Education 05-10-2018

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 5,  2018- 

5.    4:5,  ... 120  ... ? . 4 . 8 . 20 . 6 :  : a:b = 4:5, LCM = 120 .�.�. = LCM /(axb) = 120/(4x5) = 6 -3: �  .�.., .�.�.    � � .�.. .�.�.� ��.

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   � � ��.

1. .. 600, ... 15     . . 4 . 3 . 2 . 6 :  : � (.�.)/(.�.�) = 600/15 = 40 � 40  ���  (1, 40), (2, 20), (4, 10), (5, 8) �  �   (1, 40) (5, 8) � ��   = 2 �

8 x9 x4    ?

5

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

  � �    ��� �.     : � N  � , N = 2px3q x5rx7s  ���  = (p+1)(q+1)(r+1)(s+1) 1 ��   ��  = (p+1)(q+1)(r+1)(s+1)-1 1,   ��  ���  = (p+1)(q+1)(r+1)(s+1)-2 �  ���  = p(q+1)(r+1)(s+1) �  ���  = (q+1)(r+1)(s+1) � N  ���   = {(2p+1-1)/(2-1))((3q+1-1)/(3-1))((5r+11)/(5-1)}...... � N   ��� � � ��  i. 1/2[(p+1)(q+1)(r+1)] (N   �) ii. 1/2[(p+1)(q+1)(r+1)](N  ) � N  ���   = N1/2[(p+1)(q+1)(r+1)] � N  � ���  = p+q+r+s 1. 220, 284   ? : � 220 = 22x51x111 ���  = (2+1)(1+1)(1+1) = 3x2x2 = 12 ���  = {(22+1-1)/(21))((51+1-1)/(5-1)}{(111+1-1)/(11-1)} = 7(24/4)(120/10) = 504 284 = 22x711 ���  = (2+1)(1+1) = 3x2 ���  = {(22+1-1)/(2-1)) ((711+1-1)/(71-1)) = 7(5040/70) = 504 : �   ���  � �   �. : 220, 284   2. 1995   ? . 8 . 16 . 32 . 64 :  : � 1995 = 31x51x71x191 � ��� (��)  1995 = (1+1)(1+1)(1+1)(1+1) = 16 3. 240   ? . 750 . 754 . 744 . 792 :  : � 240 = 24 x 31 x 51 ���   � = ((24+1-1)/(2-1))((31+1-1)/(3-1)) {(51+1-1)/(5-1)} = (32-1/1)(9-1/2)(25-1/4) = 31x4x6 = 744 4. 28  ? . 21952 . 24944 . 25864 . 24594 :  �

: � 28 ��� = 4x7 = 22x71 =281/2{(2+1)(1+1)} = 283 = 21952 5. 64      ? -4 . 4 . 5 . 6 . 8 :   :  � 64 = 26 �� ��  = 1/2[(6+1)+1] = 4 [64 ] 6. 144   ? . 2 . 3 . 4 . 5 :  : � 144 = 24x32 p = 4, q = 2 �  ���  = (q+1)(r+1)(s+1) = (2+1) = 3 7. 144   ? . 10 . 12 . 15 . 18 :  : � �

 ���  = (4+1)(2+1) = 15 8. 85x94x48   ? . 39 . 52 . 45 . 42 :  : � 85x94x48 = (23)5x(32)4x(22)8 = 215x38x216 � � ���  = ���  = 15+8+16 = 39 9. 162 1,      ? . 10 . 12 . 8 . 14 :  : � 162 = 21x34 1,   � ���  = (1+1)(4+1)-2 = 8 ..., ... : �   � �   ��� � �� �. : 12 ��� = {1, 2, 3, 4, 6, 12} �     �� 1 �     ��   �   ���    : �  �      ���   � ���  � �� ��� �. : 12 ��� = {1, 2, 3, 4, 6, 12} 18 �� = {1, 2, 3, 6, 9, 18}  ��� = {1, 2, 3, 6} :

   1, 2, 3......� �     � �. : 5 � = {5, 10, 15, 20,.......} 7 � = {7, 14, 21,.....} �    �  �    ��      �    ��    .  : �  �   � �    �� � �. : 3 � = {3,6,9,12,15,.......} 6 � = {6,12,18,24,.....}  � = {6,12,18,24,.....}    (..): �  �      ��   �� � .�.. �. : 6 � = {6,12,18,24,30,.......} 8 � = {8,16,24,32,.....}  � = {24,48,72,.....} .�.. = 24 ...  : 1. 8, 12  ... ? : � 8 � = {8,16,24,32,.......} 12 � = {12, 24, 36,.....} �� � = {24,48,72,.....} .�.. = 24 ( ��   ) : �    .�.. � �   � 5, 6  .�.. = 5x6 = 30 �  �  .�.. � �    3,7 .�.. = 3x7 = 21 �  �  ,   ��   .�.. .

8, 24� 8   24 ��. .�.. = 24 .�.�.  : 1. 6, 8 ... ? :   : � 6 � = {1, 2, 3, 6,.......} � 8 � = {1, 2, 4, 8,.....} �� ��� = {1, 2.....}  �� �(.�..�) = 2 -1: �    ..., ...: 2. 72, 108, 2100 ... ? : �   � ���  ��, ��  � �  � ���  .�.. .

72 = 23x32 108 = 33x22 2100 = 22x52x31x71 .�.. =23x33x52x71 = 37,800 3. 108, 288, 360 ... ? :

 

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   , ,  9441022571   � ���  ��, ��   ��  � ���    .�.. .

108 = 22x32 288 = 25x32 360 = 23x32x5 .�.�. =22x32 = 36 : �  �  .�.. = 1 �  �  ,   ��   .�.�. . �   .�..�� 1  �  �  �  �. �    .�.�. = 1 2 -2: � ..., ...  : �   .�.., ..�. ,    � �. � L.C.M. x G.C.F. = axb 1.   ... 1008, ... 36.     144    ? . 252 . 250 . 280 . 200 :  : � axb = LxG 144xb = 1008x36 b = (1008x36)/144 = 252 �  = 252 2.   39, 26  ... 78  ... ? . 26 . 10 . 12 . 13 :  : � LxG = axb 78xG = 39x 26 G = (39x26)/78 = 13 �  = 13 3.    4212, ... 9  ... ? . 460 . 468 . 461 . 464 :  : � LxG = axb L = (axb)/G = 4212/9 = 468 4.    7:9,  ... 630  ... ? . 70 . 90 . 10 . 20 :  : �   7x, 9x � 7x, 9x  .�.. = 63x 63x =630, x =10 7x, 9x  .�.� = x = 10 �

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 5,  2018- 

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38. Having finished work, Lavanya watched TV. The underlined word is a…

1. Present Participle 2. Past Participle 3. Perfect Participle 4. Gerund 39. The bird……out if you leave the door of the cage.

Choose the correct verb to fill in the blank.

1. flies 2. will fly 3. fly 4. would fly 40. We need not sleep on the floor as there are …

Choose the correct phrase to fill in the blank.

1. not beds enough 2. not enough beds

3. enough beds 4. beds enough 41. When ……… this new car?

Choose the correct verb and subject to complete this question 1. do you buy 2. did you bought 3. have you bought 4. did you buy 42. I was not trained enough for the game.

'Enough’ in the sentence above is: 1. an adverb 2. an adjective 3. a conjunction 4. a participle

He is not all that intelligent. It means that…

1. O that I were young again ! The declarative form of this sentence is…

1. I were a young again.

2. I wish I were a young again.

3. How did I wish I were a young again.

4. I never to be young again.

2. Fill in the blanks with suitable words: The…… of the speaker should be comfortable.

1) pasture 2) pastor 3) posture 4) prosper 3. Choose the linking word that can be used to express 'contrast'..

1. similarly 2. But 3. Thus 4. Moreover 4. The correct order of the following parts of a sentence is….

A) Some key B) An elephant C) Facets D) A legendary status E) There are F) That give 1) EACFBD 2) EACBFD 3) EACDFB 4) EADBCF 5. Could me allow me to leave the office at 5pm? It is…

1. taking permission in a formal way 2. taking permission in an informal way 3. expressing possibility 4. giving permission 6. Read the following three statements: A. He founded the company in 2003 with the little money that he had.

B. He found a company in 2003 with the little money that he had.

C. He had founded a company in 2003, just before he left for Chennai.

Now choose the appropriate option.

1. Both A and B are correct 2. Both A and C are correct 3. Only B is correct 4. All are correct 7. Identify the grammatically correct sentence.

1. I wish I drive a car.

2. I wish I knew how to drive a car.

3. I wish I know how to drove a car.

4. I wish to drive a car.

8. Fill in the blank with a suitable article.

He loves…….. .mankind.

1.A 2. an 3. the 4. no article 9. They will check if he’s locked the receipt up in the bureau. The passive form of this sentence is……..

1.

They will be checked if the receipt is locked up in the bureau.

2. It will be checked if he has locked the receipt in the bureau.

3. It will be checked if the receipt has been locked up in the bureau by him.

4. If he’s locked the receipt up in the bureau will have been checked by them.

10. He shed crocodile tears on the death of his step mother.The meaning of the underlined idiom is…

1. Deceitful actions 2. False show of grief.

3. genuine grief 4. Unbelievable grief.

11. Identify the incorrect idiom and its meaning from the following: 1. Birds of the same feather - Persons of the same nature 2. Against the rainy day - precaution for emergency 3. To leave no stone, unturned :- To make all possible efforts 4. To meet half way - To be prepared to break away 12. Read the statement given below and answer the questions that follows: Dress and address make the first and foremost impression.

The underlined word means……..

1. the place where we live 2. Our speech and manners 3. our surroundings and neighborhood 4. A stylish accent in speech

TGT Special 13. Read the following sentences and choose the correct statement.

A. He is more brave than strong.

B. He is more industrious than more intelligent.

1. Only (A) is correct 2. Only (A) is incorrect 3. Both are correct.

4. Both are incorrect.

14. They sometimes ‘skinned their noses’.

What is the figurative meaning of the phrase ‘skinned their noses?

1. were upset by failures 2. Rubbed the nose accidentally 3. scratched the nose 4. Encouraged by failures.

15. Srinu said to Venu, ‘You are a very intelligent person, aren’t you?’ The reported form of this sentence is….

1. Srinu asked Venu he was a very intelligent person, wasn’t he.

2. Srinu exclaimed that Venu was a very intelligent person.

3. Srinu advised Venu to be very intelligent.

4. Srinu asked Venu whether he was very intelligent.

16. ‘I really must have a rest’, Swathi said The sentence can be reported as…

1) Swathi said to have a rest.

2) Swathi insisted to have rest.

3) Swathi insisted on having a rest.

4) Swathi said on having rest.

17. The Noun “obedience” is formed from the verb…

1. Obedient 2. Obey 3. Obediently 4. Obese 18. Identify the part that has an error.

Without waiting for (A) / the instructions from the Government, (B) / some cable operators in the city had block the news. (C) /No error (D)

1. D 2.C 3. A 4.B 19. The …….. threw the stones at the police. Fill in the blank.

1. mob 2. fleet 3. crew 4. crowd 20. Meat is to the vegetarian as ……….is to the teetotaler. Fill in the blank.

1) violence 2)alcohol 3) robbery 4) gambling 21. Fill in the blanks in the following sentence with appropriate Auxiliary Verbs.

If I……enough money, I would have married her.

