UPKAR PRAKASHAN, AGRA-2

ByDr. Lal, Jain

&Ashok Yadav

© Publishers

Publishers

UPKAR PRAKASHAN2/11A, Swadeshi Bima Nagar, AGRA–282 002Phone : 4053333, 2530966, 2531101Fax : (0562) 4053330E-mail : care@upkar.in, Website : www.upkar.in

Branch Offices :4845, Ansari Road, Daryaganj,New Delhi—110 002Phone : 011–23251844/66

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8-310/1, A. K. House,Heeranagar, Haldwani,Distt.—Nainital—263 139(Uttarakhand)Mob. : 7060421008

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63-64, Kailash Marg,Ground Floor,Shreeji Avenue, Malharganj,Indore—452 002 (M.P.)Mob. : 08899588088

● The publishers have taken all possible precautions in publishing this book, yet if any mistake hascrept in, the publishers shall not be responsible for the same.

● This book or any part thereof may not be reproduced in any form by Photographic, Mechanical,or any other method, for any use, without written permission from the Publishers.

● Only the courts at Agra shall have the jurisdiction for any legal dispute.

ISBN : 978-81-7482-152-2

Code No. 372

Printed at : UPKAR PRAKASHAN (Printing Unit) Bye-pass, AGRA

CONTENTS● Solved Model Paper

Section–IEnglish ................................................... 1–1031. Comprehension ................................................ 3–7

2. Composition.................................................... 8–20

3. Grammar ...................................................... 21–77I. Spelling ..................................................... 21II. Antonyms and Synonyms ......................... 22III. One Word Substitution ............................. 26IV. Correct Usage of Articles.......................... 28V. Correct Usage of Prepositions .................. 33VI. Correct Usage of Adjective Degree of

Composition .............................................. 38VII. Correct Usage of Adverbs ........................ 42VIII. Correct Usage of Conjunctions................. 47IX. Correct Usage of Noun, Pronoun and

numbers..................................................... 51X. Correct Usage of Adjectives ..................... 59XI. Words, Which are Commonly getting

Confused ................................................... 61XII. Word Order ............................................... 72

4. Idioms, Phrases and Proverbs .................... 78–855. Direct and Indirect Speech ......................... 86–946. Active and Passive Voice ........................... 95–103

Section–IIPhysics .................................................... 3–215Unit 1 : Physical World and Measurement ....... 3–11

Unit 2 : Kinematics ......................................... 12–22

Unit 3 : Mechanics (Laws of Motion, Work,Power and Energy and Gravitation)... 23–34

Unit 4 : General Properties of Matter inBulk State ........................................... 35–45

Unit 5 : Thermodynamics ............................... 46–55

Unit 6 : Oscillation and Waves ....................... 56–67

Unit 7 : Electrostatics ...................................... 68–86

Unit 8 : Current Electricity ........................... 87–105

Unit 9 : Magnetic Effect of Current andMagnetism ..................................... 106–121

Unit 10 : Electromagnetic Induction andAlternating Current ........................ 122–141

Unit 11 : Electromagnetic Waves ................ 142–149

Unit 12 : Optics ............................................. 150–169

Unit 13 : Dual Nature of Matter ................... 170–173

Unit 14 : Atoms and Nuclei .......................... 174–189

Unit 15 : Electronic Devices ......................... 190–210

Unit 16 : Communication Systems ............... 211–215

Section–IIIMathematics ......................................... 3–135● Algebra ........................................................... 3–36

1. Sets .................................................................. 32. Relation ........................................................... 63. Complex Numbers ......................................... 104. Arithmetic Progression ................................. 155. Geometric Progression .................................. 206. Permutations and Combinations ................... 257. Quadratic Equations ...................................... 288. Binomial Theorem ......................................... 32

● Matrices and Determinants ......................... 37–46

● Trigonometry ............................................... 47–621. Identities and Trigonometric Ratio’s ............. 472. Simple Identities ........................................... 533. Properties of Triangles .................................. 564. Inverse Trigonometrical Functions ............... 60

● Coordinate Geometry ................................. 63–801. Straight lines................................................... 632. The Circle ...................................................... 673. The Parabola ................................................. 704. The Ellipse ..................................................... 735. The Hyperbola ............................................... 77

● Differential Calculus .................................... 81–981. Limit and Continuity ..................................... 812. Differentiation ............................................... 91

