and CD is the

internal bisector of ∠C. If DC is produced to Esuch that AC = CE, then ∠CAE is equal toA) 45° B) 75°C) 30° D) 15°



129. If x (x – 3) = – 1, then the value of x3 (x3 – 18) isA) – l B) 2C) 1 D) 0

130. The value of (1001)3 isA) 1003003001 B) 100303001C) 100300301 D) 103003001

131. If a (2 + 3 ) = b (2 – 5 ) = 1, then the value of

2 2

1 11 1a b

++ + is

A) –5 B) 1C) 4 D) 9

132. If x sin260° 32

− sec 60° tan230° + 45 sin2 45°

tan260° = 0, then x is

A) – 1

15 B) – 4

C) – 4

15 D) – 2

133. If ∆ ABC is right-angled at B, AB = 6 units, ∠C =30°, then AC is equal toA)12 units B) 15 unitsC) 8 units D) 10 units

134. If 7 sin α = 24 cos α; 0 < α < 2π

, then the value of

14 tan α – 75 cos α – 7 sec α is equal toA) 3 B) 4C) 1 D) 2

135. ∠ACB is an angle in the semicircle of diameterAB = 5 and AC : BC = 3 : 4. The area of the triangleABC is

A) 6 2 sq cm B) 4 sq cmC) 12 sq cm D) 6 sq cm

136. A, B and C are three points on a circle such thatthe angles subtended by the chords AB and ACat the centre O are 90° and 110° respectively.Further suppose that the centre ‘O’ lies in theinterior ∠BAC. The ∠BAC isA) 40° B) 80°C) 160° D) 20°

137. If the lengths of the sides AB, BC and CA of atriangle ABC are 10 cm, 8 cm and 6 cm respectivelyand if M is the mid-point of BC and MN || AB tocut AC at N, then the area of the trapezium ABMNis equal toA) 18 sq cm B) 20 sq cmC) 12 sq cm D) 16 sq cm

138. A type of graph in which a circle is divided intosectors such that each sector represents aproportion of the whole is aA) Line graph B) Stem and leaf chartC) Bar graph D) Pie chart

139. The value of x which satisfies the equation 2

cosec2 30° + x sin2 60° – 34

tan2 30° = 10 is

A) 2 B) 3C) 0 D) 1

140. If 2 sin θ + cos θ = 73 , then the value of (tan2 θ –

sec2 θ) isA) 0 B) –l

3 37

C) 73

141. From a point 20 m away from the foot of a tower,the angle of elevation of the top of the tower is30°. The height of the tower is

A) 10 3 m B) 20 3 m

C) 10

3 m D) 203 m

142. If 29 tan θ = 31, then the value of 1 2 sin cos1 2sin cos

θ θθ θ

+−

is equal toA) 810 B) 900C) 540 D)490

143. The categories of qualitative variables arerepresented by bars where the height of each bar isA) class frequencyB) class percentageC) class relative frequencyD) All of the above

144. In a cyclic quadrilateral ∠A + ∠C = ∠B + ∠D = ?

A) 270° B) 360°C) 90° D) 180°

145. In the given figure, ∠ ONY = 50° and ∠ OMY =15°. Then the value of the ∠ MON is

A) 30° B) 40°C) 20° D) 70°Directions (Q. 146–148) : The distribution of

fruit consumption in a sample of 72 seventeen-year-old girls is given in the graph below. Studythe graph and answer the questions.



Distribution of fruit consumption

146. How many of these girls ate fewer than twoservings per day ?A) 15 B) 40C) 25 D) None of these

147. What per cent of these girls ate six or moreservings per day ?A) 12.5% B) 13%C) 10% D) 11%

148. How many of these girls ate more than twoservings but less than six servings per day ?A) 26 B) 18C) 23 D) 38

149. The following pie-chart shows the monthlyexpenditure of a family on food, clothing, rent,miscellaneous expenses and savings. What isthe central angle for savings ?

A) 54° B) 56°C) 50° D) 52°

150. The pie-chart gives the expenditure (in percentage)on various items and savings of a family during amonth. Monthly savings of the family is `3,000.On which item is the expenditure maximum andhow much is it ?

A) Others, `2,000 B) Food, `3,000C) Others, `5,000 D) Food, `5,000

Part–D : English ComprehensionDirections (Q. 151–155) : In the following

questions, some parts of the sentences have errorsand some are correct. Find out which part of asentence has an error. The number of that part isthe answer. If a sentence is free from error, youranswer is D) ie, No error.151. The new device A)/aims at eliminating B)/the risk

of short-circuiting. C)/No error D)152. I wish to heartily A)/congratulate you for B)/your

astounding success. C)/No error D)153. The visitor took the vacant seat A)/next from

mine B)/one of the many huge sofas in the room.C)/ No error D)