1. had been 2. had 3. Had had 4. Have had 22. He is not all that intelligent. It means that…

1. He is not intelligent as he is believed to be.

2. He is not very intelligent.

3. He was intelligent in the past.

4. He is intelligent but we don’t believe.

23. Neither the father nor his sons……. responsible. Fill in the blank with right form of the verb.

1. has been 2. is 3. Are being 4. Were 24. Identify the sentence that do not convey the proper meaning.

1. Going up the hill, an old temple was seen.

2. When we went up the hill, we saw an old temple.

3. Entering the room, I found the light quite dazzling.

4. When I entered the room, the light was quite dazzling.

25. Choose the word that gives the meaning of 'a number of people watching a match.'

1. audience 2. Troupe 3. Spectators 4. team 26. Who will…….. our baby when you go to office? Fill in the blank with suitable phrasal verb.

1) look after 2) lie down 3) lay down 4) go down 27. The four parts of a sentence are given below. Identify the part of the sentence that has an error.

1. The technician reminded 2. them to have a thoroughly cleaning of the 3. machine after each use.

4. No error 28. Fill in the blanks with suitable articles. .....accused were sent to......jail.

1. an. a 2. the, No article 3. the , the 4. No articles 29. Will you wait here till I …….. my lunch? Choose the best verb form.

1.finish 2.shall finish 3.have finished 4.finished 30. Identify the incorrect sentence.

1. You, he and I have passed the test.

2. She and I are good friends.

3. I, she and you will be selected.

4. I and he will be punished.

31. Choose the suitable prefix to form it’s opposite from the given root word

CH. SRINIVAS Subject Expert polampally, Thimmapur Karimnagar “significant” 1. un 2. Pre 3. In 4. De 32. Look at the spelling of the words given below: A) parallel B) occurrance C) hypocrasy Now choose the correct option given below.

1. Only C is wrong 2. Only A is correct 3. Only B is correct 4. All are correct.

33. one of these days said srinivas youll be taught a lesson. If you punctuate the sentence properly, you will get……..

1. One of these days, said Srinivas, you’ll be taught a lesson.

2. “One of these days,” said Srinivas “you’ll be taught a lesson” 3. “One of these days,” said Srinivas, “you’ll be taught a lesson.”

4. “One of these days,” said Srinivas, “youll be taught a lesson.”

34. I am obliged…….. you …….. your kindness.

Fill in the blanks with suitable prepositions.

1.to, for 2.for, to 3.with,for 4.for,with 35. I read the newspaper. It interests me. If you combine the two sentences using an appropriate conjunction, you will get, 1. I read the paper but it interests me.

2. I read the paper because it interests me.

3. Because I read the paper, it interests me.

4. Because I read the paper, so it interests me.

36. Choose the correct option with the right words in sequence.

You can…….. see the mountains on a …….. sunny day.

1. prettily, pretty 2. Clearly, clear 3. Bright, brightly, 4. True, truly 37. Which of the following sentences is grammatically correct?

1. What were the men been doing when the policemen arrived?

2. What were the men doing when the policemen had arrived?

3. When the policemen arrived what were they doing?

4. What had the men been doing when the policemen arrived?

1-1 7-1 13-1 19-1 25-3 31-3 37-4

2-3 8-4 14-1 20-2 26-1 32-2 38-3

Answers 3-2 9-3 15-4 21-3 27-2 33-3 39-2

4-3 10-4 16-3 22-1 28-2 34-1 40-2

5-1 11-4 17-2 23-4 29-1 35-2 41-3

6-4 12-2 18-2 24-1 30-3 36-2 42-1

12 X¯óÁø£yês¡+ 5.10.2018 ôV’≤<äsêu≤<é

Find the compound interest on Rs. 12,000 at 10% p.a. for...

Introduction: If the interest at the end of a year of fixed period is added to the sum lent, and the amount thus obtained becomes the principal for the next period, then the sum of money is said to be lent at compound interest.

If P is the principal, n is the number of years and R is rate % per annum.

R � � Amount =P �1 � � 100 ��

10) Find the difference between C.I and S.I on Rs. 32,000 for 3 years at 5% p.a.?

R1 � 5% p.a.; R2 � 10% p.a.

sol :

R �� R � � A � P �1 � 1 � �1 � 2 � � 100 � � 100 � 5 � � 10 � � 1� � 25000 �1 � � 100 �� �� 100 �� � Rs.28,875

Short cut Method

5) What sum will amount to Rs. 15,000 in 3 years at 25% p.a. compound interest?

n

n

Note(1): When the interest is compounded half yearly.

R � � � � 2 Amount = P �1 � � 100 � � � �

sol : P � Rs.25, 000;

2n

n

R � � =Amount = P �1 � � 200 �� Note(2): When the interest is compounded quarterly.

R � � � � 4 Amount =P �1 � � 100 � � � �

4n

R � � sol : 3087 � 2800 �1 � � 100 �� 3087 441 � � � 2800 400 2

4n

2) At what rate percent per annum compound interest will Rs. 6250 amount to Rs. 6760 in 2 years?

2

2

14) The S.I. on a certain sum of money for 2 years at 5% p.a. is Rs. 600.

What is the C.I. on the same sum at same rate for the same time?

P � 2�5 � 600 � P � Rs.6000 100 At Compound Interest .

sol :

2

5 � � A � 6, 000 �1 � � � Rs.6615 � 100 � � C.I . � 6, 615 � 6000 � Rs.615

2

� 3� �2 � � 2�

10 � � � 24000 �1 � � � 100 � 21 21 21 � 27783 A � 24000 � � � 20 20 20 � C.I . � 27783 � 24000 � Rs.3783 8) Find the difference betweenC.I and S. I 1 on Rs. 6400 for 2 years at 12 %p.a?

2 PNR 6400 � 2 25 sol : S.I. � � � � Rs.1600 100 100 2 � � 252 �� C.I . � 6400 �1 � � � 6400 100 � � C.I . � 8100 � 6400 � Rs.1700 � Difference between C.I. and S.I. = 1700-1600=Rs.100 2

676 � 26 � � R � � � � � �1 � � 625 � 25 � � 100 � R R 26 1 �I � � � � 100 25 100 25 � R � 4% p.a.

3) Find the compound interest on Rs. 12,000 at 10% p.a. for 2 years 6 months?

10 � � �102 �� � Sol : A =12000 �1 � � � �1 � � 100 � � 100 � �110 110 � � 21 � A � 12000 � � �100 100 �� �� 20 �� � 15246

Senior Faculty Hyderabad ph:9492956214

3

� C.I . � 39930 � 30000 � Rs.9930

2

� 10 � sol :P � �1 � � 4,87,000 � 100 � � �110 110 � �� � � 4,87,000 � 100 100 � � � P � Rs.4,00,000

Mr. K. Kumar

7) Find the compound interest on Rs. 24,000 at 10% p.a. for 1 year 6 months, the interest being compounded half yearly?

� 10 � sol : A � 24, 000 �1 � � 100 ��

3

� 10 � Sol : A =30000 �1 � � 100 �� 110 110 110 � � A =30000 � 100 100 100 A =39930

11) The value of a building increases by 10% annually. If its present value is Rs.4,87,000. What was it s value two years ago?

2

2

R � R � � � 21 � � 1 � � � 1 � � � � � �� 100 �� � 20 � � 100 � 21 R � � 1� � R � 5% p.a 20 100

EXAMPLES 1) Find the compound interest on Rs. 30,000 for 3 years at 10% p.a.?

2

3

6) At what rate percent compound interest, will Rs. 2800 amount to Rs. 3087 in 2 years?

2

R � � =Amount =P �1 � � 400 ��

R � � Sol : 6760 =6250 �1 � � 100 ��

R � 25 � � � sol : A � P �1 � 15000 � P 1 � �� 100 �� � 100 �� 5 5 5 � 15000 � P � � � 4 4 4 � P � Rs.7680

100 3 D ( for 3 years ) P� 2 R (300 � R) 100 �100 �100 � D � 32000 � � D � Rs.204 20(305)

Prepared by

1

� C.I. = 15246-12000=Rs.3246 4) Find the amount on Rs. 25,000 in 2 years, the rate of interest being 5% for the first year an d10% for the second year?

Short cut Method The difference between S.I and C.I PR 2 for 2 years at R% p.a. is given by D= 1002 1 � 25 25 � � D=6400 � � � � � � 2 2 � 100 �100 D=Rs.100

9) The difference between C.I and S.I on Rs. 2000 for 2 years is Rs. 5, what is the rate percent per annum? sol : Short cut Method 100 2 D ( for 2 years ) P� R2 100 �100 � 5 � 2000 � � R � 5% p.a.

R2

competitive exams special

arithmetic

12) At C.I a certain sum becomes twice itself in 7 years. In how many years will it becomes 32 times?

7

7

R � R � � � sol :2 P � P �1 � � 1 � �2 � � � � 100 � � 100 � �� R � 1 � �� � �� 100 �

7

5

� 5 � � 2 � 32 �

35

R � � � �1 � � � 32 � 100 �

(OR)

35

R � � P �1 � � � 32 P 100 � � � The sum becomes 32 times of itself in 35 years.

13) The C.I on a certain sum for 2 years at 10% p.a. is Rs. 1260. What is the S.I on the same sum at the same rate for 2 years? sol : R � 10% p.a., n � 2 years, C.I.Rs.1260 If the principal is Rs .100,C .I .Rs .21 if P is Rs.100 � � � �C .I .is Rs .21 ? � � � � C.I . is Rs.1260 � P � Rs.6, 000 S .I . �

PNR 6000 � 2 � 10 � � Rs.1200 100 100

15) A sum of money amounts to Rs. 4,840 in 2 years and to Rs. 5,324 in 3 years on compound interest. What is the rate percent? sol :The Interest in 3 rd year � 5324 � 4840 � Rs.484 Rs.484 is the int erest obtained on Rs .484 in The 3rd year 484 �

4840 �1 � R 100

R � 10% p.a .

16) The value of a building is Rs.2,66,200 and that of a land is Rs.1,45,800. After how many years will the values of both be same, so that the value of the building decreases at 10% p.a. and that of land increases at 10% p.a.? sol : Let the values of both be same after n 10 � � years 2, 66, 200 �1 � � � 100 � 10 � � � 1, 45,800 �1 � � � 100 � n

n

n

1, 45,800 729 � 9 � �9� � � �� � � � 11 2, 66, 200 1331 � � � 11 � � n � 3 years

3

B|æø£ ù|J\ô|’ MT n_ÛÁbÕj·÷\qT, dü\Vü‰\qT e÷≈£î ‘Ó*j·TCÒj·T+&ç.

dipika.navatelangana21@gmail.com

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X¯óÁø£yês¡+ 5.10.2018 13

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4

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2. D çÜ…çܦ¯èþ$ 1939ÌZ MæüË-Mæü-™é¢ÌZ HÆ>µr$ ^óþÔéÆæÿ$.

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DMìü…¨-Ðé-°ÌZ çÜÆðÿO¯èþ A…Ôèý-Ðóþ$¨?

17. »Ÿ…»ê-Æÿ$$ÌZ 1849ÌZ ç³ÆæÿÐèþ$çßý…çÜ Ðèþ$…yæþ-Í° H 1. ©° Ýë¦ç³-Mæü$Ë$ {ÖÐèþ$† ÆæÿÐèþ*-»êÆÿ$$ Æ>¯èþyóþ 1. D çÜ…çܦ¯èþ$ ÝëÓÒ$ çÜçßý-f-¯èþ…§æþ Ýë¦í³…^é-yæþ$. Ë„æüÅ…™ø HÆ>µr$ ^óþÔé-Ææÿ$?

