Assam 2020-21 NTSE Stage 1 Answer Key & Question Paper With Solutions

Paper: MAT

Directions (Q. No. 1-10): Find the odd word out.

Question 1. Find the odd word out.

a. Volume
b. Shape
c. Weight
d. Large

Answer: (d)

Large is an adjective but others are nouns.

Question 2. Find the odd word out.

a. Ear
b. Heart
c. Eye
d. Kidney

Answer: (b)

All except the heart are present in pairs in the human body.

Question 3. Find the odd word out.

a. April
b. May
c. July
d. September

Answer: (a)

All months except April come in odd positions when counting from January.

Question 4. Find the odd word out.

a. Cloud
b. Rain
c. Vapour
d. Fog

Answer: (b)

Fog, clouds and vapours are formed by evaporated water (the first two by condensation on particles and the third by evaporation alone) and stay suspended in the atmosphere. However, rain is formed by the precipitation of water to the Earth’s surface.

Question 5. Find the odd word out.

a. Cabbage
b. Papaya
c. Brinjal
d. Cucumber

Answer: (b)

Papaya is the only fruit among the given options, all others are vegetables.

Question 6 Find the odd word out.

a. Haryana
b. Gujarat
c. Kerala
d. Tamil Nadu

Answer: (a)

All states except Haryana have coastal boundaries.

Question 7. Find the odd word out.

a. Assam
b. Tripura
c. Mizoram
d. West Bengal

Answer: (d)

West Bengal is not one of the northeastern seven sister states while others are.

The seven sisters are Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland, Sikkim and Tripura.

Question 8. Find the odd word out.

a. Parrot
b. Koel
c. Vulture
d. Swan

Answer: (d)

Swan is the only water bird and has webbed feet among the given options.

Question 9. Find the odd word out.

a. Wheat
b. Paddy
c. Maize
d. Mustard

Answer: (d)

Wheat, Paddy, and Maize are food grains while Mustard is oilseed.

Question 10. Find the odd word out.

a. Snake
b. Lizard
c. Turtle
d. Whale

Answer: (d)

A whale is a mammal while the other three are reptiles.

Directions (Q. No. 11-15): Find the odd numeral pair in each of the following questions.

Question 11. Find the odd numeral pair in each of the following questions.

a. 42, 4
b. 36, 6
c. 32, 2
d. 15, 5

Answer: (a)

42 is not a multiple of 4 while in other pairs the first number is a multiple of the second number.

Question 12. Find the odd numeral pair in each of the following questions.

a. 13, 21
b. 19, 27
c. 15, 23
d. 16, 24

Answer: (d)

All other pairs consist of odd numbers while the last pair consist of even numbers.

OR

All other pairs of numbers are co-prime numbers whereas 16, 24 are not coprime as they have HCF of 8.

Question 13.Find the odd numeral pair in each of the following questions.

a. 7, 18
b. 9, 26
c. 11, 36
d. 13, 42

Answer: (c)

The pattern follows in all options as:

7 × 4 – 10 = 18

9 × 4 – 10 = 26

13 ×4 – 10 = 42

But, for the third option: 11 × 4 – 10 = 34 ≠ 36, this pattern is not followed here.

Question 14.Find the odd numeral pair in each of the following questions.

a. 3, 4
b. 4, 7
c. 5, 12
d. 20, 21

Answer: (d)

All other options except the last one consist of one composite and one prime number. In option d, both the numbers are composite.

Question 15.Find the odd numeral pair in each of the following questions.

a. 9, 3
b. ½ , ⅛
c. ⅓ , 1/12
d. 24, 6

Answer: (a)

The pattern follows in all options as:

⅛ × 4 = 1/2

1/12 × 4 = 1/3

6 × 4 = 24

But, in the first option: 3 × 4 = 12 ≠ 9, this pattern is not followed here.

Directions (Q. No. 16-25) Find the odd pair in each of the following questions :

Question 16. Ship : sea :: camel : ?

a. Forest
b. Land
c. Mountain
d. Desert

Answer: (d)

The ship is used to travel by sea. Similarly, camels are used to travel in the desert. Moreover, camels are also called ships of the desert.

Question 17. Coconut : Shell :: Letter : ?

a. Letter-box
b. Stamp
c. Mail
d. Envelope

Answer: (d)

The coconut is enclosed in a shell. Similarly, the letter is enclosed in an envelope.

Question 18. Moon : Satellite :: Earth : ?

a. Sun
b. Planet
c. Solar System
d. Asteroid

Answer: (b)

Moon is a satellite and Earth is a planet.

Question 19. India : President :: State : ?

a. Prime Minister
b. Governor
c. Chief Minister
d. Mayor

Answer: (b)

The President is the constitutional head of India. Similarly, the Governor is the constitutional head of the state in India.