● Integral Calculus and DifferentialEquations ................................................... 99–1211. Indefinite Integrals ........................................ 992. Definite Integrals ......................................... 1073. Differential Equations ................................. 113

● Statistics and Probability ....................... 122–1351. Frequency Distribution, mean,

median, mode and standarddeviation ..................................................... 122

2. Probability................................................... 130

General Information

● Educational Qualification(a) Passed intermediate/10 + 2/equivalent

Examination with Mathematics, Physics andEnglish with minimum of 50% marks inaggregate and 50% marks in English. OR

(b) Passed three years Diploma Course inEngineering (Mechanical / Electrical/Electronics/Automo-bile/Computer Science/Instrumentation Technology/InformationTechnology) from a Government recognizedPolytechnic Institute with minimum 50% marksin overall aggregate and 50% marks in Englishin Diploma or in Intermediate/Matriculation, ifEnglish is not a subject in Diploma Course.

(c) Group ‘X’ & ‘Y’ (Eligible for bothTechnical and Non-Technical), PassedIntermediate/10 + 2/Equivalent examinationwith Mathematics, Physics and English withminimum 50% marks in aggregate and 50%marks in English. (Candidates will take theexamination for Group ‘X’ and Group ‘Y’subject in one sitting and can qualify for Group‘X’ and Group ‘Y’ or both i.e., if a candidatepasses in English and Reasoning and GeneralAwareness (RAGA) then he will be consideredpass in group ‘Y’ and if he passes in English.Physics and Maths, he is considered pass inGroup ‘X’). If a candidate clears in all the foursubjects , he will be considered pass in Group‘X’ and Group ‘Y’. Diploma holders areeligible to appear only for Group ‘X’.

Note—1. Boards recognized/affiliated by Council of

Boards for School Education (COBSE) and

Trades ColourVision Visual Acuity Maximum Limits

of Ref Error Leg length

Workshop Fitter (Mechanical), WorkshopFitter (Smith) Structure Fitter andPropulsion FitterWeapon Fitter, Electrical Fitter, ElectronicFitter, Mechanical System Fitter andAutomobile Fitter

CP-II

6/12 each eyecorrectable to6/6 each eye.

Hypermetropia+ 2.0D Myopia1D including± 0.50 astigmatism

‘Minimum leg lengthrequired forMechanical SystemFitter and AutomobileFitter is 99 cms.

Association of Indian Universities (AIU) willonly be permitted.

2. Exact aggregate % of marks before decimal aswritten in the marks≤ sheet of 10 + 2/Intermediate/Equivalent/Two years VocationalCourse/Three years Diploma Course OR

calculated as per the rules of concernedEducation Board/Polytechnic Institute will onlybe considered (For example 49.99% should betaken as 49% and not to be rounded off to50%).

● Mandatory Medical Standards(a) General Medical Standards—(i) Height :Minimum acceptable height : 152·5 cm. (ii) ChestMinimum range of expansion : 5 cm (iii) WeightProportionate to height and age, (iv) CornealSurgery (PRK/LASIK) not acceptable. (v)Hearing : Candidates should have normal hearing,i.e., able to hear forced whisper from a distance of6 metres with each ear separately. (vi) Dental :Should have healthy gums, good set of teeth andminimum 14 dental points. (vii) Health : TheCandidate should be free from any medical orsurgical deformity. He should be free from allcommunicable diseases and skin ailments.Candidates must be physically and mentally FIT toperform duty in any part of the world, in anyclimate and terrain, (viii) Body Tattoo : Permanentbody tattoos on inner face of the fore arms (insideof elbow to the wrist), Back (dorsal) part of thehand/reverse side of palm and Tribals with tattooswhich are as per custom and traditions of theirtribes only are permitted. However, right to decideon acceptability/ unacceptability of the individualrests with the Selection Centre. Candidates withpermanent body tattoos are to submit a photographof the Tattoo with size and type of the Tattoo.

(b) Colour Vision, Visual Standards and LegLength for Group ‘X’ (Technical) Trades are asfollows :

● Tenure & TrainingEnrolment is for an initial period of 20 yearsextendable upto the age of 57 years (subject toservice condition). Initially candidates will be sentfor a Joint Basic Phase Training (JBPT) at BasicTraining Institute, Belagavi (Karnataka). On

( vii )

successful completion of JBPT, candidates will beallocated trades and sent for trade training ofspecified durations. Training is however liable to beterminated at any time if the trainee fails to achievethe required standards in academics, profession,physical fitness and discipline or is found to bemedically unfit. After successful completion ofTraining the Airmen will be deployed onground based jobs as per their allotted trades.Alloted trade will not be changed on candidatesrequest on any grounds.

