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Answers & Solutions

for

NTSE (Stage-I) 2020-21

INSTRUCTIONS TO CANDIDATES

Read the following instructions carefully before you open the question booklet.

1. Use blue/black ballpoint pen only. There is no negative marking.

2. Part I : MAT : 1 - 100 questions

Part II : SAT : 101 - 200 questions

3. This test booklet contains 200 questions of one mark each. All the questions are compulsory.

4. Answer each question by darkening the one correct alternative among the four choices on the OMR SHEET with

blue/black ballpoint pen.

Example:

Q. No.

1

Q. No.

1

Alternatives

Alternatives

1 2 1 4

1 2 3 4

Correct way :

Wrong way :

Student must darkening the right oval only after ensuring correct answer on OMR Sheet.

5. Students are not allowed to scratch / alter / change out an answer once marked on OMR Sheet, by using white

fluid / eraser / blade / tearing / wearing or in any other form.

6. Separate sheet has been provided for rough work in this test booklet.

7. Please handover the OMR Sheet to the invigilator before leaving the Examination Hall.

8. Darken completely the ovals of your answer on OMR Sheet in the time limit allotted for that particular paper.

9. Your OMR Sheet will be evaluated through electronic scanning process. Incomplete and incorrect entries may render

your OMR Sheet invalid.

10. Use of electronic gadgets, calculator, mobile etc., is strictly prohibited.

Date: 13/12/2020 CHANDIGARH

NTSE (S-I) 20 -20 21

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PART-I : MENTAL ABILITY TEST (MAT)

Directions (1-10): In the following questions,

four items (numbers/number pairs/letter groups)

are given. Three of them are alike in a certain

way and one is different. Find the odd one out

from the alternatives.

1. (1) DE (2) PQ

(3) TU (4) WY

Answer (4)

Sol. + 1 + 1 + 1 + 2

D E , P Q , T U , W Y

2. (1) CFI (2) DGJ

(3) HKO (4) FIL

Answer (3)

Sol.

C F I , D G J , H K O F I L

+ 3 + 3 + 3 + 3 + 3 + 4 + 3 + 3

3. (1) 11 (2) 15

(3) 17 (4) 19

Answer (2)

Sol. 15 is not prime

4. (1) ZW (2) TQ

(3) SP (4) NL

Answer (4)

Sol.

Z W , T Q , S P , N L

– 3 – 3 – 3 – 2

5. (1) 441 (2) 343

(3) 289 (4) 625

Answer (2)

Sol.

4 4 1 , 3 4 3 , 2 8 9 , 6 2 5

2 12

73

1 72

2 52

6. (1) SWU (2) CGE

(3) STR (4) OSQ

Answer (3)

Sol.

S W U C G E S T R O S Q

+ 4 + 4 + 1 + 4– 2 – 2 – 2 – 2

7. (1) VUWH (2) JKLI

(3) EFGD (4) STUR

Answer (1)

Sol. V U W H J K L I E F G D S T U R

+ 1 + 1 + 1+ 1 + 1 + 1

– 1 – 1 – 1

8. (1) Carrot (2) Mango

(3) Apple (4) Orange

Answer (1)

9. (1) 25 (2) 4

(3) 49 (4) 8

Answer (4)

Sol. 52, 22, 72, 23

10. (1) 22 (2) 4444

(3) 333 (4) 5555

Answer (4)

Sol. 2 + 2 = 22

4 + 4 + 4 + 4 = 42

3 + 3 + 3 = 32

5 + 5 + 5 + 5 = 20

Directions (11-20) In the following questions,

there is a relationship between two figures on

the left of the sign(::). The same relationship

exists between the figures to the right of the

sign(::) of which one is missing. Find the missing

one from the alternatives

11. 23 : 48 :: 33 : ?

(1) 96 (2) 78

(3) 58 (4) 46

Answer (3)

Sol. 48 – 23 = 58 – 33 = 25

12. 27 : 51 :: 83 : ?

(1) 102

(2) 117

(3) 138

(4) 123

Answer (4)

Sol. 52 + 2, 72 + 2, 92 + 2, 112 + 2

13. ADH : CFJ :: LOS : ?

(1) NQU (2) MPS

(3) NQT (4) NPR

Answer (1)

Sol. A D H C F J L O S N Q U

+ 3 + 3 + 3 + 3+ 4 + 4 + 4 + 4

NTSE (S-I) 20 -20 21

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14. DCB : WXY :: HGF :?

(1) SRQ (2) STU

(3) RPM (4) RST

Answer (2)

15. 11 : 25 :: 17 : ?

(1) 33 (2) 28

(3) 37 (4) 41

Answer (3)

16. 9 : 16 :: 49 : ?

(1) 81 (2) 64

(3) 100 (4) 121

Answer (2)

Sol. 9 : 16 :: 49 : 64

32 42 72 82

17. A : Z :: D : ?

(1) Y (2) S

(3) X (4) W

Answer (4)

18. 2 : 16 :: 5 : ?

(1) 125 (2) 625

(3) 425 (4) 55

Answer (2)

Sol. 2 : 16 :: 5 : 625

24 54

19. DELHI : EDMGJ :: MUMBAI : ?

(1) NTNABH (2) NVNCBJ

(3) LVLCBJ (4) NVLMCDE

Answer (1)

20. BDI : 942 :: GFH : ?

(1) 786 (2) 876

(3) 867 (4) 678

Answer (3)

Sol. BOI : 942 :: GFH : 867

Directions (21-25): Read carefully the

information given below then answer the

questions 21 to 25.

1. A and B teach Hindi and English

2. C and B teach English and Geography

3. D and A teach Mathematics and Hindi

4. E and B teach History and Punjabi

21. Out of these teachers who teaches maximum

number of subjects?

(1) A (2) B

(3) C (4) D

Answer (2)

22. Out of the following, which pair of teachers teach

both Geography and Hindi.

(1) A and B (2) B and C

(3) C and D (4) None of these

Answer (4)

23. Which subject is taught by more than two

teachers?

(1) History (2) Hindi

(3) Punjabi (4) Math

Answer (2)

24. Which are the subjects taught by all three D, B

and A.

(1) Only English (2) Hindi and English

(3) Only Hindi (4) Hindi and Math

Answer (3)

25. Out of the following, which teacher teaches less

than two Subjects.

(1) A (2) B

(3) C (4) E

Answer (*)

Directions (26-35) : In the following questions,

numbers/ words are written in a certain

sequence. Find the missing number/ word. To

replace the question mark from the given

alternatives.