2. {糿êÐèþ ç³Ç«¨ ç³N¯é (Ðèþ$-à-Æ>-çÙ‰-) 2. ©° {糿êÐèþ ç³Ç«¨ Væü$f-Æ>™Œþ G. A…rþ-Æ>°™èþ¯èþ… °Ææÿ*Ã-Ë-¯èþ 3. ï܈ çÜ…„óü-Ðèþ*-°Mìü Mæü–íÙ ^óþÔé-Ææÿ$.

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9. Ðèþ$gêª-Ðèþ*¯Œþ çÜ¿æý¯èþ$ HÆ>µr$ ^óþíܯèþ ÐéÆæÿ$ GÐèþ-Ææÿ$? yìþ. ò³OÐèþ±² ^óþíÜ…¨?

G. §é§é-»ê-Æÿ$$ ¯úÆøi G. §óþÐèþ#yæþ$ JMæüPyóþ 3. {ºçßýÃ-çÜ-Ðèþ*-gŒýMæü$ çÜ…º…-«¨…_ DMìü…¨-Ðé-°ÌZ çÜÆðÿO¯èþ A…Ôèý-Ðóþ$-¨?

1. D çÜ…çܦ Ýë¦ç³-Mæü$Ë$ Æ>gê-Æ>ÐŒþ$ Ððþ*çßý-¯Œþ-Æ>ÄŒý$, MóüÔèý-ÐŒþ-^èþ…{§æþ-õܯŒþ, §óþÐóþ… {§æþ-¯é-£Šþ-u>-Væü*ÆŠÿË$ 2. D çÜ…çܦ¯èþ$ 1828ÌZ MæüË-Mæü-™é¢ÌZ Ýë¦í³…^éÆæÿ$.

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4. ÐèþའE§æþÅ-Ðèþ*-°-Mìü çÜ…º…-«¨…_ DMìü…¨ íÜ. ç³NÈ §æþÄæý$…™Œþ Mæü$…{l 2. »Ÿ…»ê-Æÿ$$ÌZ 1867ÌZ Ýë¦í³… ^éÆæÿ$. Ðé-°ÌZ çÜÆðÿO¯èþ A…Ôèý-Ðóþ$-¨? yìþ. çÜÆæÿ-âæý- »ê-Ìê-§óþ-ÐŒþ 3. íßý…§æþ* Ðèþ$™èþ…ÌZ çÜ…çÜP-Ææÿ-×ý-˯èþ$ ^óþç³-sôýt…§æþ$Mæü$ 1. D E§æþÅÐèþ$ {´ëÆæÿ…À-Mæü$Ë$ ÚëA-º$ªÌŒý, çÜÄæý$ŧŠþ 11. ´ëÈØ-ËÌZ Ýë…íœ$Mæü, B^éÆæÿ ÐèþÅÐèþ-à-Æ>-ËÌZ Ðèþ*Ææÿ$µ©°° HÆ>µr$ ^óþÄæý$r… fÇ-W…¨.

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G. 1,2 Ðèþ*{™èþÐóþ$ A…Ôèý-Ðóþ$-¨?

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2. {糿êÐèþ ç³Ç«¨ §óþÐŒþ-º…§Šþ G. Ææÿçßý²-Ðèþ*ÄŒý$ çÜ…çܦ G. 1,2 Ðèþ*{™èþÐóþ$ 3. ѧóþÖ ´ëË-¯èþMæü$ Ðèþņ-Æóÿ-Mæü…V> i৊þ Mö¯èþ-Ýë¼. Ðèþ$gêª-Ðèþ*¯Œþ çÜ¿æý ¼. 2,3 Ðèþ*{™èþÐóþ$ W…^é-Ë° °Ææÿ~-Æÿ$$…^éÆæÿ$. íÜ. õܯé-çÜ-Ñ$† íÜ. 3 Ðèþ*{™èþ-Ðóþ$ G. 1 Ðèþ*{™èþÐóþ$ yìþ. ¿êÆæÿ™Œþ ï܈ Ðèþ$…yæþÌŒý yìþ. ò³OÐèþ±² ¼. 2,3 Ðèþ*{™èþÐóþ$ 13. Æ>ÐŒþ$ »êgŒý-õ³Æÿ$$ »Ÿ…»ê-Æÿ$$ÌZ 192 4ÌZ »êÄŒý$- 21. ¤Äñý*-Ýë-íœ-MæüÌŒý Ý÷òÜO-sîýMìü çÜ…º…«¨…_ DMìü…¨- ÐéíÜ. 3 Ðèþ*{™èþ-Ðóþ$ °ÌZ çÜÆðÿO¯èþ A…Ôèý-Ðóþ$-¨? ÝûPsŒý E§æþÅ-Ðèþ*-°Mìü Mæü–íÙ ^óþõÜ…§æþ$Mæü$ HÆ>µr$ ^óþíܯèþ yìþ. ò³OÐèþ±² 1. D çÜ…çܦ-¯èþ$ Ðóþ$yæþ… »êÏÐŒþ-sŒýïÜP, òßý^Œþ.-G-‹Ü.-A-ÌêP-sŒýçÜ…çܦ H¨?

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11

What is a Merchant Payment Limit?

Banking Know ledge/ Financial A w areness 1) In the abbreviation IRAC, the letter R stands for what ? a) Revision b) Recognition (IRAC:Income Recognition and Asset Classification) c) Rural d) Route e) Read 2) In the abbreviation FALLCR, the letter C stands for what ? a) Clean b) Coverage ( FALLCR: Facility to Avail Liquidity for Liquidity Coverage Ratio) c) Cool d) Clever e) None of these 3) In the abbreviation HQLAs, the letter Q stands for what ? a) Quick b) Quality (HQLA: High Quality Liquid Assets) c) Quake d) Queen e) None of these 4) The increase in Facility to Avail Liquidity for Liquidity Coverage Ratio (FALLCR), announced by RBI for effect from October 1, 2018, from the existing 11 per cent to 13 per cent will take the carve out from SLR available to banks to ____ per cent of their NDTL. a) 15 b) 25 c) 30 d) 35 e) None of these 5) RBI had issued guidelines for licensing of Small Finance Banks in the private sector on November 27, 2014 with the objective of furthering financial inclusion by (i) provision of savings vehicles primarily to unserved and underserved sections of the population, and (ii) supply of credit to small business units; small and marginal farmers; micro and small industries; and other entities in the unorganized sector, through high technology-low cost operations. A minimum paid-up-capital of Rs.____ billion has been prescribed for SFB with a minimum regulatory CRAR of 15%.

Further, 75% of their adjusted net bank credit (ANBC) will go towards priority sector lending and 50% of the loan portfolio will constitute loans up to Rs.2.5 million. a) One b) Two c) five d) four e) None of these 6) Urban Co-operative Banks (CBs) with a minimum net worth of Rs. ______ million and maintaining Capital to Risk (Weighted) Assets Ratio of 9% and above are eligible to apply for voluntary transition to SFB under this scheme. a) 250 b) 500 c) 600 d) 850 e) None of these 7) The minimum net worth of the proposed Small Finance Bank (SFB) shall be Rs.1 billion from the date of commencement of business. As small finance banks are required to maintain a minimum capital adequacy ratio of _____per cent of its risk weighted assets (RWA) on a continuous basis, availability of adequate capital shall be ensured.

Promoters shall maintain at least 26% of the paid-up equity capital. a) 25 b) 15 c) 35 d) 40 e) None of these 8) What is (RTGS) Real Time Gross Settlement ? a) This is a system where the processing of funds transfer instructions takes place at the time they are received (real time). b) Also the settlement of funds transfer instructions occurs individually on an instruction by instruction basis (gross settlement). c) RTGS is the fastest possible interbank

money transfer facility available through secure banking channels in India d) All the above e) None of these 9) What is (NEFT) National Electronic Fund Transfer ? a) This system of fund transfer operates on a Deferred Net Settlement basis. b) Fund transfer transactions are settled in batches as opposed to the continuous, individual settlement in RTGS. c) NEFT operates in half hourly batches from 8 am to 7 pm on week days and working saturdays d) The above mentioned facility is available to both Retail and Corporate Internet

presented electronically to prove your identity, to access information or services on the Internet or to sign certain documents digitally. e) All the above 13) Who issues the Digital Signature Certificate? a) A licensed Certifying Authority (CA) issues the digital signature. Certifying Authority (CA) means a person who has been granted a license to issue a digital signature certificate under Section 24 of the Indian IT-Act 2000. b) The list of licensed CAs along with their contact information is available on the Controller of Certifying Authorities (CCA) portal c) Both (a) & (b) d) Planning Commission of India e) NITI Aayog

BANK PO/ CLERKS EXAM SPECIAL

Banking users of SBI (provided they have availed transaction rights). e) All the above 10) When does the beneficiary get the credit for a RTGS payment? a) Under normal circumstances the beneficiary Bank branch receives the funds in real time as soon as funds are transferred by the remitting Bank. b) The beneficiary Bank has to credit the beneficiary's account within two hours of receiving the funds transfer message. c) Both (a) & (b) d)after one year e) None of these 11) When does the beneficiary get the credit for a NEFT payment? a) NEFT operates in half hourly batches. b) There are 23 settlements from 8 am to 7 pm on week days and working Saturdays. c) Therefore, the beneficiary can expect to get the credit for the transactions put through between 8 am to 7 pm on weekdays and working Saturdays on the same day d) For transactions settled in the 6 and 7 pm batches on week days and working Saturdays, the credit will be afforded either on the same day or on the next working day. e) All the above 12) What is a Digital Signature Certificate? a) Digital Signature Certificates (DSC) are the digital equivalent (that is electronic format) of physical or paper certificates. b) Examples of physical certificates are drivers' licenses, passports or membership cards. c) Certificates serve as proof of identity of an individual for a certain purpose; for example, a driver's license identifies someone who can legally drive in a particular country. d) Likewise, a digital certificate can be