● Written TestDuration of the written test will be 60 minutes andwill comprise of English, Physics andMathematics as per 10 + 2 CBSE syllabus. WrittenTest will be objective type and Question papers willbe bilingual (English & Hindi) except for EnglishPaper. Candidates are to qualify in each paperseparately in their respective groups. Results ofthe written test will be declared on the same day.

● Adaptability TestAll candidates who pass the written test will haveto undertake Adaptability Test as per policy invogue.

● Physical Fitness Test (PFT)All candidates who pass the Written Test andAdaptability Test are to undergo Physical FitnessTest (PFT) on the same day or next day. PFTconsist of a 1·6 km run to be completed with in 8minutes. Candidates will also have to complete 20

squats followed by 10 push-ups and 10 sit-upswithin the stipulated time to qualify in the PFT.Candidates are advised to bring their sports shoesand shorts.

● InterviewCandidates who have passed the Written Test,Adaptability Test and PFT will be interviewed.Working Knowledge of English is pre-requisite.

● Medical ExaminationCandidates who qualify in the interview will bemedically examined by Air Force Medical Team asper IAF medical standards.

Medical examination would also includeBaseline Investigation of(a) Blood Haemogram, (b) Urine RE/ME, (c)Biochemistry (i) LFT, (ii) Cholesterol (iii) Urea,Uric acid, Creatinine, (iv) Sugar Fasting/PP, (d) X-Ray chest PA view, (e) ECG (R).

Note—(a) Candidates should bring latest prescription

(one month validity) and spectacles forcorrected vision, if used. The prescription mustbear the signature, stamp and registrationnumber of Eye Specialist).

(b) Candidates are advised to get tartar and stainsremoved from teeth before appearing for theMedical Examination. Ears should be free ofwax. Candidates should be prepared totravel/stay for the medical test for four to fivedays under their own arrangement. No TA/DAwill be admissible.

Syllabus

ENGLISH

I. ComprehensionA small passage followed by questions.1. To judge comprehension2. Drawing of inferences3. Use of vocabulary

II. Composition1. Agreement of subject with verb2. Pattern of verb and their use3. Sequence of tenses4. Transformation of sequences-Compound,

Complex, Simple, Negative, Affirmative.

III. Grammar1. Spellings2. Word formation3. Antonyms and Synonyms4. One word substitution5. Correct usage of articles6. Correct usage of Prepositions7. Correct usage of adjectives-degrees of

comparison8. Correct usage of conjunctions9. Correct usage of Nouns and Pronouns

10. Correct usage of numbers (Singular-Plural)11. Words, which are commonly getting confused12. Word order13. Correct usage of Adverbs

IV. Idioms and Phrases1. Use of simple idioms2. Use of Common proverbs

V. Direct / Indirect sentences : Narrationchange1. Change of various types of sentences from direct

to indirect form2. Change of various types of sentences from

indirect to direct form

VI. Active and Passive Voices1. Change of all types of sentences from active to

passive form2. Change of all types of sentences from passive to

active form

PHYSICS1. Physical World & Measurement

2. Kinematics3. Laws of Motion4. Work, Energy & Power5. Motion of System of particles & Rigid Body6. Gravitation7. Properties of Bulk Matter8. Thermodynamics9. Behaviour of Perfect Gas & Kinetic Theory of

gases10. Oscillations & Waves11. Electrostatics12. Current Electricity13. Magnetic effect of current & Magnetism14. Electromagnetic Induction and Alternating

current15. Electromagnetic Waves16. Optics17. Dual Nature of Matter18. Atoms and Nuclei19. Electronic Devices20. Communication Systems

MATHEMATICS1. Sets, Relations, functions2. Trigonometric functions3. Inverse Trigonometric functions4. Complex Numbers5. Quadratic Equations6. Sequence & Series (AP & GP)7. Permutation8. Combination9. Binomial Theorem