Question 20. Good : Bad :: Roof : ?

a. Window
b. Floor
c. Walls
d. Pillars

Answer: (b)

Bad is the antonym of good. Similarly, the floor is the antonym of the roof.

Question 21. 4 : 19 :: 7 : ?

a. 54
b. 55
c. 57
d. 59

Answer: (b)

4 × 5 – 1 = 20 -1 = 19

Similarly, 7 × 8 – 1 = 56 – 1 = 55

Question 22. 82 : 9 :: 26 : ?

a. 5
b. 6
c. 4
d. 9

Answer: (a)

9² + 1 = 81 + 1 = 82

Similarly, 5² + 1 = 25 + 1 = 26

Question 23. 5 : 9 :: 10 : ?

a. 17
b. 28
c. 65
d. 126

Answer: (b)

2² + 1 = 5 : 2³ + 1 = 9

Similarly, 3² + 1 = 10 : 3³ + 1 = 28

Question 24. 18 : 30 :: 36 : ?

a. 54
b. 62
c. 64
d. 66

Answer: (d)

18 × 2 – 6 = 36 – 6 = 30

Similarly, 36 × 2 – 6 = 72 – 6 = 66

Question 25. 8 : 32 :: 10 : ?

a. 42
b. 44
c. 45
d. 50

Answer: (d)

8² /2= 64/2= 32

Similarly, 10² /2 = 100/2 = 50

Question 26. Choose the odd letter group or odd numeral group

a. CFIL
b. PSVX
c. JMPS
d. ORUX

Answer: (b)

Question 27. Choose the odd letter group or odd numeral group

a. CZHK
b. SENO
c. XUBU
d. YDFP

Answer: (c)

We can see that except XUBU, in no other option the letter is getting repeated. So, the correct answer for the odd one out is XUBU.

Question 28. Choose the odd letter group or odd numeral group

a. XW
b. PO
c. ML
d. FG

Answer: (d)

Question 29.Choose the odd letter group or odd numeral group

a. JOT
b. OUT
c. DOG
d. DIN

Answer: (b)

In JOT, there is one vowel, i.e., “O”.

In DOG, there is one vowel, i.e., “O”.

In DIN, there is one vowel, i.e., “I”.

But in OUT, there are two vowels, i.e., “O” and “U”.

Question 30.Choose the odd letter group or odd numeral group

a. HGF
b. XWV
c. NML
d. OPQ

Answer: (d)

Question 31.Choose the odd letter group or odd numeral group

a. 383
b. 551
c. 242
d. 263

Answer: (a)

If we observe, we can see that the middle digit is the product of the other two digits. But 383 does not follow this pattern.

For example in 551, 5 × 1 = 5 (middle digit)

In 242, 2 × 2 = 4 (middle digit)

In 263, 2 × 3 = 6 (middle digit)

But in 383, 3 × 3 = 9 ≠ middle digit

Question 32. Choose the odd letter group or odd numeral group

a. 8
b. 28
c. 216
d. 125

Answer: (b)

Except, 28 all others are perfect cubes.

8 = (2³)

216 = (6³)

125 = (5³)

Question 33.Choose the odd letter group or odd numeral group

a. 19
b. 17
c. 15
d. 13

Answer: (c)

All numbers are prime numbers except 15, which is a composite number.

Question 34. Choose the odd letter group or odd numeral group

a. 21
b. 69
c. 81
d. 83

Answer: (d)

21 has 4 factors.

69 has 4 factors.

81 has 5 factors.

Hence these three numbers are composite and on the other hand, 83 is a prime number means it has only two factors: 1 and itself.

Question 35. Choose the odd letter group or odd numeral group

a. 392
b. 326
c. 414
d. 248

Answer: (a)

In 326, 3 x 2 x 6 = 36, which is a perfect square.

Similarly, for 414, 4 x 1 x 4 = 16, again a perfect square.

For 248, 2 x 4 x 8 = 64, which is a perfect square.

However, for 392, 3 x 9 x 2 = 54, which is not a perfect square.