26. 5,11,23,47, ?, 191

(1) 83 (2) 98

(3) 97 (4) 95

Answer (4)

Sol. 5 , 11 , 2 3 , 4 7 , 9 5 1 9 1

x 2+1 x 2+1 x 2+1 x 2+1 x 2+1

27. 8,19,41,85,?, 349

(1) 173 (2) 168

(3) 178 (4) 171

Answer (1)

Sol. 8 , 1 9 , 4 1 , 8 5 , 3 4 9

x 2 +3 x 2 +3 x 2 +3 x 2 +3 x 2 +3

NTSE (S-I) 20 -20 21

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28. A. E, I, M, Q, U, ?

(1) V (2) W

(3) Z (4) Y

Answer (4)

Sol. A , E , I, M , Q , U , Y

+ 4 + 4 + 4 + 4 + 4 + 4

29. 2, 4, 8, 16, 32, 64, ?

(1) 96 (2) 112

(3) 128 (4) 132

Answer (3)

Sol. 2, 4, 8, 32, 64, 128

21, 22, 23, 24, 25, 26, 27

30. BP, EG, HJ, KM, ?

(1) NQ (2) NP

(3) OP (4) NM

Answer (2)

Sol. B P , E G , H J , K M , N P

+ 3 + 3 + 3 + 3

+ 2 + 2 + 2 + 2

31. 2, 5, 9, ? 20, 27

(1) 14 (2) 16

(3) 18 (4) 24

Answer (1)

Sol. 2 , 5 , 9 , 1 4 , 2 0 , 2 7

+ 3 + 4 + 5 + 6 + 7

32. AN, BO, CP, DQ, ?

(1) EJ (2) ES

(3) EQ (4) ER

Answer (4)

Sol. A N , B O , C P , D Q , E R

+ 1 + 1 + 1 + 1

+ 1 + 1 + 1 + 1

33. 20,19, 17, ?, 10, 5

(1) 12 (2) 13

(3) 14 (4) 15

Answer (3)

Sol.

2 0 , 1 9 , 1 7 , 1 4 , 1 0 , 5

– 1 – 2 – 3 – 4 – 5

34. G, I, L, P, U, ?

(1) A (2) B

(3) Z (4) Y

Answer (1)

Sol. G , I , L , P , U , A

+ 2 + 3 + 4 + 5 + 6

35. 240,120, 40, ?, 2

(1) 5 (2) 10

(3) 20 (4) 15

Answer (2)

Sol.

2 4 0 , 1 2 0 , 4 0 , 1 0 , 2

¸2 ¸ 3 ¸ 4 ¸ 5

36. Gourav is Sunita’s brother. Sunita is Jyoti’s

daughter. Jyoti is Prem’s wife. What is the

relation of Prem with Gourav?

(1) Father (2) Brother

(3) Grand Father (4) Uncle

Answer (1)

Sol.

J y o ti = P re m

m o th e r

G o u ra v S u n ita

b ro th e r

37. Seema is Sachin’s sister. Sachin and Sourav are

brothers and Sourav is Kamla’s son. What is the

relation of Kamla with Seema?

(1) Sister

(2) Daughter

(3) Sister in law

(4) Mother

Answer (4)

Sol.

K a m a l

S e e m a S a c h in S o u ra v

M o th e r

S is te r B ro th e r

38. In a family, there is one head of the family, his

wife, three sons and their wives. Every son has

two sons and one daughter. How many male

members are there in the family?

(1) 4 (2) 10

(3) 8 (4) 12

Answer (2)

NTSE (S-I) 20 -20 21

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39. If the word READING is codes as RNIDAEG,

how can the word HISTORY be coded?

(1) HRSTOIY (2) HROTSIY

(3) HROTISY (4) HRTOSIY

Answer (2)

40. If the word PINK is coded as RGPI, how can the

word BLUE be coded?

(1) DJCW (2) DWJC

(3) DJW (4) DCJW

Answer (DJWC) (option miss printed)

41. If the word MADRAS is coded as NBESBT, how

can the word BOMBAY be coded?

(1) CPNCBX (2) CPOCBZ

(3) CQOCB (4) CPNCBZ

Answer (4)

42. If the word SUCCESS is coded as VXFFHVV,

how can the word VICTORY be coded?

(1) YLFWRUB (2) YLFXRUB

(3) YLFWSUB (4) YLFVSUB

Answer (1)

Sol.

S – U – C – C – E – S – S

+ 3 + 3 + 3 + 3

V – X – F – .................– x

....................

43. If the word COBRA is coded as 3152181, how

can the word ZEBRA be coded?

(1) 2652811 (2) 2652181

(3) 265211 (4) 2651182

Answer (2)

44. In a certain code language 851 is a code for,

“Good sweet apple”, 783 for “Good red rose” and

341 for “Rose and apple”. Find the code number

for “sweet”.

(1) 8 (2) 1

(3) 5 (4) 3

Answer (3)

45. If green colour is called yellow, yellow is called

blue, blue is called black, black is called red.

Red is called purple, then what is the colour of

human blood?

(1) Red (2) Purple

(3) Blue (4) Green

Answer (2)

46. If in a certain language FASHION is coded as

FOIHSAN, how is PROBLEM coded in that

language?

(1) ROBLEMP (2) PELBORM

(3) PRBOELM (4) PELBROM

Answer (2)

47. If the code of HINDUSTAN is 110 what will be

the code for AUSTRALIA?

(1) 100 (2) 102

(3) 104 (4) 116

Answer (2)

48. If the code of CONSTABLE is 91 what will be

code for STABLE?

(1) 97 (2) 59

(3) 79 (4) 75

Answer (2)

49. If NIGHT is coded as 58 what will be code for

TOMORROW?

(1) 111 (2) 113

(3) 115 (4) 137

Answer (4)

50. If ROSE is coded as 6821, CHAIR as 73456,

FRENCH as 961473 then SEARCH will be

coded as

(1) 246173 (2) 214678

(3) 214763 (4) 214673

Answer (4)

51. If TOM is coded as 48 and DICK is 27 then

HARRY means

(1) 67 (2) 50

(3) 60 (4) 70

Answer (4)

52. If REST is 0987 and BEAST IS 29187 then

BREAST is

(1) 229187 (2) 209187

(3) 219187 (4) 201987

Answer (2)

Sol. R–0, E–9, S–8, T–7, B–2, A–1

53. If SLIGHT is 426875 then GIST is

(1) 6845 (2) 8645

(3) 4568 (4) 4586

Answer (2)

Sol. S–4, L–2, I–6, G–8, H–7, T–5

NTSE (S-I) 20 -20 21

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54. Rohan is taller than Aman but shorter than Siya.