10. Coordinate geometry – Straight line11. Coordinate geometry – Circles12. Coordinate geometry – Parabola13. Coordinate geometry – Ellipse14. Coordinate geometry – Hyperbola15. Exponential Series16. Logarithmic Series17. Matrices18. Determinants19. Limit & Continuity20. Differentiation21. Application of Differentiation22. Indefinite Integrals23. Definite Integrals24. Application of Integration25. Deferential Equations26. Probability27. Statistics

Air Force

Airmen Selection TestGroup ‘X’ (Technical) Cadre

Solved Model Paper

7. The antonym of ‘Reckless’ is–

(A) Negligent (B) Cautious(C) Intelligent (D) Porilliant

8. The synonym of ‘Utility’ is–

(A) Habituality (B) Worthiness(C) Usefulness (D) Prevalence

9. The synonym of ‘Agreed’ is–

(A) Concurred (B) Settled(C) Suggested (D) Thought

10. Choose the correct one word substitution–

To alter a course(A) Decline (B) Deter(C) Demote (D) Deviate

11. Choose the correct one word substitution–

A thing of no importance.(A) Dwary (B) Trifle(C) Trickle (D) Twinkle

Direction—(12 and 13) Identify the incorrect part–

12. There is much to be said on both the sides.(A) (B) (C) (D)

13. The teacher said that the sun rose in the east.(A) (B) (C) (D)

14. Choose the correct verb–We.................playing cards all afternoon.(A) was (B) were(C) is (D) be

15. Choose the correct conjunction–The items are on sale in the local store.......not online.(A) but (B) and(C) though (D) nor

16. Choose the correct preposition–You have to leave your shoes...........the door whenyou enter the house.(A) in (B) over(C) to (D) byFor any activity, discipline is the key word. It should

begin with the self, then be exlended to the family,neighbours, environment, work place, society and the na-tion at large. It is from society that inspiration is drawn.Systems and institutions should provide the inspiration to

1. Identify the correct spelling—

(A) Aberant (B) Abbarant

(C) Aberrant (D) Abberant

2. Identify the Indirect speech :

The government has announced, “Taxes will beraised”.

(A) The government has announced that taxes

would be raised

(B) The government has announced that taxes

would raised

(C) The government has announced that taxed willbe raised

(D) The government has announced taxes will beraised

3. He said, “Let us leave the case at the station”.

(A) He suggested to let us leave the case at thestation

(B) He ordered to let us leave the case at the station

(C) He ordered that we should leave the case at thestation

(D) He suggested that we should leave the case atthe station

4. Change the voice—

Do you understand what I mean?

(A) What I mean is that understood by you?

(B) Was what I mean understood by you?

(C) Is what I mean understood by you?

(D) What I mean is understood by you?

5. Change the voice—

The storm did much damage :

(A) Much damage was done by the storm

(B) The storm damaged much

(C) Much damage did the storm

(D) The storm was damaged

6. The antonym of ‘Lethargic’ is –

(A) Immobile (B) Indolent

(C) Irresponsible (D) Hyperactive

ENGLISH

2 | Model Paper (Group ‘X’)

society through performance which in turn will provideleaders, capable of rebuilding and restructuring societyinto a strong nation. The ‘nationalists’ spirit then becomesinfectious.

17. What is the key word for activity according to thepassage?(A) Active Discipline(B) Key Discipline(C) Self Discipline(D) Discipline

18. According to the passage discipline should begin–

(A) With the self(B) With the self, family and neighbours

(C) With the self, family, neighbours and environ-ment

(D) With the self, family, workplace, society

19. According to the passage, where do we draw inspi-ration from?(A) Society (B) Society and nation(C) Environment (D) Nothing in particular

20. What is the meaning of the word ‘infectious’ in thepassage?(A) Dangerous(B) Spreading to everyone(C) Spreading to everyone by germs(D) Give disease

PHYSICS

21. Pressure cannot be measured in–

(A) N/m2 (B) Bar(C) Pascal (D) kg wt

22. A 1 kg mass has kinetic energy of 1 J when its speedis–

(A) 0.45 m/s (B) 1.4 m/s(C) 1 m/s (D) 4.4 m/s

23. A total of 4900 J was used in lifting a 50 kg mass. Themass was raised to height of–(A) 98 m (B) 960 m(C) 245 m (D) 10 m

24. When 1g of water at 100°C gets converted into steamat the same temperature, the change in volume isapproximately–(A) 1 c.c. (B) 100 c.c.(C) 1000 c.c. (D) 1670 c.c.