154. He was A)/a learnt man among lords, B)/and alord among learned men. C)/No error D)

155. With our great annoyance A)/we found the groundB)/filled with broken glasses. C)/No error D)Directions (Q. 156–160) : In the following

questions, sentences are given with blanks to befilled in with an appropriate word(s) . Fouralternatives are suggested for each question.Choose the correct alternative out of the four.156. Her true feelings manifested themselves in her

sarcastic remarks, only then was her ________revealed.A) sarcasm B) charmC) sweetness D) bitterness

157. The book provides an overview of European winesthat should prove inviting to both the virtual________ and the experienced connoisseur.A) zealot B) gluttonC) prodigal D) novice

158. The sun is shining brightly, please ________ thelight.A) take off B) put onC) put off D) put out

159. This practice was brought ________ to preventcertain abuses.A) down B) offC) about D) in

160. This package was supposed ________ yesterday.A) to be delivering



B) not to be deliveredC) to have been deliveredD) to deliverDirections (Q. 161–163) : In the following

questions, out of the four alternatives, choose theone which best expresses the meaning of the givenword.161. Garble

A) Confuse B) HideC) Communicate D) Explain

162. PinnacleA) Capsule B) HeartC) Summit D) Pit

163. BrutaliseA) Stir B) Ill-treatC) Devise D) StrikeDirections (Q. 164–166) : In the following

questions, choose the word opposite in meaningto the given word as your answer.164. Denounce

A) Signify B) ConfirmC) Grant D) Praise

165. CeaseA) Abandon B) InitiateC) Confront D) Confiscate

166. SeamyA) Honest B) PureC) Unpleasant D) SincereDirections (Q. 167–171) : In the following

questions, four alternatives are given for theIdiom/Phrase printed in bold in the sentence.Choose the alternative which best expresses themeaning of the Idiom/Phrase.167. The secretary’s thoughtless remark added fuel

to the fire.A) added humour to the situationB) worsened the difficult situationC) helped in improving the situationD) prevented the situation

168. He could not get money from his master becausehe rubbed him up the wrong way.A) irked or irritated himB) asked him to speed upC) suggested a wrong methodD) advised him to be strict

169. Ask Mr Das. He can give you all the news youneed : he is always in the swim.A) giving news to othersB) at the swimming poolC) in search of newsD) well-informed and up-to-date

170. You have been trying to solve this puzzle for along time, be careful so that you avoid barkingup the wrong tree.A) trying to solve problemsB) trying to find something at a wrong placeC) keep working constantlyD) climbing the wrong tree

171. I’ll be able to do my job very well when I know

the ropes.A) become bolderB) work in silenceC) learn the proceduresD) gain confidenceDirections (Q. 172–181) : In the following

questions, a part of the sentence is printed inbold. Below are given alternatives to the bold partat A), B), C) which may improve the sentence.Choose the correct alternative. In case noimprovement is needed your answer is D).172. Ram filled ink into his pen before leaving for

school.A) filled ink in his penB) filled ink on his penC) filled his pen with inkD) No improvement

173. The toys he bought for Suzy are too good to becheap.A) are so much good to be cheapB) were so good to be cheapC) are so good that to be cheapD) No improvement

174. I did one mistake in the dictation test today.A) I made a mistake inB) I did a mistake atC) I did a mistake inD) No improvement

175. John has been detained at a meeting.A) by the meeting B) in meetingC) on a meeting D) No improvement

176. The butler was as devoted as a faithful dog.A) a faithful cat B) a faithful friendC) a faithful pet D) No improvement

177. The government representative furnished thereporters all details.A) provided the reporters all detailsB) furnished the reporters with all the detailsC) furnished reporters all detailsD) No improvement

178. It was raining so heavily yesterday that I couldnot move out for my usual walk.A) I could not go out for my usual walkB) I could not go to my usual walkC) I could not move for my usual walkD) No improvement

179. There is an error in grammar in this sentence.A) a written error B) a grammatical errorC) a grammar error D) No improvement

180. He denied that he had not forged my signature.A) would not forge B) did not forgeC) had forged D) No improvement

181. To his astonishment and admiration he got theinformation that it was only the picture of acurtain.A) foundB) received the informationC) saw clearlyD) No improvement



Directions (Q. 182–188) : In the followingquestions, out of the four alternatives, choose theone which can be substituted for the given words/sentence.182. Study of caves

A) Speleology B) SeismologyC) Topology D) Numismatics

183. Government by the fewA) Oligarchy B) AutocracyC) Monarchy D) Anarchy

184. Materials that change naturally by the action ofbacteriaA) Inflammable B) PerishableC) Biological D) Biodegradable

185. Having a stale smell or tasteA) Rancid B) InsipidC) Savoury D) Tepid

186. A wooden object used for connecting animals thatare pulling a vehicleA) Rein B) LeashC) Whip D) Yoke

187. A man who knows a lot about things like food,music and artA) Priest B) OptimistC) Hostage D) Connoisseur

188. A doctor who specializes in diseases of the noseA) Rhinologist B) OtologistC) Pathologist D) PodiatristDirections (Q. 189–190) : In the following

questions, four words are given in each question,out of which only one word is correctly spelt. Findthe correctly spelt word.189. A) Inteligibelity B) Inteligibillity

C) Intelligibility D) Inteligibility190. A) Exterpate B) Extirpeit

C) Extirpate D) ExtripaiteDirections (Q. 191–200) : In the following

questions, you have two brief passages with 5questions following each passage. Read thepassages carefully and choose the best answer toeach question out of the four alternatives.