Kamal is taller than Pooja but shorter than

Aman. Deepak is taller than Kamal but shorter

than Siya. Who among them is the tallest

(1) Rohan (2) Siya

(3) Aman (4) Deepak

Answer (2)

55. If SKY is called SEA. SEA is called WATER,

WATER is called AIR, AIR is called CLOUD and

CLOUD is called RIVER, then what do we drink

when we are thirsty

(1) SKY (2) AIR

(3) WATER (4) SEA

Answer (2)

The following questions consist of two words

each that have a certain relationship with each

other. Select the pair that has the same

relationship as the original pair of words

56. Sale : Purchase

(1) Give : Receive

(2) Shop : Market

(3) Cash : Credit

(4) Profit : Loss

Answer (1)

57. Graphite : Lubricant

(1) Movement : Friction

(2) Iron : Steel

(3) Carbon : Non Metal

(4) Diamond : Abrasive

Answer (4)

58. War : Death

(1) Chimney : Smoke (2) Coal : Fire

(3) Fire : Smoke (4) Smoke :Pollution

Answer (4)

59. Import : Export

(1) Expenditure : Revenue

(2) Expenditure : Debt

(3) Expenditure : Tax

(4) Deficit: Expenditure

Answer (1)

60. Geologist : Earth

(1) Architect : Building

(2) Aquarium : Fish

(3) Archaeologist : Artifacts

(4) Biology : Science

Answer (1)

61. Green : Colour

(1) Night : Dark

(2) Child : Play

(3) Walk : Health

(4) Snake : Reptile

Answer (4)

62. Brass : Alloy

(1) Car : Road (2) Truck : Load

(3) Pencil : Stationary (4) Police : Thief

Answer (3)

63. Cream : Cosmetics

(1) Mountain : Valley (2) Tiger : Forest

(3) Magazine : Editor (4) Teak : Wood

Answer (4)

64. Family : Members

(1) Nation : States (2) Country : Citizens

(3) Town : Village (4) Minister : M.P.

Answer (2)

65. Sprain : Fracture

(1) Devotion : Blessing

(2) Excitement : Frenzy

(3) Sleep : Dream

(4) Fever : Malaria

Answer (2)

Directions (66-70) In the following questions,

you are given a combination of letters/numbers

followed by four alternatives 1, 2, 3 and 4.

Choose the alternative, which most closely

resembles the mirror image of the given

combination.

66. SCHOOL

(1) (2)

(3) (4)

Answer (2)

NTSE (S-I) 20 -20 21

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67.

(1) (2)

(3) (4)

Answer (1)

68. 98724

(1) (2)

(3) (4)

Answer (3)

69.

(1) (2)

(3) (4)

Answer (4)

70. AMBULANCE

(1) (2)

(3) (4)

Answer (3)

Directions (71-75): In the following questions,

you are given a combination of letters/numbers

followed by four alternatives 1, 2, 3 and 4.

Choose the alternative, which most closely

resembles the water image of the given

combination.

71. RAJ

(1) (2)

(3) (4)

Answer (1)

72. VAYU36

(1) (2)

(3) (4)

Answer (2)

73.

(1) (2)

(3) (4)

Answer (3)

74.

(1) (2)

(3) (4)

Answer (4)

75. Wrote

(1)

(2)

(3)

(4)

Answer (2)

Directions (76-80) : In the following questions

left hand side is problem figure in which there is

one ? on the right hand side are answer figures.

Choose the correct option to replace the?

76.A B C D (1 ) (2 ) (4 )(3 )

Answer (4)

Sol. 3 × 4 = 12

4 × 5 = 20

5 × 6 = 30

6 × 7 = 42

77.A B C D (1 ) (2 ) (4 )(3 )

Answer (4)

78. A B C D (1 ) (2 ) (4 )(3 )

Answer (4)

79.A B C D (1 ) (2 ) (3 ) (4 )

Answer (3)

80.A B C D (1 ) (2 ) (3 ) (4 )

Answer (4)

Directions (81–85) In each of the following

questions find out which of the figures (a), (b),

(c), (d) can be formed from the pieces of given

figure X.

81.

(1 ) (2 ) (3 ) (4 )(X )

Answer (1)

NTSE (S-I) 20 -20 21

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82.

(X )

(1 ) (2 ) (3 ) (4 )

Answer (1)

83.

(X )

(1 ) (2 ) (3 ) (4 )

Answer (2)

84.

(X )

(1 ) (2 ) (3 ) (4 )

Answer (2)

85.

(X )

(1 ) (2 ) (3 ) (4 )

Answer (2)

Directions (86-90) In the following questions

there is a different rule according to which cells

are filled and one is left empty with a?. From the

given alternative find the correct option that can

replace the?.

86. 11

(1) 6 (2) 8

(3) 10 (4) 14

Answer (3)

Sol. 8 + 6 = 14

8 + 6 = 14

6 + 4 = 10

87.

11

(1) 75 (2) 26

(3) 25 (4) 20

Answer (2)

Sol. 22 + 42 = 20

32 + 92 = 90

12 + 52 = 26

88. 11

(1) 18 (2) 16

(3) 12 (4) 10

Answer (2)

89. 1

(1) 8C (2) 12B

(3) 16C (4) 18C

Answer (1)

Sol. 4 × 2 = 8

8C

90. 1

(1) 13 (2) 14

(3) 20 (4) 21

Answer (2)

Sol. [15 + 5 = 20, 1 + 19 = 20, 17 + 3 = 20, 16 + 4 =

20, 2 + 18 = 20, 6 + 14 = 20]

NTSE (S-I) 20 -20 21

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Directions (91-95) : In the following questions,

in certain code language if ‘+’ means ‘×’, ‘–’

means ‘+’, ‘×’ means ‘ ¸ ’ and ‘’ means ‘ ¸ ’, then

answer the following questions

91. 16 + 4 ¸ 2 – 21 × 7 ¸ 21

(1) 33 (2) 44

(3) 48 (4) 39

Answer (2)

92. 28 ¸ 36 – 49 × 7 + 2

(1) 12 (2) 10

(3) 8 (4) 6

Answer (4)

93. 8 ¸6 – 9 × 12 + 4

(1) 5 (2) 7

(3) 9 (4) 13

Answer (1)

94. 225 × 15 – 196 × 14 ¸625 × 25

(1) 8 (2) 16

(3) 4 (4) 12

Answer (3)

95. 23 + 46 – 80 × 20 ¸ 40

(1) 1122 (2) 1048

(3) 1126 (4) 1022

Answer (4)

Directions (96-100) : In the following questions,

in a certain code language if ‘+’ means ‘–‘, ‘–‘

means ‘×’, ‘×’ means ‘ ¸ ’, and ‘ ¸ ’ means ‘×’, then

answer the following questions

96. 14 × 2 – 6 + 10 + 4 × 2

(1) 30 (2) 40

(3) 1 (4) 16

Answer (1)

97. 15 ¸ 5 + 15 ¸ 10 × 2

(1) 54 (2) 205

(3) 0 (4) 225

Answer (3)

98. 11 ¸ 15 × 3 + 6 – 5

(1) 55 (2) 35

(3) 165 (4) 25

Answer (4)

99. 13 + 3 – 20 + 25

(1) –314 (2) 313

(3) 318 (4) –312

Answer (4)

100. 196 × 14 ¸ 25 × 5 + 225 × 15

(1) 70 (2) 55

(3) 85 (4) 196

Answer (2)

❑ ❑ ❑

NTSE (S-I) 20 -20 21

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PART-II : SCHOLASTIC APTITUDE TEST (SAT)

101. Which of the following indicated the main

objectives of French Constitution in 1791?