Directions (Q. No. 36-40) Complete the series :

Question 36.7, 12, 19, 28, 39, ___

a. 49
b. 51
c. 52
d. 57

Answer: (c)

Question 37. 17, 19, 22, 27, 34, 45, ___

a. 58
b. 57
c. 56
d. 59

Answer: (a)

Question 38. 2, 7, 28, 63, 126, ___

a. 210
b. 213
c. 215
d. 219

Answer: (c)

We can observe the following pattern:

2 = (1)³+1

7 = (2)³-1

28 = (3)³+1

63 = (4)³-1

126 = (5)³+1

215 = (6)³-1

Question 39. ND, IY, DT, YO, TJ, ___

a. MP
b. NQ
c. OF
d. OE

Answer: (d)

Question 40. Z, X, V, T, R, P, ___

a. N
b. M
c. K
d. S

Answer: (a)

Directions (Q. No 41-45): Arrange the items in the following questions in a meaningful order

Question 41. Arrange the items in a meaningful order

(1) Consultation (2) Illness

(3) Doctor (4) Treatment

(5) Recovery

a. 2, 3, 1, 4, 5
b. 2, 3, 4, 1, 5
c. 4, 3, 1, 2, 5
d. 5, 1, 4, 3, 2

Answer: (a)

First, we should have an illness to go to the doctor. We take the consultation from him, and he provides the treatment using which we recover.
So, the order is: (2) Illness, (3) Doctor, (1) Consultation, (4) Treatment, (5) Recovery.

Question 42. Arrange the items in a meaningful order

(1) Country (2) Furniture

(3) Forest (4) Wood

(5) Trees

a. 1, 3, 5, 4, 2
b. 1, 4, 3, 2, 5
c. 2, 4, 3, 1, 5
d. 5, 2, 3, 1, 4

Answer: (a)

We have forests in the country. In the forests we can find trees which have wood, using which we can make furniture.

So, the order is: (1) Country, (3) Forest, (5) Trees, (4) Wood, (2) Furniture

Question 43. Arrange the items in a meaningful order

(1) Mother (2) Child

(3) Milk (4) Cry

(5) Smile

a. 1, 5, 2, 3, 4
b. 2, 4, 1, 3, 5
c. 2, 4, 3, 1, 5
d. 3, 2, 1, 5, 4

Answer: (b)

Whenever a child starts crying, the mother comes and feeds the baby using milk, making the child smile.

So, the order is: (2) Child, (4) Cry, (1) Mother, (3) Milk, (5) Smile

Question 44. Arrange the items in a meaningful order

(1) Study (2) Job

(3) Examination (4) Earn

(5) Apply

a. 1, 2, 3, 4, 5
b. 1, 3, 2, 5, 4
c. 1, 3, 5, 4, 2
d. 1, 3, 5, 2, 4

Answer: (d)

We have to study and give examinations first. Then we can apply for a job and earn money.

So, the order is: (1) Study, (3) Examination, (5) Apply, (2) Job, (4) Earn

Question 45. Arrange the items in a meaningful order

(1) Curd (2) Grass

(3) Butter (4) Milk

(5) Cow

a. 5, 2, 4, 1, 3
b. 5, 2, 3, 4, 1
c. 4, 2, 5, 3, 1
d. 2, 5, 4, 3, 1

Answer: (a)

The cow eats grass to produce milk. Using the curdling process, we can make the curd from the milk, which then is churned to get the butter.

So, the order is (5) Cow, (2) Grass, (4) Milk, (1) Curd, (3) Butter

Directions (Q. No 46-48): Find which one word can be made from the letters of the given word:

Question 46. MEASUREMENT

a. MASTER
b. MANTLE
c. SUMMIT
d. ASSURE

Answer: (a)

All the letters of the word MASTER are present in MEASUREMENT as highlighted.

Question 47. CHOCOLATE

a. TELL
b. HEALTH
c. LATE
d. COOLER

Answer: (c)

All the letters of the word LATE are present in CHOCOLATE as highlighted.

Question 48. VENTURESOME

a. ROSTRUM
b. SERMON
c. TRAVERSER
d. SEVENTEEN

Answer: (b)

All the letters of the word SERMON are present in VENTURESOME.

Question 49. If ‘+’ means ‘÷’, ‘–’ means ‘×’, ‘÷’ means ‘+’ and ‘×’ means ‘–’, then 36 × 12 + 4 ÷ 6 + 2 =?

a. 2
b. 18
c. 42
d. 6 ½

Answer: BONUS

We know that + means ÷, – means ×, ÷ means + and × means –.

Therefore, 36 – 12 ÷ 4 + 6 ÷ 2 = 36 – 3 + 3

= 36

Question 50. If ‘P’ denotes ‘’÷, ‘Q’ denotes ‘×’, ‘R’ denotes ‘+’ and ‘S’ denotes ‘–’, then the value of 18Q12P4R5S6 is:

a. 53
b. 59
c. 65
d. 51

Answer: (a)

We know that,

P denotes ÷, Q denotes ×, R denotes + and S denotes -.

