N.Sunil Kumar

Senior Faculty

Define unit vector, null vector and position vector

PhysicsJr.Inter

M O TIO N IN A PLA N EVERY SHORT ANSWER QUESTIONS

SHORT ANSWER QUESTIONS

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18

1. In a certain code language GERMINA-

TION is written as IMGRENNOAIT.

How is ESTAB-LISHED written in

that code?

(a) BATESLDEIHS (b) BAETSLDEIHS (c) BAETSLEDIHS (d) BEATSLDEIHS(e) None of these

2. In a certain code language POULTRY

is written as PRQXNVTY. How is

TREASON written in that code?

(a) TVSGCUQN (b) TVTGCUQN (c) TTVGCUQN (d) TVTHCUQN(e) None of these

3. If R is denoted by N, D is denoted by T,

I by U, O by I, E byR, T by O, U by D,

N by C and C by E; then how will the

word 'INTRODUCE' be written?

(a) UCOINTDER (b) UCONTIDER(c) UCONITDER (d) UCONIDTER(e) None of these

4. In a certain code 'COVALENT' is writ-

ten as 'BWPDUOFM' and 'FORM' is

written as 'PGNS'. How will 'SILVER'

be written in that code?

(a) MJTWFS (b) MJTSFW(c) KHRSFW (d) MJTUDQ (e) None of these

5. If in the English alphabet, all the letters

at odd numbered positions are written

in serial order from left to right fol-

lowed by the letters at even numbered

positions written in reverse order,

which letter will be sixth to the left of

seventeenth letter from left?

(a) D (b) B (c) V (d) U (e) None 6. If it is possible to make a meaningful

word from the second, fourth, fifth,

eleventh and thirteenth letters of the

word ESTABLISHMENT using each

letter only once, write second letter of

that word as your answer, if more than

one such word can be formed, write

'M' as your answer and if no such word

can be formed, write 'X' as your

answer.

(a) B (b) A (c) E (d) M (e) X7. How many such pairs of letters are

there in the word 'ENTHUSIASTIC'

each of which has as many letters

between them in the word as there are

between them in the English alphabet?

(a) Two (b) Three (c) Four (d) More than four (e) None of these

8. In a row of girls facing North, Rinky is

10th to the left to Pinky who is 21 st

from the right end. If Minky who is

17th from the left end is 4th to the right

of Rinky, hoe many girls are there in

the row?

(a) Data inadequate (b) 44 (c) 37 (d) 43 (e) None of these

9. In a row of 40 girls, when Kamal was

shifted to her left by 4 places her num-

ber from the left end of the row became

10. What was the number of Sujata

from the right end of the row if Sujata

was three places to the right of Kamal's

original position?

(a) 22 (b) 26 (c) 25 (d) 24 (e) None of these

10. If 3 is subtracted from the middle digit

of the following numbers and then the

position of the digits are reversed,

which of the following will be the last

digit of the middle number after they

are arranged in descending order?

589 362 554 371 442(a) 5 (b) 4 (c) 2 (d) 1 (e) 3

11. D, the son-in-law of B is the brother-in-

law of A who is the brother of C. C is

daughter of A. How is A related to B?

(a) Brother (b) Son (c) Father (d) Data inadequate (e) None of these

12. Which of the following pairs has simi-

lar relationship as Run : Race?

(a) Party : Dance (b) Study : Book(c) Lecture : Study (d) Enjoy : Journey(e) None of these

13. Four of the folloiwng five pairs have

same relation between their elements

as in the case of the pair UNDERWAY

: 39412576 and hence form a group.

Which one does not belong to the

group?

(a) WARDEN :572419 (b) DERANU :412793 (c) NEDAYU : 924763 (d) ENDWAR :194572 (e) URADYE :327461

14. Four of the following five pairs have

same relation between their elements

and hence form a group. Which one

does not belong to the group?

(a) PLENTY :LEPTYN (b) COWARD :OWCRAD (c) ALWINS : LWANIS (d) EXAMIN :XAEIMN (e) LOCATE :OCLTAE

15. Among P, Q, R, S, T and U, P is taller

than R and S, but not shorter than T

and U: and Q is taller than R, S, T, and

U but not as tall as P. Who amongst

them is tallest?

(a) Data inadequate (b)T (c) R (d) P (e) None of these

(16-20): Each of the questions below con-

sists of a question and two statements

numbered I and II given below it. You

have to decide whether the data pro-

vided in the statements are sufficient to

answer the question. Read both the

statements and

Give answer (a) : if the data in statementI alone are sufficient to answer the ques-tion, while the data in statement II aloneare not sufficient to answer the question.Give answer (b) : if the data in statementII alone are sufficient to answer the ques-tion, while the data in statement I aloneare not sufficient to answer the question.Give answer (c) : if the data either instatement I alone or in statement II aloneare sufficient to answer the question.Give answer (d) : if the data in bothstatements I and II together are not suffi-cient to answer the question.Give answer (e) : if the data in both state-ments I and II together are necessary toanswer the question.

16. Which village is to the North-East of

village 'A'?

I. Village 'B' is to the North of village A,villages C and D are to the East and Westof village B, respectively.II. Village 'P' is to the South of village 'A'and village 'E' is to the East of village 'P',village 'K' is to the north of village 'P'.

17. Can Rohan retire from office 'X' in

January 2006, with full pension bene-

fits?

I. Rohan will complete 30 years of serv-ice in office 'X' in April 2006 and desires

to retire.II. As per office 'X' rules an employee hasto complete minimum 30years of serviceand attai age of 60. Rohan has 3 years tocomplete age of 60.

18. Among five friends P, Q, R, S and T,

who ranks third in terms of salary

obtained by them?

I. T's salary is more than P and Q but notmore than S.II. R's salary is lowest among them.

19. How is P related to Q?

I. J has two daughters, oneof them 'R' ismarried to 'P'.II. Q is the mother of 'S', the youngerssistr of 'R'.

20. Which word in the code language

means 'flower'?

I. 'de fu la pane' means 'rose flower isbeautiful' and 'la quiz' means 'beautifultree'.II. 'de la chin' means 'red rose flower' and'pa chin' means 'red tea'.

(21-25): Answer the following questions

based on the arrangement given below:

Y W @ 1 & C N 3 P L B 9 + =D 5 E 2 ÷ M V $ 7 # 4 F G 5

21. C13W :74VG is in the same way as?

(a) $F2D (b) VF2D (c) $42D (d) $E÷ D (e) $F25

22. Four of the following five are alike in a

certain way based on the above

arrangement and hence form a group.

Which one does not belong to the

group?

(a) &LNP (b)+2DE (c) 5 V2M (d) VF74 (e) LDB=

23. If the numbers immediately preceding

the symbols are attached the value dou-

bled their numerical value, then what

will be the sum of the value of all such

numbers?

(a) 22 (b)36 (c) 26 (d) 38 (e) None of these

24. How many such symbols are there in

the above arrangement which are not

immediately preceded by a number

and also not immediately followed by a

letter?

(a) Nil (b) One (c) Two (d) Three (e) None of these

25. If YW@1 are written in the reversed

order, & CN3 are written in the

reversed order and so on, then in the

new arrangement which of the follow-

ing will exactly be in the middle

between 9 and $?

(a) = (b) M (c) + (d) D (e) None of these

(26-28) : In each question below are given

some statements followed by four con-

clusions numbered I, II, III and IV. You

have to take the

given statements to

be true even if they

seem at variance

from commonly

known facts. Read

all the conclusions

and then decide

which of the given

conclusions logically

follows from the two

given statements ,

disregarding com-

momly known facts.