Passage–I(Q. No. 191–195)

A crucial element that defines the soap opera isthe open ended nature of the narrative, with storiesspanning several episodes. One of the defining featuresthat makes a television program a soap opera accordingto Albert Moran is “that form of television that workswith a continuous open narrative. Each episode endswith a promise that the storyline is to be continued inanother episode.”

In 2012, Robert Lloyd of the Los Angeles Timeswrote of daily dramas, “Although melodramaticallyeventful, soap operas such as this also have a luxuryof space that makes them seem more naturalistic,indeed, the economics of the form demand long scenes,and conversations that a 22- episodes-per-season

weekly series might dispense with in half a dozen linesof dialogue may be drawn out, as here, for pages. Youspend more time even with the minor characters, theapparent villains grow less apparently villainous.”

Soap opera storylines run concurrently, intersectand lead into further developments. An individualepisode of a soap opera will generally switch betweenseveral different concurrent narrative threads that mayat times interconnect and effect one another or mayrun entirely independent of each other. Evening soapoperas and serials that run for only a part of the yeartend to bring things to a dramatic end of seasoncliffhanger.191. A soap opera has the space for it to be more

A) artistic B) naturalisticC) dramatic D) tragic

192. The economics of a soap opera form demands forit to haveA) long scenesB) luxurious spaceC) melodramatic eventsD) promising storylines

193. An individual episode of a soap opera generallyswitches betweenA) more time spent with minor charaters.B) apparent villains that grow less apparent

villainous.C) successive intersections of events.D)different concurrent narrative threads.

194. Soap operas that run for a part of the year usuallyend inA) a cliff B) an episodeC) a cliffhanger D) a sequence

195. What does the author mean by the open-endednature of soap operas ?A) Each episode ends with a promise that the

storyline is to be continued in another episodeB) Every episode has a different storyC) Every episode ends abruptlyD) Consecutive episodes have no connection

Passage–II(Q. No. 196–200)

Two or three days and nights went by; I reckon Imight say they swum by, they slid along so quiet andsmooth and lovely. Here is the way we put it in thetime. It was a monstrous big river down there -sometimes a mile and a half wide; we ran nights, andlaid up and hid daytimes; soon as night was most gonewe stopped navigating and tied up - nearly always inthe dead water under a towhead; and then cut youngcottonwoods and willows, and hid the raft with them.Then we set out the lines. Next we slid into the riverand had a swim, so as to freshen up and cool off; thenwe set down on the sandy bottom where the water wasabout knee deep and watched the daylight come. Not asound anywhere - perfectly still - just like the wholeworld was asleep only sometimes the bullfrogs acluttering maybe. The first thing to see, looking away



over the water was a kind of dull line - that was thewoods on the other side; you couldn’t make nothingelse out; then a pale place in the sky; then morepaleness spreading around; then the river softenedup away off, and wasn’t black any more, but gray; youcould see little dark spots drifting along ever so faraway - trading scows and such things and long blackstreaks - rafts; sometimes you could hear a sweepcreaking or jumbled up voices, it was so still andsounds come so far and by and by you could see astreak on the water which you know by the look of thestreak that there’s a snag there in a swift current whichbreaks on it and makes that streak look that way.196. They stopped navigating

A) at night B) at duskC) at daytime D) at dawn

197. After a swim in the moor theyA) set down on the sandy bottom where the water

was about ankle deep and watched the daylightcome.

B) set down on the sandy bottom where the waterwas about knee deep and watched the daylightcome.

C) set down on the sandy shore and watched thedaylight come.

D) set down on the sandy bottom and watchedthe daylight come.

198. In the stillness of the nightA) sounds come so farB) the bullfrogs also were asleepC) the whole world was asleepD) a sweep creaking or jumbled up voices could

be heard199. The streak on the water looks as it does because

A) the swift current has broken the streakB) the streak has been swept by the swift current

to the shore.C) of a snag there in the swift current which

breaks on it.D) the streak has been swept by the swift current.

200. How did the days and nights go by, according tothe writer?A) They slid along so quiet and smooth and lovely.B) They slid along so smooth and quietly.C) They slid along so smooth and soft and quietly.D) They slid along so quietly and smooth and

softly.

Answers and explanations1. C; As, 23 – 10 = 13

Similarly,54 – 10 = 44

2. B; As, Seismometer is a scientific instrument formeasuring the intensity of earthquakes.Similarly, thermometer is used for measuringtemperature.