Therefore, 18Q12P4R5S6 = 18 × 12 ÷ 4 + 5 – 6

= 18 × 3 + 5 – 6

= 54 + 5 – 6 = 53

Question 51. If 9 × 3 = 36; 11 × 7 = 81 then 5 × 13 = ?

a. 65
b. 66
c. 81
d. 51

Answer: (c)

The pattern follows as:

If 9 × 3 = 36; 9 + 3 = 12 then 12/2 = 6 and 6² = 36

If 11 × 7 = 81; 11 + 7 = 18 then 18/2 = 9 and 9² = 81

Similarly, 5 × 3 = 81; because 5 + 13 = 18 then 18/2 = 9 and 9² = 81

Question 52. If 31 + 72 = 26; 52 + 45 = 32 then 47 + 83 = ?

a. 88
b. 44
c. 65
d. 130

Answer: (b)

The pattern follows as:

If 31 + 72 = 26; 3 + 1 + 7 + 2 = 13 and 13 × 2 = 26

If 52 + 45 = 32; 5 + 2 + 4 + 5 = 16 and 16 × 2 = 32

Similarly, 47 + 83 = 44; because 4 + 7 + 8 + 3 = 22 and 22 × 2 = 44.

Directions (Q. No 53-55) Find the absolute truth out of the given alternatives :

Question 53. A fan always has

a. Switch
b. Blades
c. Current
d. Wire

Answer: (b)

Blades are a mandatory component of the fan whereas switch, current, and wire are not.

Question 54. Milk always contains

a. Sugar
b. Fats
c. Calcium
d. Water

Answer: (c)

Sugar, fats, and water can be a part of the milk but calcium is the most essential constituent of milk.

Question 55. A child must have

a. Toys
b. Friends
c. Parents
d. Education

Answer: (c)

Toys, friends, and education are not important for the existence of a child. However, parents are a necessity to bear the child. Hence, a child must have parents.

Question 56. A and B are brothers, C and D are sisters. A’s son is D’s brother. How is B related to C?

a. Father
b. Brother
c. Uncle
d. Grand Father

Answer: (c)

C is the sister of son of A. Hence, C is the daughter of A. So, C is the daughter of B’s brother. Hence, B is the uncle of C.

Question 57. Kumud is the brother of Anil. Kumud is the son of Parimal. Bimal is Parimal’s father. How is Anil related to Bimal?

a. Son
b. Grandson
c. Brother
d. Grand Father

Answer: (b)

Question 58. A + B means A is the son of B. A – B means A is the wife of B. What does P + R – Q mean?

a. ‘Q’ is the father of ‘P’
b. ‘Q’ is the son of ‘P’
c. ‘Q’ is the uncle of ‘P’
d. ‘Q’ is the brother of ‘P’

Answer: (a)

P + R – Q means P is the son of R and R is the wife of Q. Hence, Q is the father of P.

Question 59. ‘A × B’ means ‘A is the brother of B’ ‘A ÷ B’ means ‘A is the mother of B’. What does P × R ÷ Q mean?

a. ‘P’ is the brother of ‘Q’
b. ‘P’ is the father of ‘Q’
c. ‘P’ is the uncle of ‘Q’
d. ‘P’ is the nephew of ‘Q’

Answer: (c)

P × R ÷ Q means P is the brother of R and R is the mother of Q. Hence, P is the uncle of Q.

Question 60. A + B means A is the father of B. A ÷ B means A is the daughter of B. What does P ÷ R + Q mean?

a. ‘P’ is the father of ‘Q’
b. ‘P’ is the brother of ‘Q’
c. ‘P’ is the mother of ‘Q’
d. ‘P’ is the sister of ‘Q’

Answer: (d)

P ÷ R + Q means P is the daughter of R and R is the father of Q. Hence, P is the sister of Q.

Directions (Q. No 61-65): In each of the following questions, three figures are similar in a certain way. Choose the figure which is different from the rest.

Question 61. Choose the figure which is different from the rest

Answer: (c)

In all the circles except the circle labelled (c), the line passes through the centre of the circle.

Question 62. Choose the figure which is different from the rest

Answer: (d)

The figure labelled (d) is the only figure which shows a complete arrow along a single diameter of the circle.

Question 63. Choose the figure which is different from the rest

Answer: (c)

The figure labelled (c) is the only figure which starts with a caret (^) symbol and hence the odd one out.

Question 64. Choose the figure which is different from the rest

Answer: (b)

In all the figures except in (b) mirror images are present. The correct mirror image of in (b) should have been

Question 65. Choose the figure which is different from the rest

Answer: (c)

It can be seen in figures (a), (b) and (d) the line inside the square lies on the 4th vertex and in (c) it is on the 3rd vertex. In all the images, the line inside the square intersects at the upper end, whereas in the image labelled (c) it intersects at the lower end.