26. Statements : Some ice are rings. No ringis paint. Some rings are gold.Conclusions :

(I) No any gold is paint. (II) No any ice is gold.(III) Some rings are paints.(IV) All golds are rings.(a) Only I and III follow (b) Only I and II follow(c) Only III and IV follow (d) Only II and III follow(e) None of these

27. Statements :

All gates are flowers.Some gates are fruits.Some flowers are clips.Conclusions :

(I) Some flowers are fruits.(II) Some clips are fruits.(III) Some clips are gates.(IV) No any flower is fruit.(a) Only I follow (b) Only I and IVfollow(c) Only II and IV follow (d) Only I andIII follow(e) None of these

28. Statements :

No candle is bell.Some shoes are bells.All tables are shoes.Conclusions :

(I) Some tables are bells.(II) No tables is bell.(III) Some shoe are candles.(IV) No shoes is candle.(a) Only I and IV follow (b) Only I andII follow(c) Only III and IV follow (d) Only I andIII follow(e) None of these

W hich village is to the N orth-East o f village 'A '?

Panditi

Meenakshi pavan

Senior Faculty

Reasoning Model questions

1.a2.d3.c4.b5.d6. d

7.a8.d9.d10.e11.b12.d

13.c14.a15.d16.a17.e18.d

19.e20.d21.a22.e23.d24.c

25.c26.e27.a28.e

ANSWERS

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PARTS OF SPEECHPREPOSITIONS» A preposition is a word that exp-resses the relationship between anoun or pronoun and some otherpart of the sentence. It is said togovern the noun or pronoun thatfollows.What are you doing at Christmasthis year?She works for a charity.At: denotes point of time, place orposition, state or condition,direction, rate etc.at 2.30 this afternoon, at school,at my feet, at war, at rest, at thetarget, at Rs. 50 a dozen.In: denotes period of time, place,activity, dress, circumstances, condition etc.in the evening, in May, in Chen-nai, in a cottage, in my back, inthe army, in the grey suit, in therain, in sorrow, in prison.On: denotes time, membership,condition, reason etc.on Friday, on the death of hisfather, on the committee, on fire,on the charge of theft.By: to mean near, during, not laterthanby her side, by him, by day, bytomorrow.To show method, means oftransport.by cheque, by train, by car.Of: to indicate possession, cause,deprivation, measure etc.The leg of the chair, the poems ofKeats, die of small-pox, a sheetof paper, a piece of bread.For: to express a period of time,destination, purpose, occasion,meaning etcfor two weeks, for Chennai, forchildren, for sale, for Christmas. CONJUNCTIONS» A conjunction joins words orgroups of words. » Manoj and Vishnu are brothers.Wait here till I return.» Conjunctions can be divided intotwo classes.Co-ordinating and Subordinating:» Co-ordinating conjunctions joinparts of sentences which are ofequal status.» A frog can live on land and inwater.» She is very hard-working but notvery imaginative.» Is it Saturday or Sunday today?» Either you leave now or I callthe police!» We listened eagerly, for he brought news of our families.» Subordinating conjunctions joinclauses which are not equal inrank. The clause introduced by a subordinating conjunction dep-ends on the other and can standby itself.» The reason she is so irritable isbecause she's tired.» Is it true that she has gone backto teaching?» If anyone calls, tell them I'm notat home.» Put that away before it gets bro-ken.» The report was critical though fair.Model Questions1. We went _____ the market lastSunday.Choose the correct word to fill inthe blank in the sentence.1) up 2) into3) to 4) off2. a) She likes Englishb) She likes MathematicsIf you combine the above twosentences you will get:1) She not only likes English, butalso Mathematics2) She likes not only English, butalso Mathematics3) Not only English but also shelikes Mathematics4) She likes English and not onlyMathematics3. a) Vimala likes singing.b) She likes dancing.Identify the correct sentence youwill get if you combine the abovesentences.1) Vimala likes singing and aswell as dancing2) Vimala likes singing but danc-ing too3) Vimala likes singing and shelikes dancing as well as.4) Vimala likes dancing andsinging4. What do you say when you see aman who is eight feet tall?1) How tall he is! 2) How tall is he!3) How tall she is!4) How big is he!5. Pick out the correct sentenceamong the following.1) No sooner had I put the phonedown than it rang again2) No sooner than I had put thephone down, it rang again3) No sooner than had I put thephone down, it rang again4) No sooner I had put the phonedown, it rang again6. The lives of those who are ____cancer are uncertain in spite ofadvancement in the medicalfield.1) struck with2) stricken by 3) struck from4) stricken with7. The fashion that is _____ todaymay become obsolete within ashort span of time.1) in vague 2) in vougue3) in vogue4) out of vogue8. Though there was vehement opp-osition to our ideas, we decidedto ___ our plans.1) adhere with2) adhere of 3) adhere to4) adhere in9. The villagers charged the policeofficials with misleading the case__ local leaders.1) with the behest of 2) at the behest of3) on the behest of4) in the behest of10. _____ Mission Bhageeratha sch-eme is aimed at supplying drink-ing water to all the villages ofTelangana, it has received appre-ciation from the Central Govern-ment.1) Though 2) Yet3) Since 4) So11. _____ everyone pays income tax,the Government can't increasethe source of revenue for thedevelopment of the country.1) Unless 2) If3) So 4) As12. It is very hot ____ the day butquite cold _____ night.1) at, in 2) in, in3) in, at 4) on, at13. She seems bent ____ making lifedifficult for me.1) over 2) of3) with 4) on14. a) Kiran finished first in the race.b) He began late.If you combine the following twosentences, you will get:1) Kiran finished first in the raceyet he began late2) Kiran finished first in the racethough he began late3) Kiran finished first in the racedespite he began late4) Kiran finished first in the race even that he began late15. Pick out the correct sentenceamong the following.1) I hate to waste a drop of gas,since it is very expensive thesedays.2) I hate to waste a drop of gas,for it is very expensive thesedays.3) I hate to waste a drop of gas,as it is very expensive thesedays.4) I hate to waste a drop of gas,because of it is very expensivethese days.16. Fill in the blank with suitableconjunction.I am allergic to cats, _______ Ihave three of them.1) or 2) for3) yet 4) soDirections (Q.No. 17-20): Fill inthe blanks with suitable preposi-tions. 17. He is ______ the parent's com-mittee.1) in 2) on3) of 4) by18. _______ the new regulationsspending on office equipmentwill be strictly controlled.1) As according2) By 3) To4) Under19. It's illegal to drive ______ a redlight.1) through 2) with3) along 4) before20. Too much drinking isn't good_______ you.1) to 2) for3) about 4) withKEY1) 3 2) 2 3) 4 4) 1 5) 16) 4 7) 2 8) 3 9) 2 10) 111) 1 12) 3 13) 4 14) 2 15) 216) 3 17) 2 18) 4 19) 1 20) 2Too much drinking isn't good..R. Srinivasa RaoSenior FacultyHyderabad INTERJECTIONS» An interjection is a word expressing some sudden feeling.Oh! - surprise, fear, joy etc. - Oh, how wonderful!Ah! - pleasure, admiration, sympathy - Ah! this coffee is goodAlas! - sorrow - Alas! I'm undoneHurray! - excitement - Hurray! We've won the matchMy God! - surprise, shock, annoyance - My God! I forgot to lock the doorOops! - regret about a mistake - Oops! I've typed two 'L's by mistakeOuch! - sudden physical pain - Ouch! You've stepped on my foot´ùsîæ ç³È„ýSË