14) Why is Digital Signature Certificate (DSC) required? a) Like physical documents are signed manually, electronic documents, for example eforms are required to be signed digitally using a Digital Signature Certificate b) To purchase gold c) To purchase silver d) To purchase lottery tickets e) None of these 15) What is a Merchant Payment Limit? a) Merchant Payment Limit is merely a pre-authorization of payment limit where the Corporate can set a limit by preapproving it for the purpose making payment to any Merchant (Utility bills/taxes) in a single session. Actual payment can take place only if sufficient balance is available in the account. b) By creating a Merchant Payment Limit for a merchant, payments of utility bills/taxes can be made to that merchant in a single session up to the balance available in the Merchant Payment Limit. c) Since the limit is already pre-approved by the authorizer, there will be no need for multiple users to login and authorize the merchant transactions d) The authorizer can make the payment directly in a single step by visiting the merchant website. e) All the above 16) Who is Richard Thaler ? a) Economic Nobel prizewinner in 2017 b) Physics Nobel prize winner in 2017 c) Medicine Nobel prize winner in 2017 d) Cricket player e) None of these 17) What is the nature of swap offered by RBI for the FCNR (B) deposits ? a) The swap is in the nature of a simple buy/sell foreign exchange swap from the RBI side covering just the principal portion of the deposits and not the interest component. b) Loss coverage c) Profit making d) No profit no loss basis e) None of these 18) What is an EEFC Account and what are its benefits? a) Exchange Earners' Foreign Currency Account (EEFC) is an account maintained in foreign currency with an Authorised Dealer Category - I bank i.e. a bank authorized to deal in foreign exchange. b) It is a facility provided to the foreign exchange earners, including exporters, to credit 100 per cent of their foreign exchange earnings to the account, so that the account holders do not have to convert foreign exchange into Rupees and vice versa, thereby minimizing the transaction

costs. c) Both (a) & (b) d)It is fixed deposit e) None of these 19) Who can open an EEFC account? a) All categories of foreign exchange earners, such as individuals, companies, etc., who are resident in India, may open EEFC accounts. b) Only Ministers c) Only MLAs d)Only politicians e) None of these 20) What are the different types of EEFC accounts? Can interest be paid on these accounts? a) An EEFC account can be held only in the form of a current account. b) No interest is payable on EEFC accounts. c) Both (a) &(b) d) It is non-profitable e) None of these 21) What is an Automated Teller Machine (ATM)? a) Automated Teller Machine is a computerized machine that provides the customers of banks the facility of accessing their account for dispensing cash and to carry out other financial & non-financial transactions without the need to actually visit their bank branch. b) Cash Box c) Tiffin Box d) Printing Machine e) None of these 22) What are White Label ATMs (WLAs)? a) Automobiles b) ATMs set up, owned and operated by non-banks are called White Label ATMs. Non-bank ATM operators are authorized under Payment & Settlement Systems Act, 2007 by the Reserve Bank of India. c) Cell Phones d) Ipads e) None of these 23) What is the difference between ATM and WLA (White Label ATM)? a) In White Label ATM scenario, logo displayed on ATM machine and in ATM premises pertain to WLA Operator instead of a bank b) However, for a customer, using WLA is just like using the ATM of other bank (bank other than card issuing bank). c) Acceptance of cash deposits at the WLAs is not permitted at present d) All the above e) None of these 24) What is Personal Identification Number (PIN) for ATMs? a) PIN is the numeric password which is separately mailed / handed over to the customer by the bank while issuing the card. b) Most banks require the customers to change the PIN on the first use. c) Customer should not disclose PIN to anybody, including to bank officials.

Customers should change the PIN at regular intervals. d) All the above e) None of these 25) Are customers charged for any transaction at ATMs? a) Yes, customers can be charged for transactions at ATMs over and above the mandated number of free transactions b) In case a bank decides to levy charges, the customer can be charged a maximum of Rs. 20/- per transaction (plus service tax, if any) by his/her bank. c) Both (a) & (b) d) Only penalties e) None of the above

Praturi Potayya Sarma Answers 1) b 2) b 3) b 4) a 5) a

6) b 7) b 8) d 9) e 10) c

11) e 12) e 13) c 14) a 15 e

16) a 17) a 18) c 19) a 20) c

21) a 22) b 23) d 24) d 25) c

10

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1) ¯]l¯]l²Ä¶æ$ ¿¶ær$t 2) ¯éÆ>Ķæ$×æ ¿¶ær$t 3) ´ëÐ]l#Ë*Ç Ð]l$Ëϯ]l 4) ѧéůé£ýl$yýl$ "¯]lÆó‡…{§ýl Ð]l$–VóSÔ¶æÓÆ>ËĶæ*Ë$' A¯ól õ³Æý‡$™ø 108 ÕÐéËĶæ*˯]l$ °ÇÃ…_¯]l ™èl*Æý‡$µ ^éâ¶æ$MýSÅ Æ>k GÐ]lÆý‡$?

1) Ððl¬§ýlsìæ AÐ]l$ÃÆ>k 2) ÑÐ]l$Ìꨙèl$Åyýl$ 3) Ððl¬§ýlsìæ ^éâ¶æ$MýSÅ ÁÐ]l¬yýl$ 4) Æð‡…yø ÑfĶæ*¨™èl$Åyýl$ ¿êÆý‡¡Ä¶æ$ ¯éÅĶæ$Ô>{Ý뢰MìS B«§éÆý‡OÐðl$¯]l Ķæ*fqÐ]lËP çÜÖ†Oò³ "Ñ$™é„ýSÈ' õ³Æý‡$™ø ÐéÅRêů]l… Æ>íÜ…¨ GÐ]lÆý‡$?

1) Ñgêq¯ólÔ¶æÓÆý‡$yýl$ 2) OgñæÑ$± 3) MýS×ê§ýl$yýl$ 4) MýSí³Ë$yýl$ ´ëÐ]l#Ë*Ç Ð]l$Ëϯ]l ™èl¯]l "VýS×ìæ™èlÝëÆý‡ çÜ…{VýSçßæ…' {VýS…£é°² H ¿êçÙÌZ Æý‡_…^éyýl$?

1) ™ðlË$VýS$ 2) çÜ…çÜP–™èl…

3) {´ëMýS–™èl…

4) MýS¯]l²yýl… Æ>fÆ>f ¯]lÆó‡…{§ýl$yýl$ "¯]l…§ýl…ç³Nyìl' {V>Ð]l*°² A{VýSàÆý‡…V> GÐ]lÇMìS §é¯]l… ^ólÔ>yýl$?

1) ¯]l¯]l²Ä¶æ$ ¿¶ær$t 2) ¯éÆ>Ķæ$×æ ¿¶ær$t 3) ´ëÐ]l#Ë*Ç Ð]l$Ëϯ]l 4) ÝùÐ]l$§ólÐ]l çÜ*Ç ™èl*Æý‡$µVø§éÐ]lÇ hÌêÏ "¼MýSPÐøË$'ÌZ Æ>fÆ>gôæÔ¶æÓÆý‡, VøÍ…VóSÔ¶æÓÆý‡, ^èl…{§ýlÔóæQÆý‡ §ólÐéËĶæ*˯]l$ °ÇÃ…_¯]l ^éâ¶æ$MýSÅ Æ>k GÐ]lÆý‡$?

1) Æ>fÆ>f ¯]lÆó‡…{§ýl$yýl$ 2) AÐ]l$Ã…VýS §ólÐ]l#yýl$ 3) VýS$×æVýS ÑfĶæ*¨™èl$Åyýl$ 4) Ððl¬§ýlsìæ ^éâ¶æ$MýSÅ ÁÐ]l¬yýl$ ™ðlË$VýS$ ¿êçÙÌZ ™öÍ ÐéÅMýSÆý‡×æ {VýS…£ýlOÐðl$¯]l "B…{«§ýlԶ溪 _…™éÐ]l$×ìæ' Æý‡^èlƇ¬™èl GÐ]lÆý‡$?

1) }¯é£ýl$yýl$ 2) ¯]l¯]l²Ä¶æ$ ¿¶ær$t 3) ´ù™èl¯]l 4) ¯éÆ>Ķæ$×æ ¿¶ær$t Ðól…W (Ìôæ§é) ™èl*Æý‡$µ ^éâ¶æ$MýSÅ Æ>kË "Æ>f Ìê…bèl¯]l…' H¨?

1) Ð]lÆ>çßæ…

2) íÜ…çßæ…

3) ç³#Í 4) ^ólç³ "çÜ¦Ë Ð]l$çßæ™éÅË$' A…sôæ..?

1) Ý린MýS §ólÐ]l™èlË VýS$Ç…_ ÑÐ]lÇ…^ól MýS£ýlË$ 2) {»êçßæÃ×æ {V>Ð]l*Ë$ 3) {V>Ð]l$ çÜ¿¶æË$ 4) ¯éÅĶæ$Ý릯éË$ "º–çß晌æ çÜ…íßæ™èl' {VýS…£ýl Æý‡^èlƇ¬™èl GÐ]lÆý‡$?

1) M>ã§éçÜ$ 2) Ð]lÆ>çßæÑ$íßæÆý‡$yýl$ 3) çÜ${Ô¶æ$™èl$yýl$ 4) ç³™èl…fÍ Ð]lÆý‡¢MýS {Ôóæ×æ$˯]l$ "¯]lMýSÆý‡…'V> õ³ÆöP¯ólÐéÆý‡$. ™èl*Æý‡$µ ^éâ¶æ$MýS$ÅË M>Ë…ÌZ ÒsìæMìS {糫§é¯]l MóS…{§ýl… H¨?

41.

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1) ÁÐ]l$Ð]lÆý‡…

3) {§é„>Æ>Ð]l$…

2) HË*Æý‡$ 4) ò³¯]l$Vö…yýl

™èl*Æý‡$µ ^éâ¶æ$MýS$ÅË M>Ë…ÌZ "Mö§ðl¯]l' A¯ól çÜ$…M>°² ÐólsìæOò³ Ñ«¨…^ólÐéÆý‡$?

1) Ð]l$V>YË ™èlĶæ*È 2) Vöyýl$VýS$Ë ™èlĶæ*È 3) Æ>^èl¿¶æ*Ð]l¬Ë$ 4) ¯]l*¯ðl ¡Ä¶æ$yýl…

"AÀ§é¯]l _…™éÐ]l$×ìæ' {VýS…£ýl Æý‡^èlƇ¬™èl GÐ]lÆý‡$?

1) ò³§ýlMøÐ]l$sìæ ÐólÐ]l*Æð‡yìlz 2) GËMýS*_ »êËçÜÆý‡çÜÓ† 3) ÑÔóæÓÔ¶æÓÆý‡ MýSÑ 4) õßæÐ]l*{¨ {§é„>Æ>Ð]l$ "ÁÐól$Ô¶æÓÆ>ËĶæ$…', ÝëÐ]l$Æý‡ÏMør "^éâ¶æ$MýSÅ ÁÐól$Ô¶æÓÆ>ËĶæ$…' °ÇÃ…_¯]l ™èl*Æý‡$µ ^éâ¶æ$MýSÅ Æ>k GÐ]lÆý‡$?

1) Æ>fÆ>f ¯]lÆó‡…{§ýl$yýl$ 2) ÑÐ]l$Ìꨙèl$Åyýl$ 3) Ððl¬§ýlsìæ ^éâ¶æ$MýSÅ ÁÐ]l¬yýl$ 4) VýS$×æVýS ÑfĶæ*¨™èl$Åyýl$ "ç³NÆý‡Ó Ò$Ð]l*…çÜ' (MýSÆý‡Ã Ð]l*Æý‡Y…) Ðé§é°MìS Ð]lÊË ç³#Æý‡$çÙ$yýl$ OgñæÑ$± AƇ¬™ól, gêq¯]lÐ]l*Æ>Y°² {糆´ë¨…_¯]l "E™èl¢Æý‡ Ò$Ð]l*…çÜ' Ðé§é°MìS Ð]lÊËç³#Æý‡$çÙ$yýl$ GÐ]lÆý‡$?

1) ç³™èl…fÍ 2) MýS×ê§ýl$yýl$ 3) MýSí³Ë$yýl$ 4) »ê§ýlÆ>Ķæ$×æ$yýl$ OÐðlçÙ~Ð]l Ð]l$™èl…ÌZ "ç³…^éÆ>{™èl' {MýS™èl$Ð]l#¯]l$ {糆´ë¨…_¯]lÐéÆý‡$?

1) MýSÔ¶æÅç³#yýl$ 2) Ð]l*™èl…VýS$yýl$ 3) Ô>…yìlË$Åyýl$ 4) Mú…yìl¯]l$Åyýl$ ™ðlË$VýS$ÌZ ™öÍ Ô>çܯ]lOÐðl$¯]l "MýSâ¶æÏÐ]l$ËÏ' Ô>çܯ鰲 ÐólƇ¬…_¯]l Æ>k GÐ]lÆý‡$?