Directions (Q. No. 66-70) In each of the following questions, there are three problem figures followed by a question mark (?) for the fourth one. There exists a relationship between the first two problem figures. A similar relationship should exist between the third and fourth figures. Find the one from the answer figures that correctly replaces the question mark.

Question 66. Find the one from the answer figures that correctly replaces the question mark

Answer: (a)

The two circles of the first figure overlap in the second figure.

Similarly, two pointed structures of the third figure overlap in the fourth figure.

Question 67. Find the one from the answer figures that correctly replaces the question mark

Answer: (c)

There is an addition of one dot at the centre in the second figure.

Similarly, one dot is added at the centre in the fourth figure.

Question 68. Find the one from the answer figures that correctly replaces the question mark

Answer: BONUS

Two white dots from the first figure go out of the shape and one black dot takes their place in the second figure.

Similarly, two white dots are taken out of the shape and one black dot is placed at their position in the fourth figure.

Question 69. Find the one from the answer figures that correctly replaces the question mark

Answer: (b)

There is an increment of one side in both the interior triangle and exterior triangle to form two rectangles. So, from a square which has 4 sides (both inside and outside), we’ll obtain a figure that has 5 sides both inside and outside. Most suitable is (b).

Question 70. Find the one from the answer figures that correctly replaces the question mark

Answer: (d)

The pattern follows here as:

(Number of sides) x (Number of sides + 1)

Question 71. How many straight lines are contained in the figure given below?

a. 9
b. 10
c. 11
d. 12

Answer: (a)

It is clear from the figure that:

Horizontal lines = 2

Vertical lines = 3

Slanting lines = 4

Hence, the figure contains 9 straight lines.

Question 72. How many triangles are contained in the figure given below?

a. 8
b. 10
c. 12
d. 14

Answer: (c)

Total number of triangles = 4+4+2+2 = 12

Question 73. How many squares are contained in the following figure?

a. 6
b. 7
c. 8
d. 9

Answer: (d)

Total number of squares = 6+1+1+1 = 9

Question 74. How many rectangles are there in the following figure?

a. 8
b. 17
c. 18
d. 19

Answer: (c)

There are 18 rectangles contained in the figure as shown.

Total number of rectangles = 8+5+2+2+1 = 18

Question 75. How many triangles are there in the following figure?

a. 8
b. 9
c. 16
d. 11

Answer: (c)

There are 16 triangles in the figure as shown

Total number of triangles = 6 + 3 + 6 + 1 = 16

Directions (Q. No. 76-82) In each of the following questions, numbers are placed in the figures on the basis of some logic. One place is vacant and indicated by a question mark (?). Find out the correct alternatives to replace the question mark.

Question 76. Find out the correct alternatives to replace the question mark.

a. 4
b. 8
c. 2
d. 16

Answer: (b)

If we see column-wise, we can observe that the bottom-most number is obtained on multiplication of the above three numbers.

For the first column, 6×5×4 = 120

For second column, 6×7×3 = 126

Similarly, 8×5×? = 320

? = 320/40 = 8

Question 77. Find out the correct alternatives to replace the question mark.

a. 3
b. 5
c. 4
d. 6

Answer: (b)

If we see column-wise, we can observe that the bottom-most number is the square of the sum of the above three numbers.

For first column, (1+4+2)² = 7² = 49

For second column, (4+2+2)² = 8² = 64

Similarly, (?+5+3)²= 169 = 13²

?+5+3 = 13

? = 5

Question 78. Find out the correct alternatives to replace the question mark.

a. 6
b. 7
c. 8
d. 9

Answer: (a)

If we see row-wise, we can observe that the sum of the three numbers is constant.

For first row, 3+6+8 = 17

For second row, 5+8+4 = 17

Similarly, 4+7+?= 17

? = 6

Question 79. Find out the correct alternatives to replace the question mark.

a. 5
b. 10
c. 15
d. 21

Answer: (b)

If we see row-wise, we can observe that the rightmost number is the sum of the two left numbers.

For first row, 6+9 = 15

For second row, 8+12 = 20

Similarly, 4+6 = ? = 10

Question 80. Find out the correct alternatives to replace the question mark.

a. 25
b. 48
c. 59
d. 73

Answer: (d)

If we see column-wise, we can observe that the bottom-most number is obtained on the addition of the cubes of the above three numbers.