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OÐðlG‹ÜBÆŠæ hÌêÏ l ÝùÐ]l$ÐéÆý‡… l ¯]lÐ]l…ºÆŠæ l 20 l 201714 ѧýlÅModel QuestionsDirections (Q.No. 1-5):What sh-ould come in place of the questionmark (?) in the following questions?1. a) 18 b) 112.5 c) 16d) 24 e) None of these2. 15.8 × 3 + 8.1 − 21.5 = ? + 14.6a) 14.9 b) 20.1 c) 18.4d) 19.4 e) None of these3. 8327.3÷ 831.4 × 8346.8 = 8331.9 +83?a) 64.1 b) 41.9 c) 40.8d) 39.1 e) None of these4. 43% of 586 = 341.2 − ?a) 76.28 b) 49.53 c) 82.99d) 48.96 e) None of these5. a) 5 b) 2.9 c) 7d) 4 e) None of theseDirections (Q.No. 6-10): In thefollowing questions two equationsnumbered I and II are given. You ha-ve to solve both the equations and fi-nd out the relationship between x andy. Then give answer accordingly:a) x > y b) x ≥ y c) x < y d) x ≤ ye) x = y or the relationship cannotbe established.6. I: x2 + x − 12 = 0II: y2 + 2y −8 = 07. I: 4x2 − 13x + 9 = 0II: 3y2 − 14y + 16 = 08. I: 8x2 + 18x + 9 = 0II: 4y2 + 19y + 21 = 09. I: 3x2 + 16x + 21 = 0II: 6y2 + 17y + 12 = 010. I: x2 = 49II: y2 − 4y − 21 = 0Directions (Q.No.11-15): Whatapproximate value should come inplace of the question mark (?) in thefollowing number series?11. (8423 + 3120 + 6543) ÷ (1536 +377 + 189) = ?a) 15 b) 14 c) 9d) 18 e) 2312. (13% of 7439) × (3.23% of 537)= ?a) 16243 b) 16135 c) 16674d) 16824 e) 1677413. a) 288 b) 268 c) 318d) 300 e) 35014. a) 215 b) 210 c) 220d) 224 e) None of these15. (15.28 × 3.56) ÷ 3.15 = ?a) 12 b) 9 c) 27 d) 17 e) 2416. The average of four consecutiveeven numbers P, Q, R and Srespectively (in increasing order)is 51. What is the product of Pand R?a) 2592 b) 2400 c) 2600d) 2808 e) None of these Directions (Q. No. 17-19) : Stu-dy the information given below andanswer the questions that follow:An article was bought for Rs.5600. If price was marked up by12%. Thereafter, it was sold at adiscount of 5% on the market price.17. What was the marked price of thearticle?a) Rs. 6207 b) Rs. 6242c) Rs. 6292 d) Rs. 6192e) Rs. 627218. What was the percent profit onthe transaction? a) 6.8% b) 6.3% c) 6.4%d) 6.6% e) 6.2%19. What was the amount of discountgiven?a) Rs. 319.6 b) Rs. 303.6c) Rs. 306.3 d) Rs. 313.6e) Rs. 316.9Directions (Q.No.20-24) : Studythe table and answer the givenquestion.20. What is the average number ofcakes baked by all the bakeriestogether in June?a) 178 b) 194 c) 172d) 188 e) 18221. What is the sum of the 60% ofthe total number of cakes bakedby bakery A in April and Maytogether and the number of cakesbacked by bakery C in June andJuly together?a) 524 b) 484 c) 444d) 482 e) 51222. If the total number of cakes bakedby all the given bakeries together increase by 24% from July toAugust, what is the total numberof cakes baked by all the givenbakeries together in August?a) 1028 b) 1104 c) 1054d) 1132 e) 118623. Number of cakes baked bybakery D increased by whatpercent from March to July?a) b) c) d) e) 24. Bakery E bakes only two types ofcakes i.e. butter cakes and spongecakes. The respective ratiobetween the butter cakes andsponge cakes baked by bakery Ein March April May together was11 : 8. What was the total numberof butter cakes baked by bakery Ein March, April and Maytogether?a) 352 b) 374 c) 396d) 418 e) 33025. A and B together complete apiece of work in 6 2/3 days. If Aalone takes 3 more days to com-plete the same piece of work thanthe number of days taken by Balone. How many days B alonetakes to complete the work?a) 18 days b) 15½ daysc) 12½ days d) 12 dayse) 15 days 142 %3139 %3 149 %3245 %3147 %32 3 7896( 6 ?) 19 ÷ =

7 3 4 ?5 8 5121 ÷ × × =

13 4 ?172 17+ =

3969 1.4 ? 2.5÷ = ×

What is the total number of cakes?N. Vinaykumar ReddyDirector, IACE, Hyderabad. SpecialSpecialSpecialSpecialSpecialSpecialSpecialSpecialSpecialSpecialSpecialQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeQuantitativeAptitudeIBPSIBPSIBPSIBPSIBPSPOs, Clerks

IBPSIBPSIBPSIBPSKey & Solutions1.⇒ ? × 2.5 = 63 ÷ 1.4 Ans: a2. ? + 14.6 = 15.8 × 3 + 8.1 − 21.5? + 14.6 = 47.4 + 8.1 − 21.5? = 34.00 − 14.6 = 19.4 Ans: d3. 8331.9 + 83? = 8327.3 ÷ 831.4 ×8346.8⇒8327.3−1.4+46.8 = 8372.7⇒31.9 + ? = 72.7⇒ ? = 72.7 − 31.9⇒ ? = 40.8 Ans: c4.⇒251.98 = 341.2 − ?⇒ ? = 89.22 Ans: e5.? = 3 Ans: e6. I: x2 + x − 12 = 0⇒ x2 + 4x − 3x − 12 = 0⇒ (x −3) (x + 4) = 0⇒ x = 3 or −4II: y2 + 2y −8 = 0⇒ y2 + 4y −2y −8 = 0⇒ (y + 4) (y−2) = 0⇒ y = − 4 or 2 Clearly, relationship cannot beestablished Ans: e7. I: 4x2 −13x + 9 = 0

⇒ 4x2 − 4x − 9x + 9 = 0⇒ (x −1) (4x −9) = 0⇒ x = 1 or II: 3y2 −14y + 16 = 0⇒ 3y2 − 6y −8y + 16 = 0⇒ (y−2)(3y−8) = 0⇒ y = 2 or Clearly, relationship cannot beestablished. Ans: e8. I: 8x2 + 18x + 9 = 0⇒ 8x2 + 12x +6x + 9 = 0⇒ (2x + 3) (4x + 3) = 0II: 4y2 + 19y + 21 = 0⇒ 4y2 + 12y +7y +21 = 0⇒ (y + 3)(4y+7) = 0⇒ y = −3 or Clearly, x > y Ans: a9. I: 3x2 +16x + 21 = 0⇒ 3x2 + 9x +7x +21 = 0⇒ (3x +7) (x +3) = 0⇒ x = or −3II: 6y2 + 17y +12 = 0⇒ 6y2 + 9y + 8y + 12 = 0⇒ (2y + 3) (3y+4) = 0 Clearly, x < y Ans: c10. I: x2 = 49

⇒ x = ±7II: y2 − 4y −21 = 0⇒ y2 − 7y + 3y −21 = 0⇒ (y + 3) (y−7) = 0⇒ y = −3 or 7Clearly, relationship cannot beestablished Ans: e11. (8423 + 3120 + 6543) ÷ (1536 +377 + 189) = ?⇒ 18086 ÷ 2102 = ?⇒ ? = 9(approx.) Ans: c12.⇒ 967.07 × 17.3451 = ?⇒ ? = 16774 (approx.) Ans: e13.? = 288(approx.) Ans: a14. (9216) ÷ (42.9) = ?? = 215 (approx.) Ans: a15. (54.3968) ÷ 3.15=?