1) Æó‡¯ésìæ ^øyýl Æ>k «§ýl¯]l$…fĶæ¬yýl$ 2) fĶæ$íÜ…çßæ Ð]lËÏ¿¶æ$yýl$ 3) ´ë…yýl$Æý‡…VýSyýl$ 4) Ķ欧ýl®Ð]l$Ë$Ïyýl$ MìS…¨ ÐésìæÌZ çÜÇM>° f™èl H¨?

1) ¯]l¯ðl²^øyýl$yýl$ & MýS$Ð]l*Æý‡ çÜ…¿¶æÐ]l…

2) ´ëË$PÇMìS ÝùÐ]l$¯é£ýl$yýl$ & ç³…yìl™éÆ>«§ýlÅ ^èlÇ{™èl 3) ÐólÐ]l¬ËÐéyýl ÁÐ]l$MýSÑ & ºçÜÐ]l ç³#Æ>×æ…

4) Ð]l$ÍÏM>Æý‡$j¯]l ç³…yìl™éÆ>«§ýl$Åyýl$ & ÕÐ]l™èl™èl¢ÓÝëÆý‡… Ð]l¬çÜ$¯]l*Ç {´ùËĶæ$ ¯éĶæ$MýS$yìl Æ>f«§é° H¨?

1) A§ýlª…MìS 2) ^èl…§ýlÐøË$ 3) Æó‡MýSç³ÍÏ §ýl$Æý‡Y… 4) BÐ]l$¯]lVýSË$Ï M>MýS¡Ä¶æ$ Æ>fÅ ç³™èl¯é…™èlÆý‡…, B…{«§ýl§ólÔ¶æ…ÌZ Ð]l$çßæÐ]l$éĶæ$ §éyýl$˯]l$ Ð]lÇ~…_¯]l Ô>çܯ]l… H¨?

1) VýS×æõ³Ô¶æÓÆý‡ Ô>çܯ]l…

2) ÑËçÜ ™é{Ð]l$ Ô>çܯ]l…

3) BÆ>ÅÐ]lr Ô>çܯ]l…

4) çßæ¯]l$Ð]l$Mö…yýl Ô>çܯ]l…

B…{«§ýl§ólÔ>©Ô¶æÓÆý‡, {ç³RêÅ™é…{«§ýl çÜ$Æý‡{™é×æ$yýl$ A¯ólÑ GÐ]lÇ ¼Æý‡$§ýl$Ë$?

1) ´ù™èl¯]l ¯éĶæ$MýS$yýl$ 2) M>Ð]l$¯]l ¯éĶæ$MýS$yýl$ 3) {´ùËĶæ$ ¯éĶæ$MýS$yýl$ 4) Ð]l¬çÜ$¯]l*Ç M>ç³Ä¶æ$ ¯éĶæ$MýS$yýl$ "§ýlĶæ*¿êVýS' Æý‡^èlƇ¬™èl GÐ]lÆý‡$?

1) Ñõœ$²Ô¶æÓÆý‡ 2) MýS$ËÏMýS ¿¶ært 3) ÑÔ¶æÓÆý‡${§ýl 4) iÐ]lÊ™èl Ðéçßæ¯]l$yýl$ Æð‡yìlz & ÐðlËÐ]l$ Æ>kË Ð]l$«§ýlÅ A¯]l$çÜ…«§é¯]l MýSÆý‡¢V> Ð]lÅÐ]lçßæÇ…_¯]lÐéÆð‡Ð]lÆý‡$?

1) ´ù™èl¯]l 2) }¯é£ýl$yýl$ 3) ÐólÐ]l$¯]l 4) ÑÔóæÓÔ¶æÓÆý‡MýSÑ }MýS–çÙ~ §ólÐ]lÆ>Ķæ$Ë ´ë˯é M>Ë… H¨?

1) {MîS.Ô¶æ. 1485 - 1502

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2) {MîS.Ô¶æ. 1509 - 1530 3) {MîS.Ô¶æ. 1533 - 1545 4) {MîS.Ô¶æ. 1550 - 1565

™èl¯]l Oòܯ]lÅ…ÌZ 糨 ÐólË Ð]l$…¨ Ð]l$çßæÐ]l$éĶæ¬Ë¯]l$ °Ä¶æ$Ñ$…_¯]l ÑfĶæ$ ¯]lVýSÆý‡ Æ>k GÐ]lÆý‡$?

1) Ððl¬§ýlsìæ §ólÐ]lÆ>Ķæ$Ë$ 2) Æð‡…yø §ólÐ]lÆ>Ķæ$Ë$ 3) }MýS–çÙ~§ólÐ]lÆ>Ķæ$Ë$ 4) Æ>Ð]l$Æ>Ķæ$Ë$ "çœÆŠæV>sñ毌æ G…Oò³ÆŠæ' {VýS…£ýl Æý‡^èlƇ¬™èl GÐ]lÆý‡$?

1) Æ>ºÆŠæt ïÜÐðlÌŒæ 2) gôæÐŒl$Þ òœÆý‡*YçܯŒæ 3) ¸ë§ýlÆŠæ ïßæÆ>‹Ü 4) òßæ^Œæ.h. ÐólÌŒæÞ O^ðl¯é §ólÔ>°MìS ™èl¯]l Æ>Ķæ$»êÇ° ç³…í³¯]l ÑfĶæ$¯]lVýSÆý‡ Æ>k GÐ]lÆý‡$?

1) Ððl¬§ýlsìæ º$MýSPÆ>Ķæ$Ë$ 2) Æð‡…yø çßæÇçßæÆý‡Æ>Ķæ$Ë$ 3) Æð‡…yø §ólÐ]lÆ>Ķæ$Ë$ 4) }MýS–çÙ~ §ólÐ]lÆ>Ķæ$Ë$ ÑfĶæ$¯]lVýSÆý‡ Ýë{Ð]l*fÅ…ÌZ ÑÐéçßæ çÜ$…M>˯]l$ Æý‡§ýl$ª ^ólíܯ]l ´ëËMýS$yýl$ GÐ]lÆý‡$?

1) ™èl$â¶æ$Ð]l ÒÆý‡¯]lÆý‡íÜ…çßæ$yýl$ 2) }MýS–çÙ~§ólÐ]lÆ>Ķæ$Ë$ 3) Ððl¬§ýlsìæ çßæÇçßæÆý‡ Æ>Ķæ$Ë$ 4) º$MýSPÆ>Ķæ$Ë$ MìS…¨ ÐésìæÌZ Ķæ*^èlMýS Ð]l–†¢Oò³ Ñ«¨…_¯]l 糯]l$² H¨?

1) ç³#ËÏ… 糯]l$² 2) AyìlM>çÜ$ 糯]l$² 3) VýS×ê^éÇ ç³¯]l$² 4) í³…k×ìæ íܧé®Ä¶æ$… "í³…k×ìæ íܧé®Ä¶æ$…' A¯ól 糯]l$²¯]l$ GÐ]lÇ/ §ól°Oò³ Ñ«¨…^ólÐéÆý‡$?

1) ÐólÔ¶æÅË$ 2) §ýl*¨° HMìS §éÆý‡… ¡õÜÐéÆý‡$ 3) ^ól¯ól™èl ç³°ÐéÆý‡$ 4) ç³Ô¶æ$Ð]l#Ë$ Ðól$õÜ ç³_aMýS ºÄ¶æ$â¶æ$Ï "{ºçßæçólÐ]l {V>Ð]l*Ë$' A…sôæ HÑ$sìæ?

1) Ð]l$u>«¨ç³™èl$ËMýS$ C^óla ¿¶æ*Ð]l¬Ë$ 2) {»êçßæÃ×æ$ËMýS$ §é¯]l…V> C^óla 糯]l$²Ë$ Ìôæ° {V>Ð]l*Ë$ 3) Æ>gZ§øÅVýS$ËMýS$ C^óla {V>Ð]l*Ë$ 4) Ô>ç܈Ðól™èl¢ËMýS$ C^óla {V>Ð]l*Ë$ "¿¶æ…yéÆý‡ ÐéÆý‡ {V>Ð]l*Ë$' A…sôæ HÑ$sìæ?

1) Ð]l–†¢ ç³°ÐéÇMìS C^óla {V>Ð]l*Ë$ 2) Ð]l$u>«¨ç³™èl$ËMýS$ C^óla {V>Ð]l*Ë$ 3) Æ>^èl{V>Ð]l*Ë$ (Æ>kËMýS$ C^ólaÑ) 4) ç³…yìl™èl$Ë$, MýSÐ]l#ËMýS$ C^óla {V>Ð]l*Ë$ ÑfĶæ$¯]lVýSÆý‡ Æ>kË MýS$ËO§ðlÐ]l…?

1) ÑÆý‡*´ë„ýS$yýl$ 2) ÕÐ]l#yýl$ 3) ÑçÙ$~Ð]l# 4) çÜ*Æý‡$Åyýl$

çÜÐ]l*«§é¯éË$ 1) 4; 5) 4; 9) 2; 13) 4; 17) 1; 21) 4; 25) 2; 29) 4; 33) 3; 37) 2; 41) 3; 45) 3; 49) 4; 53) 1; 57) 2;

2) 2; 6) 3; 10) 4; 14) 3; 18) 2; 22) 3; 26) 2; 30) 1; 34) 2; 38) 4; 42) 4; 46) 3; 50) 2; 54) 1; 58) 2;

3) 1; 7) 1; 11) 3; 15) 2; 19) 3; 23) 1; 27) 1; 31) 1; 35) 1; 39) 2; 43) 3; 47) 2; 51) 2; 55) 2; 59) 3;

4) 1; 8) 3; 12) 4; 16) 2; 20) 4; 24) 1; 28) 3; 32) 2; 36) 1; 40) 4; 44) 1; 48) 4; 52) 2; 56) 3; 60) 1.

ѧýlÅ

OÐðlG‹ÜBÆŠæ hÌêÏ l Ô¶æ${MýSÐéÆý‡… l AMøtºÆŠæ l 5 l 2018

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"VýS-×ìæ™èl… çÜ…çÜP–-†MìS A§ýlª… Ð]l…sìæ-¨' A° õ³ÆöP¯]l²ÐéÆý‡$? Ķæ*Æý‡ÏVýSyýlz Ð]l¯]l…Æ>k

çÜ*PÌŒæ AíÜòÜt…sŒæ, {糿¶æ$™èlÓ E¯]l²™èl ´ëuý‡Ô>Ë

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VýS×ìæ-™èl-Ô>{çÜ¢ »Z«§ýl¯]l E§ólª-Ô>Ë$, ÑË$-Ð]lË$ H çœÍ-™é-˯]l$ BÕ…_ »Z«¨Ýë¢Ððl* Ðésìæ¯ól "»Z-«§ýl¯]l BÔ¶æ-Ķæ*Ë$ Ìôæ§é E§ólª-Ô>-Ë$' A…sêÆý‡$.

CÑ »Z«§ýl¯]l ç³NÇ¢ AƇ¬¯]l ™èlÆ>Ó™èl íܨ®-Ýë¢Æ‡¬. Ð]l$¯]l… ^ólõÜ {糆- MýS–-™éÅ-°MìS ¨Ô> °Æó‡ªÔ¶æ… ^ólçÜ*¢ VýSÐ]l*Å°² ^ólÆý‡$-Mø-Ð]l-yé-°MìS Eç³-MýS-Ç…^ól¨ E§ólªÔ¶æ…. ● fĶæ*-ç³-f-Ķæ*-˯]l$ Ð]l*糯]l… ^ólõÜ Ý뫧ýl¯]lÐól$ E§ólª-Ô¶æ… A° gꯌæ yýl*ÅƇ¬ õ³ÆöP ¯é²Æý‡$. ● ѧéÅ Ñ«§é¯]l… çÜOÆð‡¯]l M>Æý‡Å-Æý‡*ç³… §éËayýl… §éÓÆ> ѧýlÅ E§ólªÔ>˯]l$ Ý뫨…-^èl-Ð]l^èl$a.