For first column, 2³ + 1³ + 3³ = 8 +1 + 27 = 36

For third column, 0³ + 4³ + 3³ = 0 + 64 + 27 = 91

Similarly, 4³ + 2³ + 1³ = 64 + 8 + 1 = ? = 73

Question 81. Find out the correct alternatives to replace the question mark.

a. 42
b. 36
c. 6
d. 4

Answer: (d)

If we see column-wise, we can observe that the bottom-most number is obtained by following pattern:

Topmost number + (middle number×2) = Bottom number

For first column, 13 + (7×2) = 27

For second column, 54 + (45×2) = 144

Similarly, ? + (32×2) = 68

? = 68 – 64 = 4

Question 82. Find out the correct alternatives to replace the question mark.

a. 15
b. 18
c. 20
d. 25

Answer: (d)

If we see row-wise, we can observe that the middle number is obtained by the following pattern:

For the first row, 28/7 × 5 = 4 × 5 =20

For second row, 84/12 × 5 = 7 × 5 = 35

Similarly, 45/9 × 5 = 5 × 5 = ? = 25

Directions (Q. No. 83-85): Study the following diagram and answer the given questions

Question 83. Study the following diagram and answer the given questions

a. 11
b. 13
c. 15
d. 17

Answer: (a)

If we observe the common diagram, we see that on multiplying 13 and 8, we are getting 104.

Similarly, here also on multiplying 14 and ? we should get 154.

Therefore, 14×? = 154

? = 154/14 = 11

OR

If we observe the common diagram, we see that 85-64 = 21, which is also equal to 13+8.

Similarly, here 221-196 = 25

Now 14+? = 25

? = 11

Question 84. Study the following diagram and answer the given questions

a. 125
b. 90
c. 105
d. 225

Answer: (d)

If we observe the common diagram, we see that on the left side box with the number (8) and its square (64) is on the right-hand side box.

Similarly, here we should get the square of 15 on the right-hand side box.

15² = 225

Question 85. Study the following diagram and answer the given questions

a. 33
b. 81
c. 243
d. 42

Answer: (b)

If we observe the common diagram, we see that on multiplying 13 and 8, we are getting 104.

Similarly, here also on multiplying 27 and 3, we should get the value of ?.

Therefore, 27 × 3 = ? = 81

Directions (Q. No. 86-90) In each of these questions, which character from the given options when placed at the sign of question mark (?) shall complete the matrix?

Question 86. Choose the right character from the given options that shall complete the matrix

a. K
b. N
c. O
d. P

Answer: (a)

We can see the pattern along the row as:

Question 87. Choose the right character from the given options that shall complete the matrix

a. U
b. V
c. W
d. X

Answer: (c)

We can observe a pattern along the columns as:

(+2, +3), (+3,+4) and (+4,+5) is the logic column wise

Question 88. Choose the right character from the given options that shall complete the matrix<

a. G
b. R
c. T
d. V

Answer: (d)

Question 89. Choose the right character from the given options that shall complete the matrix

a. I
b. L
c. O
d. U

Answer: (d)

P, Q, R: equal spacing of 1 between them.

N, O: spacing of 1 between them, similarly for S, T.

O, T: spacing of 5 between them, similarly for N, S.

Hence, the gap needs to be constant for the other major diagonal as well. The difference between MQ is 4, which should be equal to the difference between Q and the next letter. Therefore, the next letter is U.

Question 90. Choose the right character from the given options that shall complete the matrix

a. V
b. W
c. X
d. Y

Answer: (b)

Directions (Q. No. 91-95) Study the following figure carefully and answer the questions given below it. The rectangle represents artists, the circle represents players and the triangle represents doctors :

Question 91. How many players are neither artists nor doctors?

a. 3
b. 8
c. 22
d. 25

Answer: (d)

Players who are neither artists nor doctors = part of the circle which is not in the rectangle nor in the triangle

Question 92. How many artists are players ?

a. 30
b. 29
c. 25
d. 22

Answer: (c)

Artists who are players = Part of the rectangle which is inside the circle.

Question 93. How many doctors are both players and artists?

a. 3
b. 4
c. 8
d. 11

Answer: (a)

Doctors who are both players and artists = Area of the triangle both in the circle as well as the rectangle.

Question 94. How many doctors are neither players nor artists?

a. 30
b. 27
c. 22
d. 8

Answer: (b)

Doctors who are neither players nor artists = Area of the triangle which is not in circle or rectangle

Question 95. How many artists are neither players nor doctors?

a. 22
b. 24
c. 29
d. 30

Answer: (d)

Artists who are neither players nor doctors = Area of the rectangle which is not in circle or triangle

Question 96. Select from the given diagrams, the one that illustrates the relationships among the given three classes Tennis fans, Cricket players, Students

Answer: (a)

In a group of students, some can be tennis fans and some can be cricket players.

Now, out of the cricket players, some can be tennis fans as well and not all of the players or fans must be students.

Question 97. Choose from the four diagrams given below, the one that illustrates the relationship among: Language, French, German

Answer: (c)

German and French both are languages spoken in two different countries.