25. 5g of ice at 0°C and 20g of water at 45°C are mixed.The temperature of the mixture is–(A) 10° C (B) 20° C(C) 30° C (D) 40° C

26. A green leaf placed in a dark room is illuminated byred light. The leaf will appear to be–(A) Green (B) Red(C) Yellow (D) Black

27. Two plane mirrors are inclined at an angle of 36°.How many images will be formed if an object is placedbetween them?(A) 3 (B) 6(C) 9 (D) 10

28. The refractive index of water and glass is 1.33 and 1.5respectively. What is the ratio of speed of light inwater and glass?(A) 1 : 1 (B) 8 : 9(C) 9 : 8 (D) 7 : 6

29. If a bar magnet is cut lengthurise into 3 parts, thetotal number of poles will be–(A) 2 (B) 3(C) 4 (D) 6

30. The energy possessed by wind is–

(A) Kinetic energy (B) Potential energy(C) Thermal energy (D) Sound energy

31. The temperature of the surface of seen is about–

(A) 4000 K (B) 6000 K(C) 104 K (D) 106 K

32. A car undergoes a constant acceleration of 6 m/s2

starting from rest. In the 2nd second it travels a dis-tance of–(A) 3 m (B) 9 m(C) 12 m (D) 15 m

33. Light of which of the following colours has the short-est wavelength?(A) Red (B) Yellow(C) Blue (D) Green

34. Two charges, one positive and one negative, are ini-tially 2cm apart and are then pulled away from eachother until they are 6 cm apart. The force betweenthem is now smaller by a factor of–(A) 27 (B) 9

(C) 3 (D) 3

35. A 115 V, 1 kW electric oven is by mistake connectedto a 230 V powerline that has a 15 A fuse. The ovenwill–(A) Give off less than 1 kW of heat(B) Give of 1 kW of heat(C) Give off more than 1 kW of heat(D) Blow the fuse

36. A 12 V potential difference is applied across a seriescombination of four 6 resistors. Current in eachresistors is–(A) 0.5 A (B) 2 A(C) 8 A (D) 18 A

37. Light year is a unit of–

(A) Light intensity (B) Time(C) Distance (D) Illumination

Model Paper (Group ‘X’) | 3

38. A rubber ball dropped form a certain height is anexample of–(A) Uniform acceleration(B) Uniform retardation(C) Uniform speed(D) Non-uniform speed

39. A concave lens has focal length 0.25 m. Its power is–

(A) – 0.25 D(B) 4 D(C) 1.25 D(D) – 4 D

40. The number of electrons is excess to number of pro-tons on a body is 2.5 × 1017. The charge on the bodyis–(A) 2.5 C (B) 0.25 C(C) 25 C (D) 0.04 C

41. The least distance for distinct vision for a normal eyeis–(A) 2.5 cm (B) 2.5 m(C) 25 cm (D) 25 m

42. A body moves along the circumference of a circularpath of radium R. What is displacement of the body

when it covers 3

4th of its circumference?

(A) 3 R (B)3

4R

(C)3

2R (D) 2 R

43. An ice cube is floating in a glass of water. Whathappens to the water level when the ice melts?(A) Rises (B) Falls(C) Remains the same (D) Nothing can be said

44. What is the momentum of a body of mas 100g, hav-ing a kinetic energy of 20J?(A) 2 kg m/s (B) 1/2 kg m/s(C) 2 g cm/s (D) 1/2 g cm/s

45. Which of the following forces is responsible for theflow of water in rivers?(A) Force of friction (B) Gravitational force(C) Electrostatic force (D) Magnetic force

MATHEMATICS

46. The radius of a circle is uniformly increasing at therate of 3 cm/s. What is the rate of increase in area,when the radius is 10 cm?(A) 6 cm2/s (B) 10 cm2/s(C) 30 cm2/s (D) 60 cm2/s

47. What is the value of if the straight line (2x + 3y + 4)+ (6x – y + 12) = 0 is parallel to y – axis?(A) 3 (B) – 6(C) 4 (D) – 3

48. If A =

3 4

5 6

7 8

and B = 3 5 7

4 6 8

, then which one of

the following is correct?(A) B is the inverse of A(B) B is the adjoint of A(C) B is the transpose of A(D) None of the above

49. The value of the determinant

2 2 2

2 2 2

2 2 2

1

1

1

x y z

y z x

z x y

is–

(A) 0 (B) x2 + y2 + z2

(C) x2 + y2 + z2 + 1 (D) None of these

50. Three coins are tossed simultaneously. What is theprobability that they will fall two heads and one tail?

(A)1

3(B)

1

2

(C)1

4(D)

3

8

51. What is the most probable number of successes in10 trials with probability of success 2/3 ?(A) 10 (B) 7(C) 5 (D) 4

52. What is sin 1 13 4

sin sin5 5

equal to?