CÑ A…†Ð]l$ E§ólªÔ>Ë$. ● JMýS Ð]lÅMìS¢ Mö°² Ð]lçÜ$¢-Ð]l#-˯]l$ Mö¯]l$-VøË$ ^ólÝë¢yýl$. ©°² Eç³Äñæ*V>™èlÃMýS ÑË$Ð]lÌZ ^ðl¼™ól °™èlÅ-i-Ñ-™èl…ÌZ VýS×ìæ-™é°² Eç³-Äñæ*-WÝë¢yýl$ A° ^ðlç³µÐ]l^èl$a. A§ól E§ólªÔ¶æ Æý‡*ç³…ÌZ AƇ¬™ól ѧéÅǦ VýS×ìæ-™é°² °™èlÅ iÑ-™èl…ÌZ Eç³-Äñæ*-W…-^ólÌê ^ólĶæ$yýl…. ● VýSÐ]l*ÅË$, E§ólª-Ô>Ë$, BÔ¶æ-Ķæ*Ë$ A¯ólÑ ç³Æ>ÅĶæ$ 糧éË$. ● E§ólªÔ>Ë$ Æð‡…yýl$ Æý‡M>Ë$. AÑ.. Ý뫧é-Æý‡× , °ÇªçÙt E§ólª-Ô>Ë$ ● Ý뫧é-Æý‡×æ E§ólª-Ô>-˯ól çÜ…„ìS-ç³¢…V> E§ólª-Ô>Ë$V> í³Ë$-Ýë¢Æý‡$. CÑ ©Æý‡ƒ-M>-Ë…ÌZ Ý뫨…^ólÑV> E…sêƇ¬. Ð]lÊÌêÅ…-MýS¯]l… ^ólĶæ$yýl…

MýSçÙt…. ÝëÐ]l*-hMýS AÐ]l-çÜ-Æ>-ËMýS$ A¯]l$-VýS$×æ…V> Ð]l*¯]l-Ð]l#° AÐ]l-çÜ-Æ>Ë$ ¡Æó‡aÌê E…sêƇ¬. ѧéÅ-Ñ-«§é-¯]l…ÌZ Ð]l*Æý‡Y-§ýl-Æý‡ØMýS Üç *{™éË$ Üç *¦Ë…V> E…sê Ƈ¬. Òsìæ° JMýS §ólÔ>-°MìS ^ðl…¨¯]l Æ>f-MîSĶæ$, ÝëÐ]l*-hMýS, BǦMýS, Ô>{çÜ¢, Ýë…MóS-†MýS °ç³#-×æ$Ë$ °Æý‡~-Ƈ¬Ýë¢Æý‡$. ● °ÇªçÙt E§ólª-Ô>-˯]l$ ™èlMýS$PÐ]l çÜÐ]l$-Ķæ$…ÌZ Ìôæ§é Ððl…r¯ól Ý뫨…-^èl-Ð]l^èl$a. Òsìæ¯ól çÜ…„ìSç³¢…V> »Z«§ýl¯é Ë„>Å-Ë$ A…sêÆý‡$. {´ë£ýl-Ñ$MýS ´ëuý‡-Ô>Ë Ýë¦Æ‡¬ÌZ VýS×ìæ™èl »Z«§ýl¯]l E§ólª-Ô>Ë$ ● VýS×ìæ™èl… ç³rÏ BçÜ-MìS¢° ò³…´÷…-¨…-^èlyýl… ● VýS×ìæ™èl ¿êÐ]l-¯]l-ËOò³ AÐ]l-V>-çßæ-¯]l-™ø-´ër$ °f iÑ™èl çÜÐ]l$-çÜÅË ç³Ç-ÚëP-Æý‡…ÌZ Eç³-Äñæ*-W…^èl$-Mö¯ól O¯ðlç³#-×êÅË$ ò³…-^èlyýl…. çÜÐ]l$-çÜÅË Ý뫧ýl-¯]lÌZ ÐólVýS…, MýS_a-™èl™èlÓ… AË-Ð]l-yýlr…. ● ѧéÅ-Æý‡$¦ÌZÏ ™éÇPMýS BÌZ-^èl¯é Ô¶æMìS¢° A…^èl¯é ÐólõÜ ÝëÐ]l$-Æ>¦ÅË$ ò³…´÷…-¨…-^èlyýl… §éÓÆ> Ð]l*¯]l-íÜMýS {MýSÐ]l$-Õ-„ýS×æ AÀ-Ð]l–¨® ^ðl…§ýlyýl…. ● {MýSÐ]l$™èl, Ô¶æ${¿¶æ™èl, çܵçÙt-™èlMýS$ çÜ…º…-«¨…-_¯]l ÑË$-Ð]lË$, OÐðlQ-Æý‡$Ë$ AË-Ð]lÆý‡$aMøÐ]lyýl….

çÜ*PÌŒæ AíÜòÜt…sŒæ& MýS…sñæ…sŒæ OÐðlÔóæÏíÙMýS Æó‡Rê VýS×ìæ™èl…

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VýS×ìæ™èl ¿êçÙ, VýS$Æý‡$¢Ë$ ç³Ç-^èlĶæ$… ^ólĶæ$yýl…

E¯]l²™èl Ýë¦Æ‡¬ VýS×ìæ™èl »Z«§ýl¯]l E§ólª-Ô>Ë$ ѧéÅ-Æý‡$¦ÌZÏ ™èlÆý‡P ÑÐól-^èl¯]l, ÑÔóæÏ-çÙ×æ Ô¶æMýS$¢-˯]l$ ò³…´÷…-¨…-^èlyýl….

VýS×ìæ™èl Ô>{çÜ¢ O¯ðlç³#-×êÅ-˯]l$, §ýl–MýSµ-£é-˯]l$ ѧéÅǦ °™èlÅ iÑ-™é-°MìS Ñ°-Äñæ*-W…-^èl$-Mö¯ólÌê ^ólĶæ$yýl…. ѧéÅ-Æý‡$¦-˯]l$ E™éµ-§ýl-MýS™èl, çÜ–f-¯é-™èlÃ-MýS™èl, °Æ>Ã-×ê-™èlÃ-MýS iÑ-™é°² VýSyýl-ç³-yé-°MìS íܧýl®… ^ólĶæ$yýl…. ѧéÅ-Æý‡$¦ÌZÏ Æý‡Ýë-¯]l$-¿¶æ*†, ™èl–í³¢, Ð]lÅMìS¢-VýS™èl ÑM>çÜ… Ððl¬§ýl-OÌñæ¯]l Ðésìæ° ò³…´÷…-¨…^èlyýl….

E§ólª-Ô>˯]l$ Ý뫧ýl¯é M>Ìê°² ºsìæt Æð‡…yýl$ Æý‡M>-Ë$V> Ñ¿¶æ-hÝë¢Æý‡$.

1) ™èl„ýS×æ E§ólª-Ô>Ë$ 2) §ýl*Æý‡çܦ E§ólª-Ô>Ë$ VýS×ìæ-™ø-´ë-«§éÅ-Ķæ¬yýl$ VýS×ìæ™èl »Z«§ýl-¯]l¯]l$ G…§ýl$MýS$ ^ólĶæ*ÌZ ™ðlË$-çÜ$-Mø-Ð]l-yé-°MìS VýS×ìæ™èl »Z«§ýl-¯ø-§ólª-Ô>Ë$ çÜçßæ-MýS-Ç-Ýë¢Æ‡¬. {´ë£ýl-Ñ$MýS, {´ë£ýl-Ñ$-Mø-¯]l²™èl, òÜMýS…-yýlÈ, MýSâêÔ>Ë Ýë¦Æ‡¬ÌZ VýS×ìæ™èl »Z«§ýl-¯]lMýS$ ÑÑ«§ýl Æý‡M>Ë E§ólª-Ô>-Ë$-¯]l²-ç³µ-sìæMîS Ý뫧é-Æý‡-×æ…V> E…yólÑ...

1) {ç³Äñæ*-f-¯ø-§ólªÔ¶æ…

2) E§ýlÆý‡ ´ùçÙ-×Z-§ólªÔ¶æ…

3) {MýSÐ]l$-Õ-„ýS-×Z-§ólªÔ¶æ…

4) Ð]l–†¢ çÜ…º…-«§ýl-OÐðl$¯]l E§ólªÔ¶æ…

5) gêq¯ø-§ólªÔ¶æ…

6) ÖÌZ-§ólªÔ¶æ…

7) Ýë…çÜP–-†-Mø-§ólªÔ¶æ…

8) çܯé²-çßZ-§ólªÔ¶æ…

9) çÜÓĶæ$… A«§ýlÅ-Ķæ$-¯ø-§ólªÔ¶æ….

"G…-§ýl$MýS$ »Z«¨…-^éÍ?' A¯ól {ç³Ô¶æ²MýS$ çÜ…™èl–í³¢-MýS-Æý‡-OÐðl$¯]l çÜÐ]l*-«§é-¯]lÐól$ "ѧéÅ ÑË$-Ð]l-Ë$'.

VýS×ìæ™èl »Z«§ýl¯]l §éÓÆ> ѧéÅ-Æý‡$¦ÌZÏ ò³…´÷…¨…-^ól Ô¶æMýS$¢-˯ól "VýS-×ìæ™èl »Z«§ýl¯]l ÑË$-Ð]l-Ë$' A…sêÆý‡$. »Z«§ýl¯é ÑË$-Ð]l-˯]l$ B«§éÆý‡… ^ólçÜ$-Mö° G¯ø² çœÍ-™éË$, {ç³Äñæ*-f-¯é-˯]l$ BÕ…_ VýS×ìæ-™é°² »Z«¨Ý뢅. ÑË$Ð]l A¯ól¨ E§ólªÔ¶æ…Oò³, E§ólªÔ¶æ… ÑË$Ð]lOò³ B«§é-Æý‡-ç³yìl E…sêƇ¬. ѧéÅ ÑË$-Ð]lË$ JMýS §ólÔ¶æ Æ>f-MîSĶæ$, ÝëÐ]l*hMýS, BǦMýS íܧ鮅-™é-˯]l$ §ýl–íÙtÌZ ò³r$t-Mö° °ÇÃ-™èl-Ð]l$-Ð]l#-™éƇ¬.