⇒ ? = 17 (approx.) Ans: d 16. P + Q + R + S = 4 × 51 = 204∴ P + (P + 2) + (P + 4) + (P + 6)= 204∴ 4P + 12 = 204And R = 48+4 = 52∴ P × R = 48 × 52 = 2496Ans: e17. Marked price of the articleAns: e18. S.P. of article = 6272 ×= Rs. 5958.40∴ Reqd % profit Ans: c19. Amount of discount given= 6272 × = Rs. 313.60Ans: d20. Average Ans: e21. Required sum Ans: c 22. Total number of cakes baked inAugust(175 + 147 + 188 + 224 +116) =1054 Ans: c23. Increased percent Ans: c24. Total number of butter cakesbaked by bakery E in March,April and May together= (174 + 183 + 251) × Ans: a25. Suppose B alone takes tocomplete the work in x days andA alone takes to complete thework in (x + 3) daysNow, 20(2x + 3) = 3x (x + 3)3x2 − 31x − 60 = 0 On solving:x = 12, 1.67Hence, B alone takes tocomplete the work in 12 daysAns: d1 1 33 20+ =

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Number of cakes baked by 5bakeries during 5 monthsBakeriesMonths A B C D EMarch 127 148 189 150 174April 166 159 163 156 183May 254 171 151 168 251June 153 193 132 174 258July 175 147 188 224 116

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07 20 2017- ntbhadradri.comntnews.com

Krupakar Pendli

Senior IIT Faculty,

Hyderabad

7893774888

STATES OF MATTER

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Ê°®Ω’† ≤ƒn°œçî√®Ω’ ? – Ç©s®˝d ¶„®˝o£æ…®˝f ØÓ¶„™¸✤ v°æA àö« ØÓ¶„™¸ •£æ›´’AE à ®ÓV† •£æ›éπ

J≤ƒh®Ω’? – úÕÂÆç•®Ω’, 10✤ ´’ü¿®˝ ü∑ÁJ≤ƒq à ü˨¡ç™ ïEtç*çC ?

– ߪ·íÓ≤ƒxNߪ÷✤ ¶µ˜Aéπ, ®Ω≤ƒßª’† ¨»Y≤ƒ©™ ØÓ¶„™¸ °æ€®Ω≤ƒ\®√©†’

Åçü¿ñ‰ÊÆ ÆæçÆæn àC ?– ®√ߪ’™¸ Æ‘yúÕ≠ˇ Åé¬úøO’ Ç°∂ˇ ÂÆjØÁqÆˇ

✤ ✤ à ü˨»EéÀ îÁçC† §˘®Ω’©’ ÅûªuCµéπçí¬ ØÓ¶„™¸ °æ€®Ω ≤ƒ\®√©†’ §ÒçüΔ®Ω’?– Å¢Á’Jé¬

✤ ØÓ¶„™¸ °æ€®Ω≤ƒ\®√Eo Åçü¿’èπ◊†o ûÌL ´’£œ«∞¡ á´®Ω’? – ¢Ë’úø¢˛’ ¢Ë’J èπÿuJ

✤ ØÓ¶„™¸ •£æ›´’ûª’©†’ à ü˨¡ç v°æüΔ†ç îËÆæ’hçC?– Æ‘yúøØ˛

✤ 1903™ ¶µ˜Aé𠨻YÆæç™, AJT 1911™ ®Ω≤ƒßª’† ¨»YÆæç™ ØÓ¶„™¸ Å¢√®Ω’f©†’ §ÒçC† ´uéÀh á´®Ω’?

– ¢Ë’K èπÿuJ✤ 1917, 1944, 1963 Ææç´ûªq®√©™ ØÓ¶„™¸ ¨»çA

°æ€®Ω≤ƒ\®√Eo §ÒçC†C?– È®ú˛vé¬Æˇ ÉçôÍ®o≠憙¸ éπN’öÀ

✤ ØÓ¶„™¸ °æ€®Ω≤ƒ\®√Eo Åçü¿’èπ◊†o ûÌL ¶µ«®ΩBߪ·úø’á´®Ω’? – ®ΩOçvü¿Ø√ü∑˛ ®∏√í∫÷®˝

✤ à Ææç´ûªq®Ωç™ ®ΩOçvü¿Ø√ü∑˛ ®∏√í∫÷®˝ ØÓ¶„™¸ °æ€®Ω≤ƒ\®√Eo Åçü¿’èπ◊Ø√o®Ω’? – 1913™

✤ ®ΩOçvü¿Ø√ü∑˛ ®∏√í∫÷®˝ à ®Ωçí∫ç™ ØÓ¶„™¸ •£æ›´’AE§ÒçüΔ®Ω’ ? – ≤ƒ£œ«ûªu ®Ωçí∫ç

✤ à ví∫çü∑ΔEo ®Ω*ç*†çü¿’èπ◊ ®ΩOçvü¿Ø√ü∑˛ ®∏√í∫÷®˝ èπ◊ ØÓ¶„™¸ °æ€®Ω≤ƒ\®√Eo ÅçCçî√®Ω’?– Uû√çïL

✤ 2005 Ææç´ûªq®Ωç™ ØÓ¶„™¸ ¨»çA °æ€®Ω≤ƒ\®Ωç á´JéÀ©Gµç*çC? – ´’£æ«tü˛ ᙸ •®√C

✤ Åçûª®√bBߪ’ Åù’ Éçüµ¿† ÆæçÆæn(âáÉá) v°æÆæ’hûªúÁjÈ®éπd®˝ ï†®Ω™¸ á´®Ω’? – ´’£æ«tü˛ ᙸ •®√C

✤ 2005™ ≤ƒ£œ«ûªu ®Ωçí∫ç™ ØÓ¶„™¸ °æ€®Ω≤ƒ\®Ω ví∫£‘«ûª á´®Ω’? – £æ«®√™¸f °œçô®˝

✤ ´‚úø´≤ƒJ Åçûª®√bBߪ’ Åù’ Éçüµ¿† ÆæçÆæn îµÁj®ΩtØ˛í¬✤ Ø√®˝h ÑÆæd®ΩØ˛ È®j™‰y v°æüµΔ† 鬮Ωu≤ƒn†ç?–íÓ®Ωé˙°æ‹®˝

✤ ®Ωûªoí∫®Ωs¥ ÅE à ®√w≥ƒdEo °œ©’≤ƒh®Ω’?– Ççvüµ¿v°æü˨¸ ✤ ûª÷®Ω’p ´’üµ¿u È®j™‰y v°æüµΔ† Íéçvü¿ç áéπ\úø ÖçC?

– £æ…@°æ‹®˝ ✤ v§ƒ<†é¬©ç™ ´’† ü˨»EéÀ Ö†o Ê°®Ω’?– ¶µº®Ωûª ´®Ω{ç✤ ®ÓØ√™¸f®√Æˇèπ◊ Ææç•çCµç*† Å稡ç àC?– ´’™‰Jߪ÷✤ ¶µ«®Ωûªü˨¡ ûÌL NüΔu¨»ê ´’çvAí¬ °æE îËÆœ† ´uéÀh?

– ´’¯™«Ø√ Å•’™¸ éπ™«ç Çñ«ü˛

✤ ™é˙Æ涵º ¢Á·ü¿öÀ Æ‘péπ®˝ á´®Ω’? – >.N.´’¯™«çéπ®˝ ✤ Íé´©ç äÍé äéπ ®ÓV §ƒö«o £j«éÓ®Ω’d <°∂ˇ ïÆœdÆˇí¬

°æEîËÆœ† Ø√uߪ’´‚Jh á´®Ω’? – G.°œ. ®Ωó«✤ Åûªu©p é¬©ç ®√w≠æd°æAí¬ °æü¿O ¶«üµ¿uûª©’ E®Ωy£œ«ç

*† ´uéÀh á´®Ω’? – ñ«éî˝ £æ›ÊÆqØ˛ ✤ ¶µ«®Ωûªü˨¡ ¢Á·ôd¢Á·ü¿öÀ Ö°æví∫£æ«¢Á’i† Ç®Ωu¶µºôd†’

ÅçûªJéπ~ç™éÀ á°ærúø’ °æ秃®Ω’? – 1975✤ ÅçûªJéπ~ç™ †úÕ*† ûÌL ´÷†´€úø’ Å™„éÃq á LØÓ¢˛

v°æߪ÷ùÀç*† ؈éπ àC? – ´≤Ú\ú˛–2 ✤ ü˨¡ç™ È陫x ÅA°ü¿l ؈é¬v¨¡ßª’ç àC? – ´·ç•®· ✤ v°j¢Ëö¸ ®Ωçí∫ç™ EJtç*† ü˨¡ç™È陫x ¢Á·ôd¢Á·ü¿öÀ

Åçûª®√bBߪ’ N´÷Ø√v¨¡ßª’ç àC? – éÓ* ✤ ¶µ«®Ωûªü˨¡ç Ææyûªçvûªçí¬ ÅGµ´[Cm îËÆœ† ¢Á·ôd¢Á·ü¿öÀ

Ææ÷°æ®˝ éπç°æ‹uô®˝ àC? – °æ®Ω¢˛’ ✤ ¶µ«®Ωûªü˨¡ç™ ûÌL Æ涸¢Á’È®jØ˛ ´‚u>ߪ’熒 2002

Ææç.™ áéπ\úø ≤ƒn°œçî√®Ω’? – N¨»ê°æôoç ✤ v°æ°æçîªç™ Åûªu©p ¢Áj¨»©uç í∫© ü˨¡ç?