3. C; As, Actors take part in play. Similarly, musiciansperform concert.

4. B; As,

5. A; As,

6. B; 17 × 9 = 15324 × 9 = 216

7. D; Flee is different from the other three words. Fleemeans escape. Duck, Avoid and Dodge implymore or less similar meaning.

8. A; Except 36, all other numbers are multiples of 8.9. B; Except in the number pair (83, 6) in all other

pairs the first digit of the first number is thesecond number.

10. B;

11. D; Emu is a large Australian bird that runs quicklybut cannot fly. Penguin is a black and white seabird living in the Antarctic. It cannot fly butused their wings for swimming. Kiwi is a birdwith a long beak, short wings and no tail, foundin New Zealand. It cannot fly. Eagle is a largestrong bird that hunts and eats small animals.

12. D 13. A14. B; R K S B P M / R K S B P M / R K S15. B; G G H I H I I G G J K L M G I H I G16. A; There are two alternating series:

17. B;



18. A;

19. C; On arranging according to the fairness, we havethe following :O > LM > OThus, N > M > O > L

20. C; The father of Anjali’s sister’s brother meansfather of Anjali. Only son of Anjali’s fathermeans brother of Anjali.

21. A; There is no S letter in the given word. Therefore,the words FUNDS and NOSE cannot be formed.There are no T and R letters in the given word.Therefore, the word DETRIMENTAL cannot beformed.

22. A; There are only one A and T in the given word.Therefore, the word MATHEMATICS cannot beformed.

23. C; Let the required years be x.Now, according to the question,

26 142 2

−=

−xx

⇒ 52 – 2x = 42 – x⇒ x = 10 years

24. A; As,

Similarly,

25. C; As, I N D U S↓ ↓ ↓ ↓ ↓0 3 8 6 5

and T E N N I S↓ ↓ ↓ ↓ ↓ ↓2 4 3 3 0 5

Therefore,S T U D E N T↓ ↓ ↓ ↓ ↓ ↓ ↓5 2 6 8 4 3 2

26. A; H E I G H T↓ ↓ ↓ ↓ ↓ ↓= ÷ ( × = ||

27. A; 01 : 30 – 08 : 00= 05 : 30 (5 hours 30 minutes) Normally thebell is rung 11 times. But five times it is rung

three times, ie, (5 × 3 – 5 =) 10 times extra.So, total = 11 + 10 = 21 times

28. D; E X A M I N A T I O N3 4 2 6 5 9 2 8 5 7 9

29. *; Option (A)( 121 – 9) + 5 × 4 = 1⇒ (11 – 9) + 5 × 4 =1⇒ 2 + 5 × 4 = 1 ⇔ 2 + 20 ≠ 1Option (B)( 121 + 9) ÷ 5 × 4 = 1⇒ (11 + 9) ÷ 5 × 4 =1

⇒ 205 × 4 ≠ 1

Option (C)( 121 = 9) + 5 × 4 ÷ 1

⇒ 11 ≠ 9 + 20Option (D)( 121 – 9) × 5 ÷ 4 = 1⇒ (l l – 9 ) × 5 + 4 = l⇒ 2 × 5 + 4 ≠ 1

30. B; Option (A)36 × 4 – 12 + 5 ÷ 3 = 420⇒ 36 + 4 ÷ 12 × 5 – 3 = 420

⇒ 36 + 4

12 × 5 – 3 = 420

⇒ 36 + 53 – 3 = 420

⇒ 108 5 – 9 420

3+

= ⇔ 104 420

3≠

Option (B)52 ÷ 4 + 5 × 8 – 2 = 36⇒ 52 – 4 × 5 + 8 ÷ 2 = 36⇒ 52 – 4 × 5 + 4 = 36⇒ 52 – 20 + 4 = 36 ⇔ 56 – 20 = 36Option (C)36 – 12 × 6 ÷ 3 + 4 = 60⇒ 36 + 12 + 6 – 3 × 4 = 60⇒ 3 + 6 – 12 ≠ 60Option (D)43 × 7 ÷ 5 + 4 – 8 = 25⇒ 43 + 7 – 5 × 4 ÷ 8 = 25

⇒ 43 + 7 – 52 = 25

⇒ 50 – 5 252

≠

31. A; 5 3 = – 7⇒ (5 × 3) – (5 + 3)⇒ 15 – 8 = 77 ⇒ – 73 7 = – 1⇒ (3 × 7) – (3 + 7)⇒ 21 – 10 = 11


11 ⇒ – 117 11⇒ (7 × 11) – (7 + 11)⇒ 77 – 18 = 5959 ⇒ – 59

32. D; First Column:8 × 6 = 4848 ÷ 3 = 16Second Column:4 × 9 = 3636 ÷ 3 = 12Third Column:7 × 9 = 6363 ÷ 3 = 21

33. A; First Row:3 + 8 + 7 = 18Second Row:9 + 6 + 3 = 18Third Row:2 + ? + 12 = 18⇒ ? = 18 – 14 = 4

34. A; First Column:(2 + 9) × (9 – 2) = 11 × 7 = 77Second Column:(4 + 7) × (7 – 4) = 11 × 3 = 33Third Column:(3 + 6) × (6 – 3) = 9 × 3 = 27Fourth Column:(2 + 5) × (5 – 2) = 7 × 3 = 21

35. D; Some chickens are hens → conversion → Somehens are chickens + All chickens are birds = I +A = I = Some hens are birds. Therefore,conclusion II follows. Again, Female birds layeggs → Some birds lay eggs. Therefore,conclusion I does not follow.