(A) 0 (B)1

2(C) 1 (D) 2

53. What is 1

1

20

tan

1

x

xdx equal to?

(A)2

8

(B)

2

32

(C)4

(D)

8

54. What is the sum of first eight terms of the series

1 1 11

2 4 8 +............?

(A)89

128(B)

57

384

(C)85

128(D) None of these

55. Let A = {x : x is a square of a natural number and x isless than 100} and B is a set of even natural numbers.What is the cardinality of A B ?(A) 4 (B) 5(C) 9 (D) None of these

4 | Model Paper (Group ‘X’)

56. What is the distance between the lines 3x + 4y = 9and 6x + 8y = 18 ?(A) 0 (B) 3 units(C) 9 units (D) 18 units

57. The geometric mean and harmonic mean of two non-negative observations are 10 and 8 respectively. Thenwhat is the arithmetic mean of the observations equalto?(A) 4 (B) 9(C) 12.5 (D) 25

58. What is the perimeter of the triangle with verticesA ( – 4, 2), B (0, – 1) and C (3, 3 ) ?

(A) 7 + 3 2 (B) 10 + 5 2

(C) 11 + 6 2 (D) 5 + 2

59. Out of 500 first year students, 260 passed in the firstsemester and 210 passed in the second semester. If170 did not pass in either semester, how many passedin both semesters?(A) 30 (B) 40(C) 70 (D) 140

60. What is tan 12

equal to?

(A) 2 3 (B) 2 3

(C) 2 3 (D) 3 2

61. Two poles are 10m and 20m high. The line joiningtheir trips makes an angle of 15° with the horizontal.What is the distance between the poles?

(A) 10 ( 3 1) m (B) 5 (4 3) m

(C) 20 ( 3 1) m (D) 10 ( 3 1) m

62. If 1 1 4

sin 1 sin5

= sin–1x , then what is x equal to?

(A)3

5(B)

4

5

(C) 1 (D) 0

63. If tan–1 2, tan–1 3 are two angles of a triangle, thenwhat is the third angle?(A) tan–1 2 (B) tan–1 4

(C) /4 (D) /3

64. What is the value of cos 1 14 12cos cos

5 13

?

(A) 63/65 (B) 33/65(C) 22/65 (D) 11/65

65. If y = 1

1

x

x

, then what is

dy

dxequal to?

(A)2

1x

(B) 2

2

( 1)x

(C) 2

2

( 1)x (D)

2

( 1)x

66. What is 32

2lim

8x

x

x

equal to?

(A) 1/4 (B) – 1/4(C) 1/12 (D) –1/12

67. What is the degree of the differential equation

y =

1dy dy

xdx dx

?

(A) 1 (B) 2(C) – 1 (D) Degree does not exist

68. What is the value of 2 82

1log

3 log3 9 ?

(A) 0 (B) 1

(C) 2 (D) 1/3

69. If x – iy = 2

1

i

i

, then what is value of y?

(A) 1/2 (B) –1/2(C) 1 (D) – 1

70. The value of

2 21 1

1 1

i i

i iis–

(A) 2 (B) – 1(C) 2i (D) – 2i

ANSWERS WITH EXPLANATIONS

1. (C) 2. (C) 3. (D) 4. (D) 5. (A) 6. (D)7. (B) 8. (C) 9. (A) 10. (D) 11. (B)

12. (D) Delete ‘The’. It is redundant.13. (C) Change ‘Rose’ to ‘Rise’ because the given state-

ment in Reported Speech is a universel truth.14. (B) 15. (A) 16. (D) 17. (D) 18. (A) 19. (A)20. (B) 21. (D)

22. (B) E =21

2mv

1 =1

2×1 × v2

v2 = 2v = 1·4 m/s

23. (D) E = mgh4900 = 50 × 9·8 × h

h =4900

50 9·8

= 10m24. (D)25. (B) Let the temperature of mixture be .