– ¢√öÀéπØ˛ Æœöà ✤ .v°æ°æçîªç™ ÅûªuCµéπ ïØ√¶µ« í∫© ü˨¡ç îÁjØ√ é¬í¬,

È®çúø´ ≤ƒn†ç™ Ö†o ü˨¡ç àC?– ¶µ«®Ωûªü˨¡ç ✤ ¶«Ø˛ °æôdù´· à †DB®√† Ö†oC? – È®jØ˛ ✤ Ææ÷®Ωû˝ °æôdùç à †DB®√† Ö†oC? – ûª°æA✤ Éçí¬xçú˛™ í∫© vGÆæd™¸ †í∫®Ωç à †C ãúø’f† í∫©ü¿’?

– Å¢√Ø˛✤ ûªN’∞¡Ø√úø’™ í∫© v°æÆœü¿m °æ€ùuÍé~vûª´’®·† X®Ωçí∫

°æôdùç à †CB®√† í∫©ü¿’? – 鬢ËJ✤ Å´’®˝éπçôéπ, •®Ω’î˝, £æ«Ù≠æçí¬¶«ü˛, ´÷çú≈x,

ï•©÷p®˝ ¢Á·ü¿™„j† °æôdù«©’ à †C äúø’f† í∫©´€?– †®Ωtü¿

✤ ü˨¡ç™ ¢Á·ôd¢Á·ü¿öÀ Öèπ◊\ éπ®√tí¬®Ω¢Á’i† öÀ≤Ú\í∫© ïçÂ≠ú˛°æ‹®˝ à †C äúø’f† ÖçC?

– Ææ’´®ΩgÍ®ê ✤ Ææõ„xñ¸ †C äúø’f† í∫© †í∫®Ωç àC? – ©÷C∑ߪ÷Ø√ ✤ Å≤Úç ®√w≠æd Ê°®Ω’†’ Å≤Úçí¬ ´÷®√a®Ω’. Éçûªèπÿ

Å≤Úç ņí¬? – ÅÆæ´÷†¢Á’i† àéπvU´çí¬ áEoÈéj ´’£æ«tü˛ ᙸ •®√C à ñ«Bߪ·úø’?

– Ñ>°ˇd✤ 2001™ ≤ƒ£œ«ûªu ®Ωçí∫ç™ ØÓ¶„™¸ •£æ›´’AE §ÒçC

†C á´®Ω’?– N.áÆˇ.ØÁj§ƒ™¸(¶µ«®Ωû˝) •’éπ®˝ •£æ›´’ûª’©’

✤ •’éπ®˝ v°jñ¸ à ü˨»EéÀ Ææç•çCµç*†C ?– ߪ·ØÁjõ„ú˛ éÀçí˚úø¢˛’

✤ NüËQ *vû√© N¶µ«í∫ç™ Ç≤ƒ\®˝ Å¢√®Ω’fèπ◊ Ø√N’ØËö¸Å®·† ¢Á·ü¿öÀ ¶µ«®ΩBߪ’ ÆœE´÷ àC ?

– ´’ü¿®˝ ÉçúÕߪ÷(1958)✤ Ç≤ƒ\®˝ Å¢√®Ω’fèπ◊ Ø√N’ØËö¸ ´’ü¿®˝ ÉçúÕߪ÷ ÆœE´÷

ü¿®Ωzèπ◊úø’ á´®Ω’ ? – ´’£æ«•÷¶¸ ë«Ø˛✤ í¬çDµ> 125´ ï†tCØÓûªq´ Ææçü¿®Ωs¥çí¬ ¶µ«®Ωûª v°æ

¶µº’ûªyç ØÁ©éÌLp† °æ€®Ω≤ƒ\®Ωç àC?– ´’£æ…û√tí¬çCµ ¨»çA •£æ›´’A✤ ´’£æ…û√tí¬çCµ ¨»çA •£æ›´’AE à Ææç´ûªq®Ωç™

ØÁ©éÌ™«p®Ω’? – 1995™

✤ ´’£æ…û√tí¬çDµ 125´ ´®ΩmçA, âéπu®√ïuÆæN’A Ææ£æ«†Ææç´ûªq®Ωç (Year of Tolerance) Ææçü¿®Ωs¥çí¬ßª·ØÁ≤Ú\ à®√pô’ îËÆœ† •£æ›´’A àC?– ߪ·ØÁ-≤Ú\ v°jñ¸ °∂æ®˝ ö«©È®Ø˛q

✤ éÌ*aØ˛™ í∫© ¶µ«®Ωûª ؈é¬ü¿∞¡ Péπ~ù Íéçvü¿ç?– â.áØ˛.áÆˇ.í∫®Ω’úø˝

✤ ©û√ ´’çÍí≠æ\®˝èπ◊ à Ææç´ûªq®Ωç™ ¶µ«®Ωûª®Ωûªo# ©Gµç*çC? – 2001™

✤ ¢Á·ü¿öÀ í¬çDµ ¨»çA •£æ›´’A(1996) §ÒçC†¢√®Ω’á´®Ω’? – ØÁ©qØ˛ ´’çúË™«

✤ ´’†ü˨»EéÀ îÁçC† à õ„EoÆˇ véÃú≈é¬JùÀéÀ 2005 Ææç´

ûªq®√EéÀ °æü¿tX Å¢√®Ω’f ©Gµç*çC?– ≤ƒEߪ÷ O’®√b✤ 2002™ °æü¿tX Å¢√®Ω’f†’ Åçü¿’èπ◊†o ´’† ®√Z≥ƒEéÀ

îÁçC† ¢Ájü¿’uúø’ á´®Ω’?– ú≈éπd®˝ úÕ.Ø√Íí¨¡y®˝ È®úÕf✤ ¶µ«®Ωûªü˨¡ç™ ¢Á·ü¿öÀ á©véÀdé˙ È®j©’†’ à Ææç´ûªq

®Ωç™ v§ƒ®ΩçGµçî√®Ω’? – 1929 ✤ Ææ£æ«ï ãúøÍ®´€ àC? – ´·ç•®· ✤ ¶µ«®Ωûª Åù’¨»vÆæh °œû√´’£æ›úÕí¬ á´JE °œ©’≤ƒh®Ω’?

– Nvéπç ≤ƒ®√¶µ«ß˝’ ✤ ¶µ«®Ωûªü˨¡ç™ ¢Á·ü¿öÀ È®j©’´÷®Ω_ç áéπ\úø †’çúÕ

áéπ\úøèπ◊ ¢Ëߪ’•úÕçC? – ¶Ô綫®·-–ü∑ΔØÁ ✤ ´’£æ…®√w≠æd™E å®Ωçí¬¶«ü˛èπ◊ à´’E Ê°®Ω’ ´÷®√a®Ω’?