36. B;

Clearly, the man is facing South-West direction.

37. D;

Required distance = AE = AD + DE= (5 + 10) km = 15 km

38. A

39. B;

The triangles are as given below : ∆ ADF;∆ ADE; ∆ AFE; ∆ EKM; ∆ ELK; ∆ ELM; ∆ GHJ;∆ GIH; ∆ GIJ; ∆ ABC; ∆ ANB; ∆ ANC;

40. D 41. C42. A; The letter ‘R’ is present in all the three

geometrical figures.43. A; Duck is different from Penguin. But both are

birds.

44. D; Dividend is a part of profit. Bonus is alsoconsidered as profit.

45. D 46. C 47. A 48. D49. D; R ⇒ 10, 55, 98

E ⇒ 02, 22, 43, 56, 68, 85S ⇒ 14, 23, 41, 69, 99T ⇒ 31, 33, 76, 96


Options R E S T

A) 55 43 23 69

B) 98 56 31 77

C) 10 02 69 88

D) 55 22 99 33

50. D 51. B 52. C 53. D 54. B 55. B56. A 57. A 58. D 59. B 60. D 61. B62. D 63. C 64. B 65. A 66. B 67. C68. B 69. D 70. A 71. A 72. B 73. D74. A 75. B 76. C 77. B 78. C 79. D80. A 81. A 82. C 83. C 84. B 85. B86. A 87. A 88. A 89. D 90. A 91. A92. A 93. D 94. A 95. A 96. C 97. C98. C 99. C 100. A101. D; 3x – 3x–1 = 486

⇒ 3x–1 (3 – 1) = 486⇒ 3x–1 × 2 = 486

⇒ 3x–1 = 4862 = 243

⇒ 3x–1 = 35 ⇒ x – 1 = 5⇒ x = 5 + 1 = 6

102. D; A’s 1 day’s work = 14

B’s 1 day’s work = 1

12

(A + B)’s 1 day’s work = 1 14 12

+ =3 1 4 112 12 3+

= =

∴ Required time = 3 days

103. C; A does 14

work in 10 days

∴ A will do 1 work in (10 × 4 =) 40 daysSimilarly, B will do the same work in (20 × 3 =)60 days

∴ (A + B)’s 1 day’s work = 1 140 60

+

= 3 2 5 1120 150 24

+= =

∴ Required time = 24 days104. A; (A + B) together do the work in 30 days.

∴ (A + B)’s 1 day’s work = 130

∴ (A + B)’s 20 days’ work = 20 230 3

=

Remaining work = 1 – 2 13 3

=

Time taken by A in doing 13 work = 20 days

∴ Time taken in doing 1 work = (20 × 3 =) 60 days.

105. A; Circumference of circular shape = π × diameter

= 227

× 112 = 352 cm = length of wire

∴ Perimeter of rectangle = 2 (length + breadth)⇒ 2(l + b) = 352

⇒ l + b = 3522 = 176

∴ Smaller side of rectangle =7 176

16⎛ ⎞× =⎜ ⎟⎝ ⎠ 77cm

106. B; ∵ 1 metre ≡ 99 cm∴ 100 metre ≡ 9900 cm

107. B;

Semiperimeters of ∆ ABC

6 40 802 2

+ + + +⎛ ⎞= = =⎜ ⎟⎝ ⎠a b c

90 metres

∴ Area of ∆ ABC ( )( )( )s s a s b s c= − − −

90(90 60)(90 40)(90 80)= − − −

90 30 50 10= × × ×

3 30 30 5 10 10= × × × × × = 30 × 10 15

= 300 15 sq metres∴ Area of ABCD= 2 × Area of ∆ ABC

= 2 × 300 15 = 600 15 sq metres108. A; Let the marked price of table be Rs x.