1. Constitutional Monarchy

2. Right to vote for all men above 25 years of

age

3. Declaration of Rights of man and citizens

4. Only men of 25 years and paid taxes were

allowed to vote.

(1) All the above (2) 2,3,4

(3) 1,2,3 (4) 1,3,4

Answer (4)

102. The name associated with “APRIL THESES” is

_____

(1) Karl Marx (2) Robert Owen

(3) Lenin (4) Stalin

Answer (3)

103. BUDENOVKA is

(1) Russian Coat (2) Russian Hat

(3) Russian Tie (4) Russian Uniform

Answer (2)

104. Arrange the following in the correct Chronological

order of the events

1. Pearl Harbour Attack

2. German Invasion of Russia

3. German Invasion of Poland

4. Hitler pulling Germany out of League of

Nations

(1) 1 2 3 4 (2) 2 3 1 4

(3) 4 3 1 2 (4) 4 3 2 1

Answer (4)

105. Consider the following statements and choose the

correct ones.

1. British invited German expert, DIETRIECH

BRANDIS for advice in saving forests

2. Brandis was made first Inspector General of

Forests

3. Brandis set up Indian Forest Services in 1864

4. Brandis helped formulate the Indian Forest Act

in 1869

(1) 1 2 3 4 are correct

(2) Only 1 3 4 are correct

(3) 1 2 3 are correct

(4) Only 1 is correct

Answer (3)

106. Dhangars were the pastoral community of

_______

(1) Gujarat (2) Maharashtra

(3) Karnataka (4) Chhattisgarh

Answer (2)

107. Name the French philosopher who explained –

What makes the nation?

(1) JEAN-JACQUES ROUSSEAU

(2) FREDERIC SORRIEU

(3) MONTESQUIE

(4) ERNST RENAN

Answer (4)

108. Arrange the following into correct

Chronological order : -

1. Arrival of Simon Commission in India

2. Lord Irvin announced Dominion status of India

3. Gandhiji sent the letter stating 11 demands

4. Poona Pack

(1) 1 2 3 4

(2) 2 3 4 1

(3) 3 4 1 2

(4) 4 1 2 3

Answer (1)

109. Which of the following statements are false:

1. Silk route linked ASIA-EUROPE-

NORTH AFRICA

2. Silk route was route both by land and sea

3. Budddhism travelled across silk route

4. Precious metals-Gold & Silver flowed from Asia

to Europe.

(1) 1 and 4 (2) Only 1

(3) Only 3 (4) Only 4

Answer (4)

NTSE (S-I) 20 -20 21

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110. Europeans were attracted to Africa, why?

(1) By its Natural Beauty

(2) To expand Industries

(3) By its vast land resources and mineral wealth

(4) All the above

Answer (3)

111. ______ of Korea is among world’s oldest existed

book with moveable metal types printing.

(1) Diamond Sutra (2) Bible

(3) Jikji (4) Ukiyo

Answer (4)

112. Following statement refer to the life of Baba

Ramchandra in Awadh. Choose the false

statement

(1) Peasants were led by Baba Ramchandra in

Awadh

(2) Baba Rama Chandra was a sanyasi

(3) He worked as indentured labourer in Assam

(4) He headed Oudh Kisan Sabha with J.L. Nehru

Answer (3)

113. Choose the right option of peaks in descending

order of their heights.

1. Kanchenjunga

2. Dodabetta

3. Anaimudi

4. Nanda Devi

(1) 1 2 3 4

(2) 2 3 4 1

(3) 3 4 1 2

(4) 1 4 3 2

Answer (4)

114. River Kaveri makes the second biggest water fall

in India. It is _____

(1) Jog falls

(2) Duduwa falls

(3) Shiva Samundram falls

(4) Dudhsagar Falls

Answer (3)

115. MAHAWAT is the local name of ______ rainfalls in

Indian Plains

(1) Summer (2) Winter

(3) Spring (4) Autumn

Answer (2)

116. Which of the following are the features of National

Population Policy 2000

1. Imparts free and compulsory education upto

14 years of age

2. Reducing infant mortality rate to below 30 per

1000 live births

3. Achieving Universal Immunisation of children

4. Promoting early marriage among girls.

(1) 1 2 3 4

(2) 1 3 4 Only

(3) 1 2 3 Only

(4) 2 3 4 Only

Answer (3)

117. Laterite soil is very useful in growing ____?.

(1) Rice, Wheat, Mustard

(2) Tea, Coffee and Cashewnuts

(3) Pulses, sugarcanes and resins

(4) Cotton, Maize

Answer (2)

118. Match the following :

Multi purpose Dams Name of Rivers

A. Rana Pratap Sagar

Dam

i. Bhagirathi River

B. Salal Project ii. Chambal River

C. Tehri Dam iii. Krishna River

D. Nagarjuna Sagar

Dam

iv. Chenab River

(1) A-i, B-ii, C-iii, D-iv

(2) A-ii, B-iv, C-i, D-iii

(3) A-iii, B-i, C-ii, D-iv

(4) A-iv, B-iii, C-ii, D-i

Answer (2)

119. Average climatic conditions for growing sugar cane

are_______

(1) 21oC-27oC (75 cm -100 cm rainfall)

(2) 25oC-30oC (25 cm -50 cm rainfall)

(3) Below 18oC (75 cm -100 cm rainfall)

(4) 21oC-27oC (50 cm -65 cm rainfall)

Answer (1)

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120. The first ever cement plant set up in India was

____

(1) Mumbai 1904 (2) Kolkata 1944

(3) Chennai 1940 (4) Chennai 1904

Answer (4)

121. The river associated with National Water way No.

2 is____

(1) Ganges (2) Sutleg

(3) Kaveri (4) Brahmaputra

Answer (4)

122. Consider the following facts and decide which of

these facts would you call a democracy.

1. Elections are held regularly

2. Voters are bribed by the leaders

3. Govt. arrests the leaders who protest

peacefully against the wrong policies.