– ¨¡ç¶µ«@†í∫®˝ ✤ úÁØ√t®˝\ ¢√Ææh´€u©†’ É™« Åçö«®Ω’? – úÁØ˛ ✤ ¶µ«®Ωûªü˨¡°æ€ ņCµé¬®Ω Éçí¬xçúø’ ®√ߪ’¶«J ÅE OJE

°œLîË¢√®Ω’? – üΔüΔ¶«ß˝’ ؈®Ó> ✤ éπ®√gôéπ ÆæçUûªç™ vA´‚Kh ÅE á´JE °œ©’≤ƒh®Ω’?

– ´·ûª’h≤ƒyN’ DéÀ~û√®˝ ✤ úÁï®˝d §∂ƒé˙q ÅE á´J†çö«®Ω’? – ï†®Ω™¸ ®Ó¢Á’™¸ ✤ Ææ´·vü¿í∫’°æ€hEéÀ í∫© G®Ω’ü¿’ àC?

– ÉçúÕߪ’Ø˛ ØÁ§ÚLߪ’Ø˛ ✤ Åçûª®√bBߪ’ ´’£œ«∞« CØÓûªq´ç á°ærúø’?– ´÷Ja 8✤ Åçûª®√bBߪ’ ´÷ûª[¶µ«≥ƒ CØÓûªq¢√Eo à ®ÓV†

ï®Ω’°æ€èπ◊çö«®Ω’? – °∂œv•´J 21 ✤ Ææ÷®Ω’uEéÀ ü¿í∫_®Ωí¬ Ö†o ví∫£æ«´·? – •’üµ¿’úø’ ✤ Ææ÷°æ®˝ ØÓ¢√ ņí¬? – ÅÆæ´÷†¢Á’i† ✤ ÇÆæd®√®·ú˛q àßË’ ví∫£æ…© ´’üµ¿u A®Ω’í∫’ûª’çö«®·?

– Åçí¬®Ωèπ◊úø’, í∫’®Ω’úø’ ✤ èπ◊çïØ˛ ÆæçGߪ÷®˝ ®Ω÷§ÒçCç*† Ø√ôu®Ω÷°æ¢Ë’C?

– äôd¢˛’ ü∑¿’™«x™¸ ✤ ØË≠憙¸ •’é˙ vôÆˇd†’ à Ææç.™ v§ƒ®ΩçGµçî√®Ω’?

– 1957 ✤ •’éπ®˝ •£æ›´’AE à Ææç´ûªq®Ωç™ à®√pô’ î˨»®Ω’?

– 1968™

✤ •’éπ®˝ v°jñ¸ N©’´ áçûª ? – É®Ω¢Áj ¢Ë© §˘çúø’x✤ N’Æˇ ÉçúÕߪ÷ ´®Ω™¸f–2005í¬ áç°œÈéj†C á´®Ω’ ?

– Æœçüµ¿÷®Ω í∫üÁl✤ N’Æˇ ߪ‚E´®˝q–2005 á´®Ω’? – †ö«M Èíx¶¢√✤ °æ€Lôb®˝ °æ€®Ω≤ƒ\®√Eo á°æ€púø’ ØÁ©éÌ™«p®Ω’?

– 1970™✤ ¨»ÆæØÓ©xç°∂æ’† Öü¿u´÷Eo v§ƒ®ΩçGµç*†¢√®Ω’?

– í¬çDµ@ ✤ §Úö« Å†í¬ – v°œ¢Á†{Ø˛ Ç°∂ˇ õ„v®ΩJÆˇd àïFqÆˇ ✤ ÅüÁjyûª ÆœüΔlçû√Eo v°æA§ƒCç*†C á´®Ω’?

– ¨¡çéπ®√î√®Ω’uúø’ ✤ Ç≤ƒ\®˝ °æ€®Ω≤ƒ\®√Eo à ®Ωçí∫ç™ v°æüΔ†ç îË≤ƒh®Ω’ ?

– ÆœE´÷ ®Ωçí∫ç✤ v°æ°æçîª ÆœE´÷ ®Ωçí∫ç™ Åûª’u†oûª °æ€®Ω≤ƒ\®Ωç àC ?

– Ç≤ƒ\®˝ Å¢√®Ω’f✤ Ç≤ƒ\®˝ Å¢√®Ω’f†’ ØÁ©éÌLp†C á´®Ω’ ?– Åé¬úøO’ Ç°∂ˇ ¢Á÷≠æØ˛ °œéπa®˝q, Ç®˝dq Åçú˛ ÂÆjØÁqÆˇ ¢√®Ω’✤ Ç≤ƒ\®˝ Å¢√®Ω’f†’ á°ærúø’ ØÁ™éÌ™«p®Ω’ ?

– 1929™✤ Ç≤ƒ\®˝ °æ€®Ω≤ƒ\®√Eo §ÒçC† ûÌL ¶µ«®ΩBߪ·®√©’

á´®Ω’ ? – ¶µ«†’ Åûªßª’ ❑

NüΔu®Ω’n©èπ◊ îËüÓúø’ ¢√üÓúø’

öÀÇ®¸öÀ, Éûª®Ω §Úöà °æKéπ~© v°æûËuéπç

ØÓ¶„™¸ °æ€®Ω≤ƒ\®√Eo Åçü¿’èπ◊†o ûÌL ¶µ«®ΩBߪ·úø’ á´®Ω’?

ÉçúÕߪ’Ø˛ á®·®¸ §∂Ú®¸q ÉçúÕߪ’Ø˛ á®·®¸ §∂Ú®¸q – éÀçC §ÚÆæ’d© ¶µºKhéÀü¿®ºë«Ææ’h©’ éÓ®º’ûÓçC. ¢Á·ûªhç ë«S©’ : 132 §ÚÆæ’d©’ : ™¸úÕÆœ 3, ≤Úd®¸ éð殸 4, Æ槃®· ¢√™«18, áçöÀáÆˇ 32, ¢Á’Æˇ ≤ƒd°∂ˇ 65, èπ◊é˙ 5,Ç®„pçô®¸ 4, üÓG 2, ¢√®¸f Ææ£æ…ߪ’éπ/ Çߪ÷ 1.°®·çô®¸ 2, ´©\ØÁj﮸ 2 Å®º|ûª : §ÚÆæ’d$’ Å$’ÆæJç* °æüÓûª®ºí∫A/ ÉçÒ‰¸ âöÀâ úÕ§Òx´÷ ´ßª’Ææ’ : 18 $’ç* 25 à∞¡x ´’üµ¿u Öçú≈L. áç°œéπ : ®«ûª °æKéπ~/ Æœ\™¸ õ„Æˇd / °∂œ>éπ™¸ õ„ÆˇüΔy®«. ü¿®ºë«Ææ’hèπ◊ Çꮺ’ ûËC: úÕÂÆç•®º’ 11 ¢Á¶¸ÂÆjö¸ : indianairforce.nic.in

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12 Ð-û¦-è[ª þ¼÷ªî¦ô¢Ù 20 ì÷Ùñô¢ª 2017

4. véπ-ûª-™«© ü¿l é¬çA- -véÃ-¶μº- †ç5. ÷†- ¤-úÕ éπ†’o – ®Ωçí∫’© v°æ°æçîªç

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★ é¬-•-öÀd °æôç™ îª÷°œ† èπ◊ç¶μ«-é¬®Ω éπôéπç üΔy®√È®çúø’ ¢ËÍ®y®Ω’ v°æA-Gç-¶«©’ à®Ωp-úøû√®·.

-v°æ: ´Ææ’h- ¤†’ 20 ÂÆç.O’. Ø√¶μºuç-ûª-®Ω-ç -Ö-†o èπ◊ç¶μ«-鬮Ωéπôé¬-EéÀ 30 ÂÆç.O’. ü¿÷®Ωç™ Öç*-ûË üΔE v°æA-Gç•ç áéπ\úø à®Ωp-úø’-ûª’ç-C?