Now, according to the question,

80 3200 125100 100

x × ×=

⇒ x × 80 = 3200 × 125

⇒ x = 3200 120

80×

= Rs 5000

109. D; Let the marked price of article be Rs x.Now, according to the question,

(100 12.5) 210 120100 100

× − ×=

x

⇒ x × 87.5 = 210 × 120

⇒ x = 210 120

87.5×

= Rs 288


110. C; Let CP of the article be Rs 100 and the markedprice of the article Rs x.Now, according to the question,

90 117100

x × =

⇒ x = 117 100

90×

= Rs 130

⇒ 30% above the cost prices.111. B; Volume of pile = 20 cu metre

= 20 × (100)3 cu cmVolume of one brick = (25 × 12.5 × 8) cu cm∴ Required number of bricks

= 20 100 100 100 8000

25 12.5 8× × ×

=× ×

112. D; Let the number of other workers except officersbe x.Now, according to the question,12 × 400 + x × 56 = (x + 12) × 60⇒ 4800 + 56x = 60x + 720⇒ 60x – 56x = 4800 – 720⇒ 4x = 4080

⇒ x = 4080

10204

=

∴ Total number of workers = 1020 + 12 = 1032113. D; Let the production cost of radio be Rs x.

Now, according to the question,130

100x ×

= 286

⇒ x = 286 10

130×

= Rs 220

∴ Selling price = 90% of 286

286 90

100×

= = Rs 257.40

∴ Profit = Rs (257.40 – 220) = Rs 37.40114. D; Let the total number of votes polled be x.

Now, according to the question,84 16 476

100 100x x× ×

− =

⇒ 68 476100

x=

⇒ x = 476 100 700

68×

=

115. D;Height of manHeight of pole

Lengthof shadow of manLentgthof shadow of pole

=

⇒ 169 130

Heightof pole 420=

⇒ Height of pole × 130 = 169 × 420

⇒ Height of pole = 169 420

130×

= 546 cm

116. A; Case I:

A : B : C = 1 1 1 1 1 1: : 60 : 60 : 604 5 6 4 5 6

= × × ×

[LCM of 4, 5 and 6 = 60]= 15 : 12 : 10

Sum of ratios = 15 + 12 + 10 = 37

∴ C’s share = 1037 × 555 = Rs 150

Case II:A : B : C = 4 : 5 : 6Sum of ratios = 4 + 5 + 6 = 15

∴ C’s share = 6

15 × 555 = Rs 222

∴ Required answer = Rs (222 – 150) = Rs 72117. A; Sum of 50 numbers = 50 × 33 = 1900

Sum of 48 numbers = 1900 – 45 – 55 = 1800

∴ Required average 1800

48= = 37.5

118. A; Let the required time be t years.Pr incipal Rate TimeSI

100× ×

=

∴ 6000 4 5 8000 3

100 100t× × × ×

=

⇒ 600 × 4 × 5 = 8000 × 3 × t

∴ t = 6000 4 5

8000 3× ×

× = 5years

119. A; x + 21 1x

x x+

=

∴ Its reciprocal = 2 1x

x +120. D; Let 2.75 = a and 2.25 = b

∴ The given expression = 3 3

2 2

a ba ab b

−+ +

2 2

2 2

( )( )a b a ab ba ab b

− + +=

+ + = a – b = 2.75 – 2.25

= 0.50 = 12

121. D; The given expression = 1 111

1

−−

+−

a

aa

1 11 11

= −− − +

−

a

a aa

1 11 1 (1 )1 11

= − = −− −−

−

a aa

a

11 1

= −− +

aa = 1 – 1 = 0

122. B; The given expression 2 15

1

(243) 39 3

nn

n n

+

−

×=

×55 2 1 2 15 5

2 1 2 1

(3 ) 3 (3) 3(3 ) 3 3 3

n nn n

n n n n

×+ +

− −

× ×= =

× ×2 1 3 1

2 1 3 1

3 3 33 3 3

+ +

− −

×= =

×

n n n

n n n = 33n+1–3n+1 = 32 = 9

[∵ am × an = am+n; am ÷ an = am–n; (am)n = amn]


123. A; Speed = 45 kmph45 100060 60

×⎛ ⎞= ⎜ ⎟⎝ ⎠× metres/second

45 518

×⎛ ⎞= ⎜ ⎟⎝ ⎠ metres/second

= 12.5 metres/second124. C; Distance between stations X and Y = Speed

× Time = (55 × 4 =) 220 kmNew speed = (55 + 5 =) 60 kmph

∴ Required time = 220 1160 3

= hours

= 3 hours 40 minutes.∴ Required answer = 4 hours – 3 hours 40 m

in utes = 20 minutes

125. A; The value of 1 1 1a b c

+ + will be minimum, if

values of a, b and c be maximum.∵ a + b + c = 1∴ Values of a , b and c will be maximum ifa = b = c

∴ a = b = c = 13

∴ 1 1 1a b c

+ + = 3 + 3 + 3 = 9

126. D; In ∆ ABC, ∠A + ∠B + ∠C = 180°∠A + ∠B = 118°∴ ∠C = 180° – 118° = 62°∴ ∠A + ∠C = 96°⇒ ∠A + 62° = 96° ⇔ ∠A = 96° – 62° = 34°