4. Govt. works for the welfare of the people.

(1) 1, 2, 3, 4 (2) 1 and 2

(3) Only 1 (4) 1 and 4

Answer (4)

123. Who, among the following leaders was born in

Saudi Arabia and opposed Muslim separatist

politics and later became first Education Minister of

India

(1) Jaipal Singh

(2) Abul kalam Azad

(3) G. Durgabai Deshmukh

(4) Dr. Zakir Hussain

Answer (2)

124. “Nyaya Yuth” (Struggle for Justice) was a

movement launched by Chaudhary Devi Lal

against which ruling party in Haryana?

(1) Janata Dal

(2) Congress

(3) BSP

(4) BJP

Answer (2)

125. The Constitution of Belgium has been amended

four times between the years___

(1) 1970-1992 (2) 1970-1990

(3) 1972-1992 (4) 1970-1993

Answer (4)

126. Which country among the following countries

suffered disintegration due to political fights on the

basis of religious and ethnic identities.

(1) Yugoslavia

(2) India

(3) Belgium

(4) Netherland

Answer (1)

127. Which of the following political parties came to

power in Bolivia in 2006.

(1) The Communist party

(2) The Republican party

(3) The Socialist Party

(4) The Conservative Party

Answer (3)

128. Match the following regional political parties with

their symbols

Political party Symbol

A. Telegu Desam Party i.

B. YSR Congress Party ii.

C. Shromani Akali Dal iii.

D. The Conservative Party iv.

(1) A-ii, B-iii, C-iv, D-i

(2) A-ii, B-iii, C-i, D-iv

(3) A-i, B-iv, C-iii, D-ii

(4) A-iv, B-iii, C-ii, D-i

Answer (1)

129. Match the followings :

A. Electricity Bill i. Fixed Capital

B. Computers ii. Human Capital

C. Labour iii. Working Capital

(1) A-i, B-ii, C-iii

(2) A-iii, B-i, C-ii

(3) A-ii, B-iii, C-i

(4) A-iii, B-ii, C-i

Answer (2)

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130. A person is considered poor if his or her income

level falls below a given_____.

(1) Maximum level necessary to fulfil needs

(2) Minimum level necessary to fulfil basic needs

(3) Both 1 & 2

(4) Level Below per capita income of the country

Answer (2)

131. Prime Minister Rozgar yojana was started in____.

(1) 1973 (2) 1983

(3) 1993 (4) 2003

Answer (3)

132. Yellow card is issued to ______

(1) People above Poverty Line

(2) People below Poverty Line

(3) People in government Jobs

(4) People in Private sector

Answer (2)

133. Mr. Dhiman took a loan of Rs. 20 Lakhs from bank

to purchase a house. The annual rate of Interest

on the loan is 12% per annum and loan is to be

repaid in 10 years in instalments. The bank retains

the papers of new house as collateral, which will

be returned to Mr. Dhiman only when he repays

the entire loan amount with interest.

Analyse the loan information given above and

choose the right option for the same.

(1) Mode of Repayment

(2) Interest on Loan

(3) Terms of Credit

(4) Collateral

Answer (1)

134. There are two statements marked as Assertion (A)

and Reason (R). Read the statement carefully and

choose the correct option.

Assertion (A) : The goods and services are

produced globally.

Reasson (R) : Production process is divided into

small parts but it is not spread out across the globe

(1) Both A and R are true and R is correct

explanation of A

(2) Both A and R are true and R is not the correct

explanation of A

(3) A is true and R is False

(4) A is False and R is True

Answer (1)

135. Which one of the following minerals belong to the

category of ferrous mineral?

(1) Gold (2) Copper

(3) Mangnese (4) Bauxite

Answer (4)

136. Which one of the following groups of cities is

connected by the National Highway No.7.

(1) Delhi-Amritsar

(2) Delhi-Kolkata

(3) Delhi-Mumbai

(4) Varanasi-Kanyakumari

Answer (4)

137. Name the place where the Non-cooperation

Movement turned violent?

(1) Champaran

(2) Kheda

(3) Nagpur

(4) Chauri Chaura

Answer (4)

138. Whose name of the following is associated with

Kesari?

(1) Jyotiba Phule

(2) Dr. Ambedkar

(3) Bal Gangadhar Tilak

(4) Mahatma Gandhi

Answer (3)

139. Who wrote the book ’Hind Swaraj’

(1) Mahatma Gandhi

(2) Jawaharlal Nehru

(3) Lal Bahadur Shastri

(4) Maulana Azad

Answer (1)

140. In which of the following year was Treaty of Vienna

signed?

(1) 1811 (2) 1810

(3) 1815 (4) 1812

Answer (3)

141. Which of the following compound is responsible for

the tarnishing of silver?

(1) Ag2O (2) Ag2CO

(3) Ag2S (4) AgCN

Answer (3)

Sol. 2 2 2Ag H S Ag S H+ → +

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142. Vinegar on reaction with baking soda produces a

gas which when passed through lime water turns it

milky. The milkiness is due to the formation of :

(1) Calcium Oxalate

(2) Calcium Carbonate

(3) Calcium Hydroxide

(4) Calcium Bicarbonate

Answer (2)

Sol. 3 3 3 2 2CH COOH NaHCO CH COONa CO H O+ ⎯⎯→ + +

2 2 3(milkiness)

Ca(OH) CO CaCO+ ⎯⎯→

143. Match List-I with List-II and select the correct

answer by using the codes given below the list :

List-I List-II

(Name of acid) (Source)

(A) Lactic acid (i) Tamarind

(B) Malic acid (ii) Curd

(C) Acetic acid (iii) Tomato

(D) Tartaric acid (iv) Vinegar

Codes :

(A) (B) (C) (D)

(1) (i) (iv) (ii) (iii)

(2) (ii) (i) (iv) (iii)

(3) (ii) (i) (iii) (iii)

(4) (ii) (iii) (iv) (i)

Answer (4)

144. When a coper vessel is exposed to moist air for

long time it acquires a dull green coating. This

coating is a mixture of :

(1) Coper Oxide and Coper Carbonate

(2) Copper Hydroxide and Copper carbonate

(3) Copper Oxide and Copper Hydroxide

(4) Copper Peroxide and Copper Carbonate

Answer (2)

Sol. 2 2 2 3 2Cu H O CO O CuCO Cu(OH)+ + + →

145. The Buckminster fullerene has

(1) 60 Carbon atoms (2) 58 carbon atoms

(3) 62 Carbon atoms (4) 56 carbon atoms

Answer (1)

Sol. Buckminster fullerene has C60 structure

146. Plaster of Paris can be prepared by heating _____

to a temperature of 100oC.