Then20 × 1 × (45 – ) = 5 × 80 + 5 × 1 × ( – 0)

Model Paper (Group ‘X’) | 5

900 – 20 = 400 + 5 25 = 500

= 20°C

26. (D)27. (C) No of images

n =36

1

=36

136

= 9

28. (C) ag =a

g

v

v, aw =

a

w

v

v

w

g

v

v =g

w

a

a

=

1·5

1·33

9

829. (D)30. (A)

31. (B)

32. (B) Distance moved in 1s,

S1 =21

6 12 = 3m

Distance moved in 2s

S2 =21

6 22 = 12 m

Distance moved in 2nd sec,S2 – S1 = 12 – 3 – 9 m

33. (C)

34. (B) f = k1 2

22

q q and f ´ = k

1 2

26

q q

1f

F=

2

2

2

6=

1

9

f ´ =9

f

35. (D) Resistance of oven R =

2 2(115)

1000

v

p current drawn

by it when connected to 230 volt line

I =230 1000

15 115

= 17·4 amp

Obviously the fuse will blow off36. (A) Total Resistance = 4 × 6 = 24

current =V

R=

12

24= 0·5 AA

37. (C)38. (A)

39. (D) P =(metre)

i

f

=1

0·25= – 4 D

40. (D) Charge on the body= 1·6 × 10–19 × 2·5 × 107

= 1·6 × 2·5 × 10–2

= 0·04 C

41. (C)

42. (D)

From fig. (AB)2 = R2 + R2

= 2R2

AB = 2R

43. (C)

44. (A) K =21

2mv

=2 21

2

m v

m

=21

2

p

m

20 =21

.2 0·1

p

4 = p2

p = 2 kg.m/s

45. (B)

46. (D) Let R = radius of circle, then

dr

dt= 3 cm/sec

Reqd. rate of interest in area of circle

=d

dt(R2) cm2

= 2R dR

dt(when R = 10 cm)

= 2 (10) 3 cm2/sec= 60 cm2/sec

47. (A) The equation of the given straight line is(2x + 3y + 4) + (6x – y + 12) = 0

2 (i + 3 ) x + (3 – ) y + (4 + 12 ) = 0since, it is parallel to y-axis, the coefficient of y willbe zero, i.e.,

6 | Model Paper (Group ‘X’)

(3 – ) = 0 = 3

48. (C) If A =

3 4

5 6

7 8

and B =3 5 7

4 6 8

then B is the transpose of A.

49. (A) Let =

2 2 2

2 2 2

2 2 2

1

1

1

x y z

y z x

z x y

then apply C1 C1 + C3, we get

=

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

1

1

1

x y z y z

x y z z x

x y z x y

Taking (x2 + y2 + z2) common from C1, we get

= (x2 + y2 + z2)

2 2

2 2

2 2

1 1

1 1

1 1

y z

z x

x y

= (x2 + y2 + z2).0 = 050. (D) Three coins are tossed simultaneously, then

sample spaces are as follows–

n(S) = [HHH, HHT, HTH, HTT, THH, THT, TTH,

TTT]

n(E) = [HHT, HTH, THH] Reqd. probability

=P(S) 3

P(E) 8

51. (B) Most probable number of successes in 10 trails

= 10×2

3 =

20

3

= 6.667 7

52. (C) sin 1 13 4

sin sin5 5

= sin 1 13 4

sin .cos sin5 5

+

1 13 4cos sin sin sin

5 5

=3 3 4 4

5 5 5 5

=9 16

25 25 =

9 16

25

=

25

25 = 1

53. (B) I = 1

1

20

tan

1

x

x

Put tan–1x = t

2

1

(1 )xdx = dt

and tan–1 (1) =4

1

1

20

tan

1

x

xdx =

/ 4

0. t dt

=

/ 42

02

t

=

2

16 02

=2

32

54. (C) Let S is the sum of first eight terms of the series—

1 1 11

2 4 8 +............