127. B;

In ∆ ABD, AB2 = AD2 + BD2

In ∆ ADC, AC2 = AD2 + CD2

∴ AB2 + CD2 = AD2 + BD2 + CD2

= AD2 + CD2 + BD2 = AC2 + BD2

128. D;

∠BCD = ∠DCA = 30°∠DCE = 180°∴ ∠ACE = 180° – 30° = 150°Again, AC = CE

∴ ∠CAE = ∠CEA = 302

° = 15°

129. A; x(x – 3 ) = –1⇒ x2 – 3x = – l⇒ x2 – 3x + 1 = 0The given expression = x3 (x3 – 18) = x6 – 18x3

On dividing x6 – 18x3 by x2 – 3x + 1, we get,x2–3x + 1) x6 – 18x3 (x4+3x3 + 8x2 + 3x x6–3 x5 +x4

- + - 3x5 – x4 – 18x3

3x5 – 9x4 + 3x3

- + - 8x4 – 21x3

8x4 – 24x3 + 8x2

- + - 3x3 – 8x2

3x3 – 9x2 + 3x - + -

x2 – 3x∴ x6 – 18x3 = (x4 + 3x3 + 8x2 + 3x) (x2 – 3x + 1) +x2 – 3x = 0 + x (x – 3) = – 1

130. A; 1001 × 1001 = 10020011001 × 1001 × 1001 = 1003003001

131. B; a(2 + 3 ) = b (2 – 3 ) = 1

⇒ a = 1 2 3

2 3 (2 3)(2 3)−

=+ + −

⇒ a = 2 3 2 34 3−

= = −+

and b 1

2 3=

−

2 3 2 32 3

4 3(2 3)(2 3)+ +

= = = +−− +

∴ a2 + 1 = (2 – 3 )2 + 1

= 4 + 3 – 4 3 + 1 = 8 – 4 3

b2 + 1 = (2 + 3 )2 + 1

= 4 + 3 + 4 3 + 1 = 8 + 4 3

∴ 2 2

1 1 1 11 1 8 4 3 8 4 3a b

+ = ++ + − +

8 4 3 8 4 3 1664 16 3(8 4 3)(8 4 3)

+ + −= =

− ×− +

16 16 164 48 16

= = =−

132. C; xsin260°–32

sec 60°. tan230° +45

sin245°. tan2

60° = 0


⇒ x .

2 223 3 1 4 12.

2 2 53 2⎛ ⎞ ⎛ ⎞⎛ ⎞

− × + × ×⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

2( 3) 0=

⇒ 3 3 1 4 12 3 04 2 3 5 2

− × × + × × =x

⇒ 3 61 04 5x

− + = ⇔ 3 6 5 6 114 5 5 5x − −

= − = =

⇒ x = – 1 4 45 3 15

−× =

133. A;

In ∆ ABC, sin 30° = ABAC

⇒ 1 62 AC

= ⇒ AC = (2 × 6 =) 12 units

134. D; 7 sinα = 24 cosα

⇒ sin 24cos 7

αα

= ⇒ tanα 247

=

∴ secα = 2

2 24tan 17

α ⎛ ⎞+ = + ⎜ ⎟⎝ ⎠

576 49 576 625 25149 49 49 7

+= + = = =

∴ cosα = 1 7

sec 25α=

∴ 14 tanα – 75 cosα – 7 secα

= 14 × 247

– 75 × 725 – 7 ×

257

= 28 – 21 – 25 = 2

135. D;

Angle at the semi-circle is a right angle.∴ ∠ACB = 90°AB = 5 cm (given)

Let AC and BC be 3x cm and 4x cm respectively.∴ (3x)2 + (4x)2 = (5)2 [By Pythagoras Theorem]⇒ 9x2 + 16x2 = 25 ⇒ 25x2 = 25⇒ x2 = 1 ⇒ x = 1

∴ Area of ∆ABC =12 × BC × AC

= 1 4 32

⎛ ⎞× × =⎜ ⎟⎝ ⎠ 6 sq cm

136. B;

In ∆ OAB, ∠AOB = 90°OA = OB = radii

∴ ∠OAB = ∠OBA = 180 90 45

2° − °

= °

In ∆AOC, ∠AOC = 110°OA = OC

∴ ∠OAC = ∠ACO = 180 110 70 35

2 2° − ° °

= = °

∴ ∠CAB = ∠BAO + ∠OAC = 45° + 35° = 80°

137. A;

∵ 82 + 62 = 102

∵ ABC is a right-angled triangle.CM = MB = 4 cmN is the mid-point of AC.∴ CN = 3 cm∴ Area of trapezium ABMN= Area of ∆ ABC - Area of ∆ CMN