(1) CaSO3, 2H2O (2) CaCl2, 2H2O

(3) CaCO3, 2H2O (4) CaSO4,2H2O

Answer (4)

Sol. 100ºC

4 2 4 2 2gypsum

1 3CaSO 2H O CaSO . H O H O

2 2 ⎯⎯⎯→ +

147. The atomic number of four elements, P, Q, R and

S are 6, 8, 14 and 16 respectively. Out of these

element the metalloid is :

(1) P (2) Q

(3) R (4) S

Answer (3)

148. Which of the following metals and nonmetals is

found in the liquid state at room temperature?

(1) Gallium and iodine

(2) Gallium and Bromine

(3) Mercury and Bromine

(4) Mercury and Sulphur

Answer (3)

Sol. Mercury is a metal which is liquid at room

temperature and bromine is a non metal liquid at

room temperature

149. The fluorescence on the walls of discharge tube is

due to :

(1) Cathode rays (2) Anode rays

(3) Canal rays (4) None of the above

Answer (1)

150. Isotopes of an element always have the

(1) Same number of Proton

(2) Same number of Neutron

(3) Same Charge

(4) None of the above

Answer (1)

Sol. Isotopes of an elements have same number of

protons i.e. atomic number.

151. Li is similar in behaviour to

(1) C (2) Si

(3) Mg (4) Be

Answer (3)

Sol. Diagonal relationship between Li and Mg

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152. The velocity of a reaction is defined as the

(1) increase of concentration of reactants per unit

time

(2) decrease of concentration of reactants per unit

time

(3) increase of concentration of products per unit

time

(4) both 2 and 3

Answer (4)

153. Property of self combination of the atom of the

same element to form long chain is known as

(1) Protonation (2) Carbonation

(3) Coronation (4) Catenation

Answer (4)

Sol. Self linking property of carbon atoms to form a

chain is catenation

154. When light passes from one medium to another

medium, which of the following remains

uncharged.

(1) Refractive index (2) Frequency

(3) Wavelength (4) Velocity

Answer (2)

155. Two waves have intensities in the ratio 1:9. If

these waves produce interference, then ratio of

maximum and minimum intensities is

(1) 3:1 (2) 4:1

(3) 9:1 (4) 16:1

Answer (2)

Sol.

22

max 1 2 1 1 1

2

min 2 2 21 2

( ) 1,

3( )

I a a I a a

I I a aa a

+= = =

−

2

max

min

44 :1

2

I

I

=

156. The minimum wavelength of the X-rays produced

by electrons accelerated through a potential

difference of V (Volt) is directly proportional to

(1) V (2) 2V

(3) 1/ V (4) 1/V

Answer (3)

Sol. 2 2

h h h

mv mk meV = =

157. A radioactive element has half life period 1600

years. After 6,400 years, what amount will remain?

(1) 1/2 (2) 1/16

(3) 1/8 (4) 1/4

Answer (2)

Sol. 0 04n

N NN N

z z= =

6400

1600n

=

0

0

1

16 16

N NN

N= =

158. For a transistor lc/le = 0.96. The current gain in

common emitter configuration is

(1) 6 (2) 12

(3) 24 (4) 48

Answer (3)

Sol. Ic / Ie = 0.96

Ic = 0.96 Ie

IB = Ie – Ic = Ie – 0.96 Ie

= 0.04 Ie

Gain = 0.96

240.04

C e

B e

I I

I I= =

159. The mean free path of molecules of a gas

(radius r) is inversely proportional to:

(1) 3r (2) 2r

(3) r (4) 1/2r

Answer (2)

Sol. 2

1

d nv =

2

1

d

160. If force (F), velocity (V) and time (T) are taken as

fundamental units, then dimensions of mass are:

(1) 1[ ]FVT (2) 2[ ]FVT

(3) 1 1[ ]FV T− (4) 1[ ]FV T−

Answer (4)

Sol. F = Ma

MV

FT

=

FT

MV

=

1[ ]FTV −=

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161. A conducting sphere of radius R is given a charge

Q. The electric potential and the electric field at the

centre of sphere respectively are

(1) 2

0

Zero and4

Q

R

(2)

0

and zero4

Q

R

(3) 2

0 0

and4 4

Q Q

R R

(4) Both are zero

Answer (2)

Sol. 04

kQ QV

R R= =

E = zero

162. In an ammeter 0.2% of main current passes

through the galvanometer. If resistance of

galvanometer is G, the resistance of ammeter will

be:

(1) 1

499G (2)

499

500G

(3) 1

500G (4)

500

499G

Answer (3)

Sol.

G

R

I

I1

1 .

RI I

G R=

+

0.2499

R GR

G R= =

+

Req = 500

R G G

R G

=

+

163. If the focal length of objective lens is increased

then magnifying power of:

(1) Microscope will increase but that of telescope

will decrease

(2) Microscope and telescope both will increase

(3) Microscope and telescope both will decrease

(4) Microscope will decrease but that of telescope

will increase

Answer (4)

Sol. Magnifying power of a microscope mm = (foL) (feD)

Where fo is the focal length of objective lens.

1omm f

Thus of fo increases, then mm will decrease.

Magnifying power of telescope mt = fefo

otm f

Thus if fo is increased, then mt will increase.

164. Following figures show the arrangement of bar

magnets in different configurations. Each magnet

has magnetic dipole moment →M.

Which configuration has the highest net magnetic

dipole moment?

(1) (2)

(3) (4)

Answer (2)

Sol. Pole strength will add

165. For a satellite, escape velocity is 111kms− . If the

satellite is launched at an angle of 60º with

vertical, the escape velocity will be

(1) 111kms− (2) 111 3 kms−

(3) 111/ 3 kms− (4) 133 kms−

Answer (1)

Sol. 2GM

vR

= = 11 km/s–1

166. The force Facting on a particle of mass m is

indicated by force – time graph shown below :

The change in momentum of the particle over the

time interval from zero to 8s is:

(1) 24 Ns (2) 20 Ns

(3) 12 Ns (4) 6 Ns

Answer (3)

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Sol. P = area of F–t curve

1

2 6 2 3 4 32

= + − +

= 12 Ns

167. Read the following statement and select the

correct option

(A) Wind pollinated flowers need to produce more

amount of pollen grains

(B) Seeds from cross pollinated flowers produce

weaker and less healthy plants.

(1) A is false, B is true

(2) A is true, B is false

(3) Both A and B are true

(4) Neither A nor B is true

Answer (2)

168. Which of the following is not controlled by medulla

(1) Blood pressure (2) Salivation

(3) Body posture (4) Vomitting

Answer (3)

Sol. Body posture is controlled by Cerebellum

169. Among the statements given below select the ones

that correctly describe the concept of sustainable

development.

(i) Planned growth with minimum damage to

environment.

(ii) Growth irrespective of the extent of damage to

the environment.

(iii) Stopping all developmental work to conserve

environment.