Here a = 1 and r = 1

2

S =

8(1 )

(1 )

a r

r

=

81

1 12

11

2

=

11

2561

12

=

(256 1) 2

256 3

=255 2

256 3 =

85

128

55. (A) At per question,A = { x : x square of natural numbers and

x < 100}= { 1, 4, 9, 16, 25, 36, 49, 64, 81}

B = { x : x set of even natural numbers}= { 2, 4, 6, 8, 10, 12,...........}

Model Paper (Group ‘X’) | 7

A B = { 4, 16, 36, 64}

56. (A) Reqd. distance = 2 2 2 2

18 9

6 8 3 4

=18 9

10 5 = 0

57. (C) Let the Arithmetic, Geometric and Harmonic mean

of a and b are A, G and H respectively, then

A =2

a b, G = ab and H =

2

( )

ab

a b

A × H = ( ) 2

2 ( )

a b ab

a b

= ab = G2

A =2G

H=

2(10)

8=

100

8 = 12.5

58. (B) In a triangle ABC, if A (–4, 2), B (0, –1) and C ( 3, 3),

then

AB = 2 2( 4 0) (2 1)

= 2 24 3 = 5

BC = 2 2(3 0) (3 1)

= 2 23 4 = 5

CA = 2 2(3 4) (3 2)

= 2 27 1

= 50

= 5 2

Perimeter of ABC

= 5 + 5 + 5 2 = 10 + 5 2

59. (D) Let the number of passed students in first and

second semester are n(A) and n(B), respectively.

n (A B) = n (A) + n (B) – n (A B)

(500 – 170) = 260 + 210 – n (A B)

n(A B) = 470 – 330 = 140

Total number of passed students in both

semester = 140

60. (A) tan 12

= tan 4 6

=

tan tan4 6

1 tan .tan4 6

=

11

31

1 1.3

=( 3 1) . ( 3 1)

( 3 1) . ( 3 1)

=3 1 2 3

(3 1)

= 2 – 3

61. (B) Let the distance between the poles be x m, then

(20 10)

x

= cot 15°

10

x = 2 3

x = 10 ( 2 3)

= 5 (4 2 3) m

62. (A) sin–1 x = sin–1 1 + sin–1 4

5

= sin–1 16 4

1 1 025 5

[ sin–1x + sin–1y

= sin–1 2 21 1x y y x ,

If x, y 0, x2 + y2 1]

= sin–1 . 3

5

x =3

563. (C) Let the third angle of the triangle is , then

tan–1 (2) + tan–1 (3) + tan–1 =

tan–1 2 3

1 2 3

+ tan–1 =

tan–1 = – tan–1 (–1) = –3

4

=

4

tan–1 =4

64. (B) Given Exp.

= cos 1 14 12cos cos

5 13

[ cos (A + B) = cos Acos B – sin A sin B]

8 | Model Paper (Group ‘X’)

= cos 1 4 12 16 144

cos 1 15 13 25 169

= cos 1 48 3 5

cos65 5 13

= cos 1 48 15

cos65

= cos 1 33

cos65

= 33

65

65. (B) y = 1)

( 1)

x

x

(x – 1)

d

dx (x + 1)

dy

dx=

2

( 1) ( 1)

( 1)

dx x

dxx

= 2

( 1) .1 ( 1) .1

( 1)

x x

x

= 2

2

( 1)x

66. (C) 32

2lim

8x

x

x

=2

limx

2 2

( 2)

( 2) ( 2 2 )

x

x x x

=2

limx 2

1

( ) x x

= 2

1

( 2)

=1

4 4 4 =

1

1267. (A) Given diff. equation

y =

1dy dy

xdx dx

y. dy

dx

= x.

2

1dy

dx

x.

2

1dy dy

ydx dx

= 0

Ordinary diff. equation, whose power = 1

68. (A) Given expression

= 2 82

1log

3 log3 9

= 2 . log82 (8)1/3 – 1

3. log3 (3)2

= 2 .1 1

(2)3 3

=2 2

3 3 0 (zero)

69. (A) x = iy =2

1

i

i

=

(2 ) (1 )

(1 ) (1 )

i i

i i

=

(3 )

2

i

y =1

2

70. (B)

2

2

(1 )

(1 – )

i

i

=

2

2

1 2

1 2

i i

i i

= – 1

Similarly,

2

2

(1 – )

(1 )

i

i= –1

Air Force Airmen Selection Test Group'X' (Technical) Trades

Publisher : Upkar Prakashan ISBN : 9788174821522 Author : Dr. Lal & Jain

Type the URL : http://www.kopykitab.com/product/11852

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