VýS×ìæ™èl ÑË$-Ð]lË$ & Ð]lÈY-MýS-Æý‡×æ Ķæ$…VŠæ ÑË$-Ð]lË$ 1) VýS×ìæ™èl {ç³Äñæ*-f¯]l ÑË$Ð]l 2) JMýS BÌZ-^èl¯é çÜÆý‡-ãV> VýS×ìæ™èl…

3) VýS×ìæ™èl… C™èlÆý‡ ÑË$-Ð]lË$ {»ñæíÜÏ^Œæ & ÑË$-Ð]lË$ 1. AÐ]l-V>-çßæ-¯]lË$ 2. O¯ðlç³#-×êÅË$ 3. çÜÐ]l$-çÜÅË$ & 糧ýl®-™èl$Ë$  y − y1   x − x1  − or = −     y − y2   x − x2 

Hï³ yîlGïÜÞ

Ð]l*Å£ŠæÞ Ððl$£ýlyéËi {ç³™ólÅMýS…

4. AÀ-¯]l…-§ýl-¯]lË$ 5. §ýl–MýSµ-£éË$ 6. AË-Ðér$Ï »êÏMŠæ àÆŠæ‹Üt & ÑË$-Ð]lË$ 1. §ýl–MýSµ-£éË$ 2. ¿êÐ]l-¯]lË$ 3. çÜÐ]l*-^éÆý‡… ÝëPÇÏ…VŠæ & ÑË$-Ð]lË$ 1. §ýl–MýSµ-£éË$ 2. ¿êÐ]l-¯]lË$ 3. ÝëÐ]l$-Æ>¦ÅË$ 4. çÜÐ]l*-^éÆý‡…. Ð]l¬°²MŠæ & ÑË$-Ð]lË$ 1. {ç³Äñæ*-f¯]l ÑË$Ð]l 2. íܧýl®-ç³Æó‡a ÑË$Ð]l 3. Ýë…çÜP–-†MýS ÑË$Ð]l 4. {MýSÐ]l$-Õ-„ýS×æ ÑË$Ð]l {ç³Äñæ*-f¯]l ÑË$Ð]l: °™èlÅ iÑ-™èl…ÌZ çÜÐ]l$çÜÅË ç³Ç-ÚëP-Æ>-°MìS §øçßæ-§ýl-ç³-yýl$-™èl$…¨. {糆 Ð]lÅMìS¢ ™èl¯]l Ð]l–†¢° çÜÐ]l$-Æý‡¦-Ð]l…-™èl…V> °Æý‡Ó-íßæ…-^èl-yé°MìS, Ð]lÅMìS¢-VýS™èl, ÐéÅ´ëÆý‡, BǦMýS, Ð]l–†¢ Æý‡…V>ÌZÏ çÜÐ]l$-çÜÅ˯]l$ Ý뫨…-^èl-yé-°MìS Eç³-Äñæ*-VýS-ç³-yýl$™èl$…¨. ● "çÜ-MýSË Ô>{Ýë¢-ËMýS$ Ð]lÊË…, §éÓÆý‡… Ìê…sìæ¨ VýS×ìæ-™èl…' & »ôæMýS¯Œæ ● "§ólÔ¶æ ç³#Æø-À-Ð]l–-¨®° Ý뫨…-^èl-VýSË VýS×ìæ™èl… Ð]l$Æý‡$-Ð]l-Æ>-°-¨' & ¯ðl´ù-Í-Ķæ$¯Œæ {MýSÐ]l$-Õ-„ýS×æ ÑË$Ð]l: VýS×ìæ™èl… Ððl$§ýl-yýl$MýS$ {MýSÐ]l$-Õ„ýS-×æ¯]l$ MýSÍ-WçÜ$¢…¨. ѧéÅǦ ™èl¯]l çÜÓÔ¶æMìS¢ Ò$§ýl B«§é-Æý‡-ç³yìl çÜÐ]l$ÝëÅ Ý뫧ýl-¯]lMýS$ {ç³Ä¶æ$-†²…-^èl-yýl-Ð]l$¯ól Ë„ýS×æ… §éÓÆ> A™èl¯]l$ iÑ™èl çÜÐ]l$-çÜÅ-˯]l$ G§ýl$ÆøP-VýS-Ëyýl$. ©° §éÓÆ> "çÜ-Ð]l$Ķæ$ ´ë˯é VýS$×æ…'

AÀ-Ð]l–¨® ^ðl…§ýl$-™èl$…¨. ѧéÅ-Æý‡$¦ÌZÏ ÐólVýS…, MýS_a™èl™èlÓ… AË-Ð]l-yýl$™éƇ¬. ѧéÅ-Æý‡$¦ÌZÏ {MýSÐ]l$-º-§ýl®™èl, ™éÇPMýS ÑÐól-^èl¯]l, õßæ™èl$-Ðé§ýl… A¯ól Ë„ýS-×êË$ ò³…´÷…§ýl$™éƇ¬. VýS×ìæ™èl »Z«§ýl¯]l ÑË$-Ð]l-Ë-°²…sìæÌZ {糫§é-¯]l-OÐðl$-…¨ {MýSÐ]l$-Õ-„ýS×æ ÑË$Ð]l. õßæ-™èl$-Ðé§ýl…™ø Ð]l*¯]l-Ð]l#° Ðól$£ýlçÜ$Þ íܦÆý‡-ç³yól Ð]l*Æý‡YÐól$ VýS×ìæ™èl… A° ÌêMŠæ õ³ÆöP¯é²Æý‡$. Ýë…çÜP–-†MýS ÑË$Ð]l: çÜ…çÜP–-†° ™ðlÍ-Ķæ$-gôæõÜ A…Ô>-Ë-°²…-sìæÌZ VýS×ìæ™èl ç³Ç-gêq¯]l… CÑ$yìl E…¨.

A…§ýl$-Ð]lËÏ VýS×ìæ-™é-°MìS Ýë…çÜP–-†MýS ÑË$Ð]l E…r$…¨. §ólÐé-Ë-Ķæ*Ë$, ^èlÇaË$, Ð]l$ïÜ-§ýl$Ë$, ^éÇ-{™èlMýS MýSrt-yéË$ Ð]l…sìæ Ðésìæ° VýS×ìæ™èl… B«§éÆý‡…V>¯ól °ÇÃÝë¢Æý‡$. ● "B-«§ýl$-°MýS Ð]l*¯]l-Ð]l#° M>Æý‡Å-MýS-Ìê-´ë-OÌñæ¯]l Ðé y-A„ýS… Ñ¿¶æh…^ól °çÙµ†¢ = -–(–3)/6 = 1/2.

= –x1/x2

A¯]l²ÐéÆý‡$? ×ìæfÅ…, ç³Ç-{Ôèæ-Ð]l$Ë$, {糿¶æ$™èlÓ Ä¶æ$…{™é…

1) ĶæÊMìSÏ-yŠæ-2) Oò³£é-VýS-Æý‡‹Ü VýS… Ððl¬§ýl-OÌñæ¯]l Ðér-°²…-sìæ± VýS×ìæ™èl Ô>{çÜ¢ 3) {»êyŠæ-çœ-ÆŠæz-4) ´ëçÜPÌŒæ ™èlÆý‡P… {ç³M>Æý‡… {糧ýl-ÇØ…-^èl-Ð]l-^èl$a'. & íÜÙŒæ MýSâê-™èlÃMýS ÑË$Ð]l: VýS×ìæ™èl… A°² MýSâ¶æ-ËMýS$ çÜ–íÙt- 7. Mö™èl¢ ÑçÙ-Ķæ*-˯]l$ MýS¯]l$-MøP-Ð]lyýl… Ìôæ§é E¯]l² ÑçÙ-Ķæ*-ÌZÏ° §ýl–MýSµ-£éÌZÏ Ð]l*Æý‡$µ ™ólÐ]l-yé°² MýSÆý‡¢. çÜ…X™èl…, 糧ýlÅ-Æý‡-^èl¯]l, Õ˵ MýSâ¶æË$, _{™èl HÐ]l$…sêÆý‡$? ÌôæQ¯]l…, ¯érÅ… Ððl¬§ýl-OÌñæ¯]l ËÍ™èl MýSâ¶æË AÀ-Ð]l–¨® 1) çÜ–f-¯é-™èlÃ-MýS-™èl- -2) {MýSÐ]l$-Õ-„ýS×æ VýS×ìæ™èl… Ò$§ól B«§éÆý‡ç³yìl E…¨. ● Ò×æ, íÜ™éÆý‡, ™èlºÌê Ð]l…sìæ çÜ…X™èl ÐéƇ¬3) çÜçßæ çÜ…º…-«§ýl…- -4) H©-M>§ýl$ §éÅ˯]l$ VýS×ìæ™èl çÜ*{™éË B«§é-Æý‡…-V>¯ól 8. "-A-À-¯]l…-§ýl-¯]l-Ë$' JMýS VýS×ìæ™èl Ô>{çÜ¢ ÑË$-Ð]lV> ™èlĶæ*Æý‡$ ^ólÝë¢Æý‡$. Ð]lÈY-MýS-Ç…-_¯]l Ô>{çÜ¢-Ðól™èl¢? ● "gêÅ-Ñ$† ºÎ-Ķæ$-OÐðl$…¨. MýSâ¶æ™ø MýSÍõÜ¢ §é°1) Ķæ$…VŠæ-2) Ð]l¬°²MŠæ MðS-§ýl$Æý‡$ Ìôæ§ýl$'. & ĶæÊÇ-í³-yìl‹Ü 3) ÝëPÇÏ…-VŠæ-4) {»ñæíÜÏ^Œæ ● "çÜ…-QÅ-Ë™ø Ð]lÅÐ]l-çßæ-Ç…-^ólr$Ï ™ðlÍ-Ķæ$-MýS¯ól 9. "-VýS-×ôæ-‹Ù' ™é¯]l$ ´÷…¨¯]l VýS×ìæ™èl ¿êÐ]l-¯]l-˯]l$ fÇVóS A…™èl-Æý‡Y™èl A…MýS-VýS-×ìæ™èlÓ A¿êÅ-çÜÐól$ ™èlÐ]l$ C…sìæ OÐðlÔ>ËÅ…, ^èl$r$t MöË-™èl-˯]l$ MýS¯]l$çÜ…X-™èl…'. & OÌñæ¼²gŒæ Vö-¯ól…-§ýl$MýS$ Ñ°-Äñæ*-W…-^éyýl$. C¨ H ÑË$Ð]l Ë„ýS×æ…? çÜÐ]l*-^éÆý‡ ÑË$Ð]l: ©°² "Ð]l–-™é¢…™èl ÑË$-Ð]l' 1) çܯé²-çßæ -2) {MýSÐ]l$-Õ-„ýS×æ A° MýS*yé A…sêÆý‡$. º…V>Æý‡… «§ýlÆý‡, f¯é¿ê 3) Ýë…çÜP–-†-MýS- -4) {ç³Äñæ*-f¯]l ÌñæMýSPË$, ¿¶æ*Ñ$ ÑÐ]l-Æ>Ë$ Ð]l…sìæ çÜÐ]l*-^éÆý‡… õÜMýS- 10. VýS-×ìæ™èl »Z«§ýl¯]l E§ólª-Ô>ÌZÏ B Ô>{çÜ¢… ç³rÏ H Ç…-^èlyé°MìS VýS×ìæ™èl gêq¯]l… AÐ]l-çÜÆý‡…. A…§ýl$-Ð]lËÏ Ýë¦Æ‡¬ÌZ BçÜ-MìS¢° MýSÍW…^èlÐ]l^èl$a?

VýS×ìæ-™é-°MìS çÜÐ]l*-^éÆý‡ ÑË$Ð]l E…§ýl° ^ðlç³µ-Ð]l^èl$a.