(iv) Growth that is acceptable to all the

stakeholders.

(1) (i) and (iv) (2) (ii) and (iii)

(3) (ii) and (iv) (4) (iii) only

Answer (1)

170. Which one of the following is a definition of

ecosystem?

(1) Different communities of plants, animals and

microbes together with their environment.

(2) Different communities of plants and microbes

and their environment.

(3) A community of organisms interacting with one

another

(4) An association of seven plants and animals

Answer (1)

171. The correct pathway of blood circulation is

(1) Auricles → ventricles → Arteries → veins

(2) Ventricles → Auricles → Veins → Arteries

(3) Ventricles → Veins → Arteries → Auricles

(4) Veins → Ventricles → Arteries → Auricles

Answer (1)

Sol. Blood flows from auricles to ventricles, arteries

carry blood from ventricles to body cells.

172. Choose the event that does not occur in

photosynthesis.

(1) Absorption of light of chlorophyll

(2) Reduction of carbon dioxide to carbohydrates

(3) Oxidation of carbon to carbon dioxide

(4) Conversion of light energy to chemical energy

Answer (3)

173. Which of the following statement is true?

(1) In human, there are two pairs of sex

chromosomes

(2) A child who inherits an X-chromosome from

father, will be a boy.

(3) A child who inherits a Y-chromosome from

father, will be a girl.

(4) A child who inherits an X-chromosome from

father, will be a girl

Answer (4)

Sol. A son always inherit Y chromosome from his father

and a Daughter always inherit X chromosome from

her father.

174. The accumulation of non-biodegradable

substances in a food chain in increasing amount at

each higher trophic level is known as.

(1) Accumulation

(2) Biomagnification

(3) Pollution

(4) Eutrophication

Answer (2)

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175. By adding diluted saliva in starch solution, the

starch solution stops giving iodine test. This

proves-

(1) Starch becomes non reactive in the presence

of saliva

(2) Saliva has enzyme which degrades starch into

sugars

(3) Starch was hydrolysed by water before adding

saliva

(4) None of these

Answer (2)

Sol. Saliva contain salivary amylase which cause

breakdown of starch

176. Iodine is necessary for the synthesis of which

hormone?

(1) Auxin

(2) Thyroxin

(3) Adrenaline

(4) Insulin

Answer (2)

177. In human males, all the chromosomes are paired

perfectly except one. This unpaired chromosome

is

(1) Large chromosome

(2) Small chromosome

(3) Y-chromosome

(4) X-chromosome

Answer (3)

178. The main cause of abundant coliform bacteria in

the river Ganga is

(1) Disposal of unburnt corpses into water

(2) Discharge of effluents from electroplating

industries

(3) Washing of clothes

(4) Immersion of ashes

Answer (1)

179. Accumulation of non-biodegradable pesticides in

the food chain in increasing amount at each higher

trophic level is known as

(1) Eutrophication (2) Pollution

(3) Biomagnification (4) Accumulation

Answer (3)

180. Which of the following is an example of

homologous organs?

(1) Our arm and a dog’s foreleg

(2) Our teeth and an elephant’s tusk

(3) Potato and runners of grass

(4) All of the above

Answer (4)

Sol. Homologous organs have similar structure, similar

embryological origin but performs different

functions

181. A hemispherical bowl of internal radius 9 cm is

fully of liquid. The liquid is to be filled into the

cylindrical shaped small bottle each of diameter

3 cm and height 4 cm. How many bottles are

needed to empty the bowl.

(1) 52

(2) 54

(3) 53

(4) 51

Answer (2)

Sol. Let n bottles are needed to empty the bowl.

Volume of hemisphere = n × volume of cylinder

2

22 3(9) n (4)3 2

=

n = 54

182. A ship sails 12 km due north of a port and then

sails 14 km due east. How far is the ship from

port?

(1) 15.4

(2) 16.4

(3) 18.4

(4) 17.4

Answer (3)

Sol.

A

1 4 k m B

2 2AB 12 14 18.4= + = km

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183. The area of shaded portion in the given figure,

(1) 77 sq.units (2) 74 sq.units

(3) 72 sq.units (4) 89.5 sq.units

Answer (4)

Sol. Area of shaded region = area of square – areas of

’s

21 1

12 7 12 5 52 2

= − −

= 144 - 42 - 12.5

= 89.5 sq. units

184. The thp term of an A.P. is q and the thq term is p.

Find the thr term

(1) p + q + r (2) p + q – r

(3) p – q + r (4) p – q – r

Answer (2)

Sol. ap = q a + (p–1) d = q ... (i)

aq = p a + (q–1) d = p ...(ii)

(i)-(ii)

d = –1

Substitude d in equation (i)

a + (p – 1) (–1)= q

a = p + q – 1

ar = a + (r–1)d

= p + q –1+ (r–1) (–1)

ar = p + q –r

185. If the angle of elevation of a cloud from a point “h”

meter above a lake is ' ' and the anlge of

depression of its reflection in the lake is ' ' , find

the distance of the cloud from the point of

observation.

(1) 2 sec

tan tan

h

− (2)

2

tan tan

h

−

(3) 2 sec

tan tan

h

+ (4)

2

tan tan

h

+

Answer (1)

Sol.

h

x

y

h

g + h

a

2

tan ,.........(i)tan .....(ii)y h y

x x

+ = =

(i)/(ii) tan

tan 2

y

h y

=

+

tan 2

1tan

h

y

= +

2 tan tan tan 2 tan

1tan tan tan tan

h hy

y

− = − = =

−

siny

a =

2 tan

sin sin (tan tan )

y ha

= =

−

2 sin / cos 2 sec

sin (tan tan ) tan tan

h h = =

− −

186. Shilpa sells apples to her customer at the cost

price itself but uses a weight of 800 g instead of

1 kg weight. Find the profit percentage.

(1) 30% (2) 35%

(3) 25% (4) 20%

Answer (3)

Sol. 200 g she saves

profit % = 200

100 25%800

=

187. If a natural number ' ' is divided by 7, the

remainder is 5. If natural number ' ' is divided by

7, the remainder is 3. The remainder is ‘r’ if + is

divided by 7. Find the value of 3 5

4

r +

(1) 2 (2) 7

(3) 8 (4) 11

Answer (1)

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Sol. 17 5q = +

27 3q = +

1 27( ) 8q q + = + + = 1 2 37( 1) 1 7 1q q q+ + + = +

remainder = 1

Now 3 5 3(1) 5 8

24 4 4

r + += = =

188. Ruhan’s salary in 2019 is Rs. 1,77,100. His salary

from 2016 has risen annually by 10,15 and 40

percent respectively to reach 2019 salary figures.

What was his salary in 2016.