Question 98. Select from the four alternative diagrams, the one that best illustrates the relationship between the three classes: Pigeons, Birds, Dogs

Answer: (a)

All pigeons are birds. But dogs are different from birds and hence in a different category.

Directions (Q. No. 99-100): Read the following information carefully and answer the questions:

i) Arati is older than Sanu.

ii) Muskan is older than Arati but younger than Kailash.

iii) Kailash is older than Sanu.

iv) Sanu is longer than Muskan.

v) Gargi is the eldest

Question 99. Who is the youngest?

a. Kailash
b. Arati
c. Muskan
d. Sanu

Answer: (d)

If A, S, K, M and G represent Arati, Sani, Kailash, Muskan and Gargi. According to the information given, they can be written more clearly as:

A>S

K>M>A

K>S

S<M or M>S

But S is taller than M.

Finally, G is the eldest. So,

Gargi > Kailash > Muskan > Arati > Sanu

So, we can see that Sanu is the youngest.

Question 100. Agewise, who is in the middle?

a. Kailash
b. Muskan
c. Arati
d. Sanu

Answer: (b)

According to the information given,

Gargi > Kailash > Muskan > Arati > Sanu

So, we can see that Muskan is the middle one according to age.

Assam NTSE 2020 Stage 1 SAT Paper

PAPER – SAT

Question 1. The Regulating act legislation was passed by the British Parliament in

a. 1753
b. 1763
c. 1773
d. 1783

Answer: (c)

The Regulating Act of 1773 was passed by the British Parliament. It was an attempt to check on the misgovernment of the British East India Company in India.

Question 2. Under which Viceroy the Partition of Bengal took place?

a. Robert Clive
b. Lord Dalhousie
c. Lord Curzon
d. Lord Minto

Answer: (c)

Curzon announced the partition of Bengal in July 1905. The partition came into effect on 16 October, 1905. He used the partition as a political tool to weaken the growing nationalist movement in Bengal. The partition was annulled in 1911.

Question 3. Sepoy mutiny took place in –

a. 1757
b. 1765
c. 1826
d. 1857

Answer: (d)

The Sepoy Mutiny took place in the year 1857. It is also referred to as the First War of Independence by some historians. Although unsuccessful, it was the first organised rebellion by the Indians against the British colonial powers.

Question 4. The capital of the province of “Eastern Bengal and Assam” was

a. Shillong
b. Jorhat
c. Tinsukia
d. Dhaka

Answer: (d)

The partition of Bengal in 1905 created the Eastern Bengal and Assam provinces. Dhaka served as the capital of this province from 1905 to 1912. The partition was annulled in 1911.

Question 5. Who was the first ICS from Assam?

a. Anandaram Borooah
b. Lakshminath Bezbaroa
c. Amulya Barua
d.Hem Barua

Answer: (a)

Anandaram Borooah was the first Indian Civil Servant from Assam. He was a Sanskrit scholar, first graduate from Assam and also an eminent lawyer.

Question 6. The infamous Rowlatt Act was passed by the Imperial Legislative Council in

a. 1909
b. 1919
c. 1929
d. 1939

Answer: (b)

The Imperial Legislative Council passed the Rowlatt Act on 18th March 1919. It was a draconian law that extended the emergency measures of indefinite preventive detention and incarceration without trial and judicial review for an indefinite period.

Question 7. Who wrote the famous Book “Gitanjali”?

a. Rabindranath Thakur
b. Abanindranath Thakur
c. Bipin Chandra Pal
d. Aurobindo Ghosh

Answer: (a)

Rabindranath Thakur wrote the Gitanjali. Published in 1910, it is a collection of 157 poems. He won the Nobel Prize for Literature for the same in 1913.

Question 8. Who was the founder of Assam Association

a. Manik Chandra Baruah
b. Nabin Chandra Bordoloi
c. Anandaram Dhekiyal Phukan
d. Tarun Ram Phukan

Answer: (a)

Manik Chandra Baruah formed the Assam Association in 1903. The association was the centre of political activities in Assam.

Question 9. In which year was the ‘Gyan Pradavin Sabha’ founded ‘?

a. 1827
b. 1837
c. 1847
d. 1857

Answer: (d)

The Gyan Pradavin Sabha was founded by Anandaram Dhekiyal Phukan in 1857. The sabha was founded to discuss important social reforms and other issues.

Question 10. Who composed the ‘Kirtan Ghosa”?

a. Madhavdeva
b. Bhatadeva
c. Ananta Kandali
d. Srimanta Sankardeva

Answer: (d)

Srimanta Sankardeva composed the Kirtan Ghosa during medieval times. It is a collection of poems meant to be sung by communities in the Eaksarna religion.