1) {´ë£ýl-Ñ$-MýSÐól$£ø çÜ…º…-«¨™èl ÑË$Ð]l: ѧéÅ-Æý‡$¦ÌZÏ ç³Ç-Ö-2) {´ë£ýl-Ñ$-Mø-¯]l²™èl Ë-¯é-Ô¶æMìS¢, HM>-{VýS™èl, ™éÇPMýS BÌZ-^èl¯]l, ÑÐól-^èl¯]l 3) E¯]l²-™èl-4) H©-M>§ýl$ Ððl¬§ýl-OÌñæ¯]l Ðól$£é-Ô¶æ-MýS$¢Ë AÀ-Ð]l–-¨®MìS VýS×ìæ™èl Ô>{çÜ¢… 11. Õ-˵-MýS-â¶æË$, _{™èl-Ìôæ-Q¯]l… Ððl¬§ýl-OÌñæ¯]l ËÍ™èl MýSâ¶æË §øçßæ§ýl… ^ólçÜ$¢…¨.

AÀ-Ð]l–¨® VýS×ìæ™èl »Z«§ýl-¯]l-ÌZ° H ÑË$-Ð]l¯]l$ çܯé²çßæ ÑË$Ð]l Ìôæ§é íܧýl®-ç³Æó‡a ÑË$Ð]l: JMýS ™ðlË$-ç³#-™èl$…¨? ™èlÆý‡-VýS† A«§ýlÅ-Ķæ$¯]l… Ð]lËÏ Oò³ ™èlÆý‡-VýS† A«§ýlÅ-Ķæ$-¯é1) {MýSÐ]l$-Õ-„ýS-×æ-2) Ýë…çÜP–-†MýS °MìS ѧéÅ-Ǧ° çÜ…íÜ-§ýl$®°² ^ólçÜ$¢…¨.

3) ÝëÐ]l*-h-MýS-4) Ýû…§ýl-Æ>Å-™èlÃMýS çÜ–f-¯é-™èlÃMýS ÑË$Ð]l: VýS×ìæ™èl ^èl§ýl-Æ>Ë$, VýS×ìæ™èl 12. "-B-«§ýl$-°MýS Ð]l*¯]l-Ð]l#° M>Æý‡Å-MýS-Ìê-´ë-OÌñæ¯]l ç³hÌŒæÞ, VýS×ìæ™èl ´÷yýl$ç³# MýS£ýlË$ Ððl¬§ýl-OÌñæ-¯]lÑ Ñ§éÅÐé×ìæfÅ…, ç³Ç-{Ôèæ-Ð]l$Ë$, {糿¶æ$™èlÓ Æý‡$¦ÌZÏ çÜ–f-¯é-™èlÃ-MýS-™èl¯]l$ ò³…´÷…-¨-Ýë¢Æ‡¬. Ķæ$…{™é…VýS… Ððl¬§ýl-OÌñæ¯]l Ðér-°²…-sìæ± VýS×ìæ-™èlÔ>{çÜ¢ ™èlÆý‡P… {ç³M>Æý‡… {糧ýl-ÇØ…-^èl-Ð]l-^èl$a' A° A¯]l²-§ðl-Ð]lÆý‡$? Ð]l*¨Ç {ç³Ô¶æ²Ë$ 1) »ôæMýS-¯Œæ-2) õ³ÏsZ 1. E-§ólª-Ô>-˯]l$ Ð]l*¯]l-Ð]l#° Ô¶æÈ-Æý‡…ÌZ §ól°™ø 3) Æ>‹Ü-4) íÜÙŒæ ´ùËa-Ð]l^èl$a?

13. MìS…¨ H Æð‡…yýl$ E§ólª-Ô>Ë$ JMóS ¯é×ôæ-°MìS 1) Ððl$§ýl-yýl$-2) MýS¯]l$² »ŸÐ]l*Ã, »ŸÆý‡$çÜ$ Ìê…sìæÑ?

3) ¯éË$-MýS-4) VýS$…yðl 1) {MýSÐ]l$-Õ-„ýS×æ & {ç³Äñæ*-f¯]l 2. MìS…¨ÐésìæÌZ Ý뫧é-Æý‡-×Z-§ólªÔ¶æ… M>°¨?

2) E§ýlÆý‡ ´ùçÙ×æ & {MýSÐ]l$-Õ-„ýS×æ 1) {ç³Äñæ*-f-¯ø-§ólªÔ¶æ…

3) E§ýlÆý‡ ´ùçÙ×æ & {ç³Äñæ*-f¯]l 2) E§ýlÆý‡ ´ùçÙ-×Z-§ólªÔ¶æ…

4) {MýSÐ]l$-Õ-„ýS×æ & Ýë…çÜP–-†MýS 3) {MýSÐ]l$-Õ-„ýS-×Z-§ólªÔ¶æ…

14. "-VýS-×ìæ™èl gêq¯]l… H Ð]l–†¢° G¯]l$²-MýS$¯é², H 4) H©-M>§ýl$ MýSâ¶æ¯]l$ Ð]l–†¢V> ïÜÓMýS-Ç…_¯é ç³#¯é-¨V> E…yìl 3. "VýS-×ìæ™èl… çÜ…çÜP–-†MìS A§ýlª… Ð]l…sìæ-¨' A° çÜÆý‡Ó-™ø-Ð]l¬-Rê-À-Ð]l–-¨®MìS ™øyýlµ-yýl$-™èl$…¨' A° õ³ÆöP¯]l²ÐéÆý‡$? ™ðlÍ-Ķæ$-gôæõÜ E§ólªÔ¶æ…?

1) õ³ÏsZ-2) òßæÆ>¾ÆŠæt 1) gêq¯ø-§ólª-Ô¶æ…-2) ÖÌZ-§ólªÔ¶æ…

3) »ôæMýS-¯Œæ-4) Æ>‹Ü 3) Ð]l–†¢ çÜ…º…«§ýlOÐðl$¯]l E§ólªÔ¶æ…

4. VýS×ìæ™èl »Z«§ýl¯]l G…§ýl$MýS$ ^ólĶæ*ÌZ ™ðlË$-çÜ$-Mø-Ð]l4) Ýë…çÜP–-†Mø§ólªÔ¶æ… yé-°MìS çÜçßæ-MýS-Ç…-^ólÑ? çÜÐ]l*«§é¯éË$ 1) VýS×ìæ™èl ÑË$-Ð]l-Ë$- -2) çܵïÙt-MýS-Æý‡×êË$ 3) VýS×ìæ™èl E§ólª-Ô>Ë$ -4) ´ëu>Å…-Ô>Ë$ 1) 4; 2) 4; 3) 3; 4) 3; 5. VýS-×ìæ-™é-°-MýS$…yól A™èlÅ-«¨MýS ÑË$Ð]l?

5) 1; 6) 2; 7) 1; 8) 2; 1) {ç³Äñæ*-f-¯]l-2) Ýë…çÜP–-†MýS 9) 4; 10) 1; 11) 2; 12) 4; 3) ÝëÐ]l*-h-MýS-4) Ýû…§ýl-Æ>Å-™èlÃMýS 13) 3; 14) 3.

6. ""G^èlar -ËĶæ$ VýS˧ø A^èlar çÜ…QÅ VýS˧ýl$' MýSÍõ³ çÜ…„ìSç³¢ 糧ýl®†: Æó‡RêQ…yé°² (3, 14) ¼…§ýl$Ð]l# Ñ¿¶æh…^ól §ýl™é¢…Ô¶æ…ÌZ° ¼…§ýl$Ð]l#Ë$ °çÙµ†¢ A(-–4, -–1); B(1, 2);  x − x1   3− 2  C(4, -–3) HO§lð ¯é JMýS ¼…§ýl$Ð]l#¯]l$ =−   = −   3 − 10   x − x2  (0, 0) ^ólõÜ¢ P(2,

Q(10,15)˯]l$

27),

1:2 °çÙµ†¢ÌZ A…™èlÆý‡…V> Ñ¿¶æhçÜ$¢…¨. (+ VýS$Æý‡$¢ A…™èlÆ>°² çÜ*_çÜ$¢…¨.)

A(8, –10); B(7, –3); C(0, p) Ë™ø çÜÐ]l$çÜÅÌZ x °Æý‡*ç³MýS… À¯]l²… E…¨ 4. P(2, 27), Q(10, 15)˯]l$ MýSÍõ³ HÆý‡µyól Ë…ºMø×æ {†¿¶æ$f…ÌZ ∠B = 90° M>ºsìæt  y − y1  1 Æó‡RêQ…yé°² 1 : 3 °çÙµ†¢ÌZ A…™èlÆý‡…V> AƇ¬™ól p ÑË$Ð]l? − = = 1: 7  çÜ*{™èl… ¯]l$…_ 7 Ñ¿¶æh…^ól ¼…§ýl$Ð]l#? ∠B = 90° M>ºsìæt  y − y2   21 + 4   25  °çÙµ†¢ 1:7 M>§ýl$ 1) (3, 14) 2) (2, 7) ABÐéË$ × BCÐéË$ = &1 −  = −  21 − 6 15 5     C§ólÑ«§ýl…V> Ñ$Wͯ]l ¼…§ýl$Ð]l#˯]l$ 3) (4, 24) 4) (&3, 5)  −3 + 10   p + 3  = −    = −1 3 ç³ÇÖÍõÜ¢ fÐéº$ 3 AÐ]l#™èl$…¨. f. m:n °çÙµ†¢ÌZ PQ Æó‡RêQ…yé°²  7 − 8  0 − 7  A…™èlÆý‡…V> Ñ¿¶æh…^ól ¼…§ýl$Ð]l# = 5. A(–4, –1); B(1, 2), C(4, –3) 5 : 3 °çÙµ†¢ÌZ »êçßæÅ…V> Ñ¿¶æhçÜ$¢…¨. çÜ*„îSÃMýSÇõÜ¢ p = –4  mx2 + nx1 my2 + ny1  ( & VýS$Æý‡$¢ »êàÅ°² çÜ*_çÜ$¢…¨.)

(2, &4), (5, 6)˯]l$ MýSÍõ³ Æó‡RêQ…yé°² Ë$ ÖÆ>ÛË$V> HÆý‡µyól {†¿¶æ$f OÐðlÔ>ËÅ…? ,   m+n   m+n 3. (&3, 2), (6, 1)˯]l$ MýSÍõ³ Æó‡RêQ…yé°² (19/2, 21) ¼…§ýl$Ð]l# Ñ¿¶æh…^ól °çÙµ†¢ f. {†¿¶æ$f OÐðlÔ>ËÅ… çÜ*{™èl… ¯]l$…_ MýS¯]l$Vö¯]lÐ]l^èl$a (x1, y1),(x2, y2)˯]l$ MýSÍõ³ Æó‡Rêy-A„ýS… H °çÙµ†¢ÌZ Ñ¿¶æhçÜ$¢…¨.

1 Δ = x (y − y ) + x (y − y ) + x (y − y ) 2 çÜ…„ìSç³¢ 糧ýl®†: Q…yé°² (x, y) ¼…§ýl$Ð]l# Ñ¿¶æh…^ól f. çÜ…„ìSç³¢ 糧ýl®†: Bç³¯Û l] Ï ¯]l$…_ ¯]l$…_ MýS¯]l$Vö¯]lÐ]l^èl$a. °çÙµ†¢ x-A„ýS… Ñ¿¶æh…^ól °çÙµ†¢ = –y1/y2 1

2

3

2

3

1

3

1

2

A( –4+4, –1+1), B(1+4, 2+1) C(4-+4, -–3-+4) A= (0, 0), B(5, 3), C(8, –2) (0, 0), (x1, y1), (x2, y2)Ë™ø

{†¿¶æ$f OÐðlÔ>ËÅ… Δ= =

1 ( x1 y2 − x2 y1 ) 2

1 (5)( −2) − (8)(3) 2

= 17 ^èl.ĶæÊ.

HÆý‡µyól