(1) Rs. 1,00,000 (2) Rs. 1,20,000

(3) Rs. 1,15,000 (4) Rs. 95,000

Answer (1)

Sol. Ruhan’s salary in 2019 is Rs. 1,77,100.

Let his salary in 2016 = x

10 15 40

1 1 1 177100100 100 100

x + + + =

x = 100000

189. A railway engine is travelling along a circular

railway track of radius 1500 metres with as speed

of 66 km/hr. Find the angle turned by the engine in

10 seconds.

(1) 5º (2) 6º

(3) 7º (4) 8º

Answer (3)

Sol.

1 5 0 0 m

q

Speed of train = 66 km/h

Time = 10 seconds = 10 1

60 60 360h h=

Distance travelled by train in 1

360h = speed ×

time

1

66 km360

=

1

km60

=

Now let q angle is made by train in 10 S

11

2 km360 60

rq

= = 11

1000m60

22 1

2 1500 1000360 7 60

q =

q = 7º

190. If x men can do a work in 8 days and (x + 4) can

do the work in 6 days then x is equal to

(1) 10

(2) 6

(3) 12

(4) 24

Answer (3)

Sol. x men do a work in 8 days

(x + 4) men do the work in 6 days.

x × 8 = (x + 4) × 6

8x = 6x + 24

2x = 24

x = 12

191. If 2 2 2 2x y z r+ + = where x = r cos cos ,

y = cos sinr , then z has one of the following

values

(1) cosr (2) tan cosr

(3) tan tanr (4) sinr

Answer (4)

Sol. 2 2 2 2x y z r+ + =

cos cosz r= 2 2 2 2cos cosx r=

cos siny r= 2 2 2 2cos siny r=

cos siny r= 2 2 2 2cos siny r=

2 2 2 2 2 2cos (sin cos )x y r+ = +

= 2 2cosr

2 2 2 2x y z r+ + =

2 2 2 2cosr z r + =

2 2 2cosz r r= = −

2 2(1 cos )r= −

2 2 2sinz r=

sinz r=

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192. Find the value of ‘x’ from the given figure in which

O is the centre of circle.

(1) 40º (2) 50º

(3) 80º (4) 90º

Answer (2)

Sol. 40BAC =

80BOC =

In BOC

180OBC OCB BOC + + =

2x + 80 = 180

2x = 100

x = 50º

193. Radha’s grandfather was 8 times older to her 16

years ago. He would be 3 times of her age 8 years

from now. Eight years ago, what was the ratio

Radha’s age to that of her grandfather?

(1) 1:2 (2) 3:8

(3) 11:53 (4) 1:5

Answer (3)

Sol. Let Radha’s age = x

And Radha’s grandfather’s age = y

Radha’s grandfather was 8 times older to her 16

years ago

(y – 16) = 8 (x-16)

8x – y – 112 = 0 ...(i)

He would be 3 times of her age 8 years from now

(y + 8) = 3 (x + 8)

3x – y + 16 = 0 ...(ii)

From (i) and (ii)

128 464

,5 5

x y= =

88 424

8 , 85 5

x y− = − =

Now 8 11

8 53

x

y

−=

−

194. One liters of water weighs 1 kg. How many cubic

millimetres of water weights 0.1 gms?

(1) 100 (2) 1

(3) 10 (4) 0.1

Answer (1)

Sol. 1 litres of water weights 1 kg

103 m3 of water weights 103 gram

106 mm3 of water weights 103 gram

100 mm3 of water weights 0.1 gram

195. The probability that card drawn from a pack of 52

cards will be diamond or a queen is

(1) 2

13 (2)

4

13

(3) 1

13 (4)

1

52

Answer (2)

Sol. Total diamond or a queen cards = 16

P(E) = 16 4

52 13=

196. If , ,a b cx y y z z x= = = then find the value of abc.

(1) 0 (2) 1

(3) 2 (4) 3

Answer (2)

Sol. x = ya, y = zb, z = xc

( )c by x=

bcy x=

( )bc ax x=

abcx x=

abc = 1

197. If but 2 25 3, 5 3 = − = − then equation

whose roots are

&

is

(1) 23 19 3 0x x− + = (2)

23 19 3 0x x+ + =

(3) 23 18 3 0x x− + = (4)

23 18 3 0x x+ + =

Answer (1)

Sol. 2 5 3 = − 2 5 3 = −

and and roots of 2 5 3 0x x− + =

5 + = 3 =

NTSE (S-I) 20 -20 21

- 22 -

Now equation whose roots are

and

2 0x x

− + + =

2 2

2 1 0x x +

− + =

2

2 ( ) 2 1 0x x + −

− + =

219

1 03

x x− + =

23 19 3 0x x− + =

198. If , ,x b c y c a z a b= + = + = + then find the value

of 2 2 2

2 2 2

x y z yz zx xy

a b c bc ca ab

+ + − − −

+ + − − −

(1) 0 (2) 1

(3) 2 (4) –1

Answer (2)

Sol. 2 2 2

2 2 2

x y z yz zx xy

a b c bz ca ab

+ + − − −=

+ + − − −

2 2 2

2 2 2

1( ) ( ) ( )

21

( ) ( ) ( )2

x y y z z x

a b b c c a

− + − + −

− + − + −

2 2 2

2 2 2

( ) ( ) ( )

( ) ( ) ( )

b a c b a c

a b b c c a

− + − + −=

− + − + −= 1

199. If tan sin aq+ q = and tan sin bq− q = , what is the

value 2 2( )a b ab− ¸

(1) -3 (2) -4

(3) 3 (4) 4

Answer (4)

Sol. tan sin ,tan sina bq+ q = − q =

2tan , 2sina b a b+ = q − = q

( )( ) 4 tan sina b a b+ − = q

2 2 4tan sina b− = q q ...(i)

2 2tan sina b = q − q

2 2sin (sin 1)a b = q q −

= q q2 2sin tanab

= q qsin tanab ...(ii)

(i)/(ii) 4tan sin

4sin tan

q q=

q q

200. The line segment joining the points (3,4) and (1,2)

is trisected at the points A&B. If the co-ordinates of

A&B are (a, –2) & 5

,3

b

respectively. Find the

value of a and b.

(1) 7

0,3

a b= =

(2) 7

, 03

a b= =

(3) a = 7, b = 3

(4) a = 3, b = 7

Answer (Answer not matched*)

Sol.

A B

1 : 2

2 : 1

(3 , 4 ) (1 , 2 )

Co-ordinate of 1 1 2 3 1 2 2 4

,1 2 1 2

A + +

+ +

7 10

,3 3

Co-ordinate of B 2 1 1 3 2 2 1 4

,1 2 1 2

+ +

+ +

5 8

,3 3

❑ ❑ ❑

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