ï: ´Ææ’h-ü¿÷®Ωç u = − 30 ÂÆç.O’.éπôéπ Ø√¶μºuç-ûª®Ωç f = 20 ÂÆç.O’.v°æA-Gç• ü¿÷®Ωç v = ?

1 1 1 uf★ Ææ÷vûªç: ⎯ = ⎯ − ⎯ (™‰üΔ) v = ⎯⎯

f v u u + f

★ N©’-´©’ v°æA-Íé~-°œÊÆh v =

−30 × 20 − 30 × 20⎯⎯⎯ = ⎯⎯⎯ = 60 ÂÆç.O’.−30 + 20 −10

★ v°æA-Gç•ç éπô-é¬-EéÀ 60 ÂÆç.O’. ü¿÷®Ωç™ à®Ωp-úø’-ûª’çC.

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Cy°æ¤-ö«-é¬®Ω éπôé¬-Eo Ö°æ-ßÁ÷-T-≤ƒh®Ω’.-v°æ: ¢√û√-´-®Ω-ùç™ áèπ◊\´ §Òí∫-´’ç -Ö†o v§ƒçû√--™x

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-v°æ: 60° °æôdéπ éÓùç (A) -Ö-†o °æôdéπç éπE≠æe Nîª-©†éÓùç (D) 30° Å®·-ûË °æôdéπç ûªßª÷-KéÀ NE-ßÁ÷-Tç-*† °æüΔ®Ωn ´véÃ-¶μº- † í∫’ù-é¬Eo éπ†’-éÓ\çúÕ.

ï: É*a-†N: ∠A = 60°, ∠D = 30°

★ °æôdéπ °æüΔ®Ωn ´véÃ-¶μº- † í∫’ùéπç A + D

sin ⎯⎯2

n = ⎯⎯⎯ (Ææ÷vûªç)A

sin ⎯2

N©’-´©’ v°æAÍé~°œÊÆh:

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2n= ⎯⎯⎯ = ⎯⎯

60sin ⎯ sin 30°

2

1⎯√

⎯2 2

∴ n = ⎯ = ⎯ = √⎯2

1 √⎯2 ⎯

2

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ï:

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È®ç-úø’ ´÷®Ω’\-© -v°æ¨¡o-©’-v°æ: èπ◊ç¶μ«-é¬-®Ω- éπ-ô-éπç á°æ¤púø’ ÍéçvD-éπ-®Ωù éπôéπçí¬,

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★ èπ◊ç¶μ«-é¬®Ω éπô-é¬Eo üΔE ´véÃ--¶μº- † í∫’ù-éπç- éπç-õ‰áèπ◊\´ ´véÃ-¶μº- † í∫’ù-éπç- -Ö-†o ߪ÷†-éπç™ Öç*-†-°æ¤púø’ ÅC NÍéçvDéπ®Ωù éπôéπç-™« -°æ-E-îË-Ææ’hçC.

★ -Ö-üΔ: -F-öÀ-™ à®Ωp-úÕ† í¬L- •’-úøí∫ NÍéç-vD-éπ-®Ωùéπôéπ癫- °æE-îË-Ææ’hçC.

-v°æ: 'R' ¢√u≤ƒ-®Ωl¥ç -Ö-†o §ƒ®Ωü¿-®Ωz-éπ- íÓ∞¡ç í¬L™ ÖçC.üΔE ´véÃ-¶μº´† í∫’ùéπç n. ´Ææ’h- ü¿÷-®√-EéÀ Ææ´÷†ü¿÷®Ωç-™- íÓ-∞«-EéÀ È®çúÓ ¢Áj°æ¤ Eï -v°æ-A-Gç•ç à®Ωp-ú≈-©çõ‰, v°æ-üμΔ-Ø√-éπ~ç°j íÓ∞¡ç Ö°æ-J-ûª©ç †’ç-*áçûª- ü¿÷-®Ωç™ ´Ææ’h-´¤†’ Öçî√L?

ï: ´Ææ’h- ü¿÷-®√-EéÀ Ææ´÷-†- ü¿÷-®Ωç™ v°æA-Gç•ç à®Ωp-ú≈-©çõ‰ íÓ∞¡ç™ v°æߪ÷-ùÀçîË ´véÃ-¶μº- † éÀ®Ωùç v°æ-üμΔ-Ø√-é~¬-EéÀ Ææ´÷ç-ûª-®Ωçí¬ v°æߪ÷-ùÀç-î√L. (°æô-ç-™EéÀ®Ω-ù«-©-†’ îª÷-úøç-úÕ)

-ï: °æô-ç †’ç-*: u = −x, v = ∞ (´véÃ-¶μº- † éÀ®Ωùçv°æüμΔØ√-é~¬-EéÀ Ææ´÷ç-ûª-®Ωçí¬ ûÌL ´véπ-ûª©ç †’ç-*¢ÁRxçC) -

★ n1 = 1 (í¬L- ߪ÷-†-éπç™ Öç-*-çC), n2 = n

n2 n1 (n2 − n1)★ ⎯ − ⎯ = ⎯⎯⎯⎯

v u R

(-´’-†èπ◊ Ñ Ææ÷vûªç -ûÁ©’Ææ’)n 1 (n − 1)

★ N©’-´©’ v°æA-Íé~°œÊÆh : ⎯ − ⎯ = ⎯⎯⎯∞ −x R

1 (n − 1) R⇒ ⎯ = ⎯⎯ (™‰üΔ) x = ⎯⎯

x R (n − 1)

-v°æ: äéπ Cyèπ◊ç-¶μ«-é¬®Ω éπô-éπ°æ¤ È®çúø’ ´véπ-ûª-™«© ¢√u≤ƒ-®√l¥©’ Ææ´÷†ç. (R) éπôéπ ´véÃ--¶μº- † í∫’ùéπç n =

1.5 Å®·-ûË éπ-ôéπ Ø√-¶μºuç-ûª®Ωç éπ†’-éÓ\ç-úÕ.

ï: É*a-†N: ´véÃ--¶μº´† í∫’ùéπç n = 1.5

´véπ-ûª-™«© ¢√u≤ƒ®√l¥©’ R1 = R2 = R

★ èπ◊ç¶μ«-é¬-®Ω- éπ-ô-é¬-EéÀ: R1 = + ve, R2 = − ve

1 1 1★ Ææ÷vûªç: ⎯ = (n − 1)( ⎯ − ⎯)f R1 R2

★ N©’-´©’ v°æA-Íé~-°œÊÆh:

1 1 1⎯ = (1.5 − 1)(⎯ − ⎯)f R −R

1 0.5 × 2 1∴ ⎯ = ⎯⎯⎯ = ⎯ (™‰üΔ) f = R

f R R

∴ éπôéπ Ø√¶μºuç-ûª®Ωç ´véπ-û√- ¢√u-≤ƒ-®√l¥EéÀ Ææ´÷†ç.-v°æ: Ææp≠æd- ü¿%-≠œd éπFÆæ ü¿÷®Ωç, ü¿%≠œd éÓùç ´uéÀhE •öÀd

ÅûªúÕ ´ßª’-Ææ’†’ •öÀd ´÷®Ω’ûª÷ Öçö«®·. áçü¿’--´--©x?

--ï: éπçöÀ-™E éπô-é¬-EéÀ dž’-èπ◊E -Ö†o ÆœL-ߪ’J éπçúø-®√©’ éπôéπ ´véπ-û√- ¢√u-≤ƒ-®√l¥-Eo ´÷®Ωaúøç üΔy®√éπôéπç ûª† Ø√¶μºuç--ûª®√-Eo ´÷®Ω’a-éÓ-´-ú≈-EéÀ üÓ£æ«-ü¿-°æ-úø-û√®·.