1 16 8 3 42 2

= × × − × × = 24 – 6 = 18 sq cm

138. D

139. B; 2 cosec230 + x sin260°34

− tan230° = 10

⇒ 2 × (2)2 + x ×

2 23 3 110

2 4 3⎛ ⎞ ⎛ ⎞

− × =⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠


⇒ 8 + 3 3 1 104 4 3x

− × =

⇒ 3 1

10 84 4x

= + −

⇒ 3 94 4x

= ⇒ 3x = 9 ⇔ x 9 33

= =

140. B tan2θ – sec2θ = – (sec2θ – tan2θ) = – 1

141. D;

AB = Tower, BC = 20 metresIn ∆ ABC,

tan 30° = ABBC ⇒

1 AB203

=

⇒ AB = 203 metres

142. B; 29 tanθ = 31 ⇒ tanθ = 3129

The given expression 1 2sin .cos1 2sin cos

θ θθ θ

+=

−

2 2 2

2 2 2

s in cos 2sin .cos (sin cos )sin cos 2sin .cos (sin cos )

θ θ θ θ θ θθ θ θ θ θ θ

+ + += =

+ − −

2sin cos

tan 1cos cossin cos tan 1cos cos

θ θθθ θ

θ θ θθ θ

⎛ ⎞+ +⎜ ⎟ ⎛ ⎞= = ⎜ ⎟⎜ ⎟ ⎝ ⎠−−⎜ ⎟⎝ ⎠

2 2

231 31 291 6029 2931 31 29 2129 29

+⎛ ⎞ ⎛ ⎞+⎜ ⎟ ⎜ ⎟ ⎛ ⎞= = = ⎜ ⎟⎜ ⎟ ⎜ ⎟− ⎝ ⎠⎜ ⎟ ⎜ ⎟−⎝ ⎠ ⎝ ⎠= (30)2 = 900

143. D

144. D;

The sum of opposite angles of a cyclicquadrilateral = 180°∴ ∠A + ∠C = ∠B + ∠D = 180°

145. D;

In ∆ ONY, ON = OY = radii∠ONY = 50° = ∠OYN∴ ∠NOY = 180° – 2 × 50° = 80°In ∆ OMY,OM = OY = radii∴ ∠OMY = ∠OYN = 15°∴ ∠MOY= 180° – 2 × 15° = 150°∴ ∠MON = 150° – 80° = 70°

(146–148):146. C; Required number of girls = 15 + 10 = 25147. A; Number of girls who ate six or more servings

per day = 3 + 3 + 3 = 9

∴ Required percentage 9 100

72= ×

25 12.5%2

= =

148. C; Required number of girls = 10 + 8 + 5 = 23.149. A; Food + Rent + Clothing + Miscellaneous

⇒ 108 ° + 90° + 36° + 72° = 306°∴ Savings ⇒ 360° – 306° = 54°.

150. D; Expenditure on food = 25%Savings = 15%∵ 15% ≡ Rs 3000

∴ 25% 300015

≡ × 25 = Rs 5000

151. C; Short-circuit = a failure in an electrical circuit.Therefore, replace ‘short-circuiting’ with ‘sort-circuit’

152. B; Replace ‘for’ with ‘on’.153. B; Replace ‘from’ with ‘to’.154. B; Replace ‘learnt’ with ‘learned’

Learned = having a lot of knowledge155. A; Replace ‘with’ with ‘to’.

Annoyance = the feeling of being slightlyangry; irritation.

156. D; Bitterness = very serious and unpleasant,with a lot of anger and hatred involved.

157. D; Novice = a person who is new and has littleexperience in a skill or job.

158. D; To put out = to stop something from burningor shining.

159. D; To bring in - to introduce a new law.160. B161. A; To garble = to confuse.


162. C; Pinnacle = peak, summit; the most importantor successful part of something.

163. B; To brutalise = to make somebody unable tofeel normal human emotions such as pity ;to treat somebody in a cruel or violent way.

164. D; To denounce = to strongly criticise somebody/something.To praise = to compliment ; to express yourapproval or admiration.

165. B; To cease = to stop happening or existing.To initiate = to make something begin; toset in motion.

166. B; Seamy = unpleasant and immoral; sordid.Sincere = genuine, honest.Pure = morally good ; complete; clean.

167. B; To add fuel to fire = to make an argumentcontinue or get worse.

168. A; To rub somebody the wrong way = to makesomebody annoyed or angry, often withoutintending to.

169. D; In the swim = involved in things that arehappening in society or in a particular

situation.170. B; Barking up the wrong tree = having the

wrong idea about how to get or achieve it.171. C; To know the ropes = to show

somebodyknow/learn how a particular jobshould be done.

172. C 173. D 174. A175. D; To detain = to delay somebody or prevent

them from going somewhere.176. D; Pet = an animal, a bird etc, at home for

pleasure.177. B; To furnish somebody with something = to

supply or provide something.178. A179. B; A grammatial error = An error related to

grammar.180. C; To deny = to refuse to admit.181. B 182. A 183. A 184. D 185. A186. D 187. D 188. A 189. C190. C; To extirpate = to get rid of something bad.191. B 192. A 193. D 194. C 195. A196. A 197. B 198. C 199. C 200. A

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