★ ü¿÷®Ωç™ Ö†o -´-Ææ’h-´¤†’ éπ†’o îª÷Ææ’h-†o-°æ¤púø’, ÆœL-ߪ’J éπçúø-®√©’ Nv¨»çA ÆœnA™ Öç-úø-ôç -´©x éπçöÀ-éπ-ôéπ Ø√¶μºuç-ûª-®Ωç í∫J--≠æe- ’- ¤-ûª’çC. ÉC éπô-é¬-EéÀ,È®öÃ-Ø√èπ◊ ´’üμ¿u- - Ö-†o ü¿÷®√-EéÀ Ææ´÷-†çí¬Öçô’çC.

★ Ñ ÆœL-ߪ’J éπçúø-®√© °æE-B®Ω’ ´uéÀhéÀ, ´uéÀhéÀ ´÷®Ω-úø-¢Ë’- é¬èπ◊ç-ú≈ ´ßª’-Ææ’ûÓ ¶«ô’ ¢√öÀ °æE-B-®Ω’™ûËú≈ ´Ææ’hçC. Åçü¿’-´-™‰x Ææp≠æd- ü¿%≠œd éπFÆæ ü¿÷®Ωç,ü¿%≠œd éÓùç ´uéÀhE •öÀd, Å-ûª-úÕ ´ßª’-Ææ’†’ •öÀd´÷®Ω’ûª÷ Öçö«®·.

-v°æ: ®ΩN éπ∞¡x-üΔl©’ üμ¿Jç-î√úø’. ¢√öÀ †’ç-* Å-ûª-úÕ éπ∞¡x†’í∫´’-EÊÆh ÅN °ü¿l °æJ-´÷-ùç™ éπ-E°œÆæ’h-Ø√o®·.Åûª-úÕéÀ à ®Ωéπ-¢Á’i-† ü¿%≠œd- üÓ≠æç -Öç-C? Ç ü¿%≠œdüÓ≥ƒEo îª÷Ê° éÀ®Ωù *vûªç UÆœ N´-Jç--îªç-úÕ.

ï: ®ΩN üμ¿Jç-*-çC èπ◊ç¶μ«-é¬®Ω éπôéπç. Åûªúø’ D®Ω-ü¿%≠œd(£j«°æ®˝ ¢Á’vö-°œ-ߪ÷)ûÓ ¶«üμ¿-°æ-úø’--ûª’Ø√oúø’.

★ Ñ D®Ω`-ü¿%-≠œdûÓ ¶«üμ¿-°æ--úË¢√®Ω’ ü¿í∫_-®Ωí¬ Ö†o ´Ææ’h-´¤-©†’ Ææp≠ædçí¬ îª÷úø-™‰®Ω’. áçü¿’-éπçõ‰ Ç ´Ææ’h -v°æ-A-Gç•ç È®öÃ-Ø√èπ◊ ¢Á†’éπ ¢Áj°æ¤ °æúø’-ûª’çC.

★ DE Ææ´-®Ω-ùèπ◊ èπ◊ç¶μ«-é¬®Ω éπôéπç ¢√úø-û√®Ω’.

á) D®Ω`-ü¿%≠œd üÓ≠æç

G) èπ◊ç¶μ«-é¬®Ω éπô-éπçûÓ Ææ -®Ωù

-v°æ: éπôéπ ≤ƒ´’®Ωn uç Åç-õ‰ -à-N’-öÀ? DE v°æ´÷-ù«©’àN’-öÀ?

ï: äéπ éπôéπç é¬çA éÀ®Ω-ù«-©†’ ÍéçvD-éπ-JçîË ≤ƒn®·™‰üΔ NÍéç-v-D-éπ-JçîË ≤ƒn®·E éπôéπ ≤ƒ´’®Ωn uçÅçö«®Ω’. éπôéπ Ø√¶μºuç-ûª-®Ω-ç (-O’.©™) N™´’

-v°æ: äéπ Ñûª éÌ©-†’™ Åç-¢Áç-•úÕ FöÀ™ ´·ET O’®Ω’ Ñü¿’-ûª’-Ø√o®Ω’ -Å-†’èπ◊ç-üΔç. äúø’f°j O’ ÊÆo£œ«-ûª’úø’ E©-•úÕ ÖØ√oúø’. O’èπ◊ O’ ÊÆo£œ«-ûª’úø’, Å-ûª-úÕ¢√Ææh´ áûª’h-éπç-õ‰ áèπ◊\´ áûª’hí¬ éπ-E°œ≤ƒh-ú≈ ™‰üΔ ûªèπ◊\´ áûª’hí¬ éπE°œ≤ƒhú≈?áçü¿’-éπE? (-äéπ- ´÷®Ω’\ -v°æ-¨¡o)

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¶μº´† éÀ®Ωùç ©ç•-ç- †’ç-* ü¿÷®Ωçí¬ ´çí∫’-ûª’ç-C.

-¶μ˜-Aéπ ®Ω≤ƒ-ߪ’-†-¨»-≤Yƒ-©’

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★ Ææ´÷ç-ûª®Ω é¬çA- éÀ-®Ω-ù«© ´÷®Ω_ç™ È®çúø’ ÍéçvD-éπ-®Ωù éπô-é¬-©†’ (l1, l2) Öçî√®Ω’.

★ Ææ´÷ç-ûª®Ω é¬çA- éÀ-®Ω-ù- °æ¤çïç éπô-éπç°j °æúÕ-ûË, ÅNØ√Gμ- ´ü¿l (F) ÍéçvDéπ%-ûª-´’-´¤-û√®·. -

★ Ø√-Gμ -†’ç-* -v°æ-ߪ÷-ùÀç-îË é¬ç-A éÀ®Ω-ù«-©’ È®ç-úÓéπôéπç (l2) -ü¿l - -véÃ-¶μº- -†ç -îÁç-C-† -ûª®√y-ûª -v°æ-üμΔ-Ø√é~¬-EéÀ Ææ-´÷ç-ûª®Ωçí¬ -v°æ-ߪ÷-ùÀ≤ƒh®·.

★ P1 F ¢Á·ü¿-öÀ -éπ-ôéπç l1 Ø√¶μºuç-ûª®Ωç = f1★ P2 F È®ç-úÓ éπôéπç l2 Ø√¶μºuç-ûª®Ωç = f2★ °æôç †’ç-* Ææp≠æd´’-´¤-ûª’†o N≠æߪ’ç àN’-ôçõ‰,

È®çúø’ éπô-鬩-†’ (f1 + f2) ü¿÷®Ωç™ ¢Ë®Ω’ -îË-ߪ÷-L.

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ï: á) °æûª-†-éÓùç (i1): °æûª-†- éÀ-®Ω-ù«-EéÀ °æôd-éπ ûª-©ç°jéÀ®Ωùç °æûª†ç îÁçC† Gçü¿’´¤ ´ü¿l UÆœ†©ç¶«-EéÀ ´’-üμ¿u -Ö-†o éÓùç °æûª-†- éÓùç.

G) •£œ«-®√_N’ éÓùç (i2): •£œ«-®√_N’ éÀ®Ω-ù«-EéÀ °æôd-éπ-ûª©ç ´ü¿l éÀ®Ωùç •£œ«-®Ω_ûªç îÁçC† Gçü¿’´¤´ü¿l ûª™«-EéÀ UÆœ† ©ç¶«-EéÀ ´’üμ¿u- -Ö-†o éÓùç•£œ«-®√_N’ éÓùç.

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-Tç-*ç-C) ´’üμ¿u -Ö-†o éÓù¢Ë’ Nîª-©† éÓùç 'd'.

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N©’-´†’ éπôéπ ≤ƒ´’®Ωn uç Åçö«®Ω’.1 100

éπôéπ ≤ƒ´’®Ωn uç P = ⎯⎯ = ⎯⎯⎯⎯f(O’.) f(ÂÆç.O’)

éπôéπ ≤ƒ´’-®√nu-EéÀ v°æ´÷ùç úøߪ÷-°æd®˝ (D)