Question 11. Which of the following is a man-made resource?

a. Rivers
b. Mineral Oil
c. Irrigation Canal
d. Forest

Answer: (c)

Irrigation canals are artificial channels of water. These are man-made structures constructed to transport water from one place to another, usually to supply water for farms or fields.

Question 12. Which one of the following is an abiotic resource?

a. Air
b. Plants
c. Animals
d. Fungus

Answer: (a)

Abiotic resources are non-living chemical and physical components of our environment that affect living organisms and the functioning of ecosystems. Sunlight, air, precipitation, minerals, and soil are some examples of abiotic factors.

Question 13. Which of the following is a nonrenewable resource?

a. Air
b. Water
c. Crops
d. Coal

Answer: (d)

The resources which cannot be immediately replaced or replenished when they are depleted are called non-renewable resources. These are resources that have a limited supply. Non-renewable resources include fossil fuels such as coal, petroleum, natural gas etc.

Question 14. The organization IUCN is under which of the following organizations?

a. UNESCO
b. UNO
c. WWF
d. UNEP

Answer: Bonus

The International Union for Conservation of Nature is an independent international organization working in the field of nature conservation and sustainable use of natural resources.

Question 15. Baghjan is located in the district of

a. Jorhat
b. Sibsagar
c. Dibrugarh
d. Tinsukia

Answer: (d)

Baghjan is located in the district of Tinsukia, Assam. Oil India Limited operates an oilfield in Baghjan.

Question 16. Which is the smallest continent in the World?

a. North America
b. Europe
c. Antarctica
d. Oceania

Answer: (d)

Oceania is the smallest continent in the World. Besides Australia, Oceania includes thousands of tiny islands of the Central Pacific and South Pacific, most notably Melanesia, Micronesia, and Polynesia.

Question 17. Which sea has separated the continents of Asia and Africa?

a. Mediterranean Sea
b. Red Sea
c. Caspian Sea
d. Arabian Sea

Answer: (b)

The Red Sea separates the continents of Asia and Africa. It connects the Gulf of Suez in the north and the Gulf of Aden in the south. Countries like Saudi Arabia and Yemen are located to the right, and African countries like Sudan, Ethiopia and Egypt are located to the left of the Red Sea.

Question 18. What has naturally separated Asia from Europe?

a. Ural mountain range
b. Caucasus mountain
c. Caspian Sea
d. Volga River

Answer: (a)

The Ural Mountain range or Urals are a rugged range that runs across western Russia. Extending about 2,500 km, this range forms the natural boundary between Europe and Asia.

Question 19. Which is the largest agro-based industry of Assam?

a. Silk industry
b. Rubber industry
c. Tea industry
d. Fishery

Answer: (c)

Assam alone contributes to more than half of India’s tea production. The total area under tea cultivation in Assam accounts for more than half of the country’s total area under tea. The tea industry is the largest agro-based industry of Assam.

Question 20. The industries of Assam can be classified

a. Two types
b. Three types
c. Four types
d. Five types

Answer: Bonus

Question is not clear

Question 21. The Constituent Assembly met for the first time in New Delhi on 9th December

a. 1945
b. 1946
c. 1947
d. 1948

Answer: (b)

The Constituent Assembly met for the first time in New Delhi on 9th December, 1946 in the Constitution Hall, also known as the Central Hall of Parliament House.

Question 22. Which article of the Indian Constitution declares India as “Union of States”?

a. Article 1
b. Article 2
c. Article 3
d. Article 4

Answer: (a)

Article 1 of the Constitution states – India, that is Bharat, shall be a Union of states. The territory of India shall consist of territories of the states, the union territories and any territory that may be acquired in future.

Question 23. Which of the following is not a part of the Indian Parliament?

a. President
b. Lok Sabha
c. Rajya Sabha
d. Supreme Court

Answer: (d)

The Supreme Court of India is the apex court of the country. It is a part of Judiciary and not a part of the Parliament of India. The Supreme Court of India is located in New Delhi.

Question 24. Who is the Chairperson of NITI AAYOG?

a. President
b. Vice President
c. Prime Minister
d. Finance Minister

Answer: (c)

The Governing Council of the NITI AAYOG has the Prime Minister of India as its chairperson and it also consists of Chief Ministers of all States and Lieutenant Governors of Union Territories. NITI stands for National Institution for Transforming India which is the premier policy-making institution that is expected to foster the economic growth of the country.

Question 25. Who was the first president of Independent India?

a. Pandit Jawaharlal Nehru
b. Dr. Rajendra Prasad
c. V.V. Giri
d. Dr. Zakir Hussain

Answer: (b)

Dr. Rajendra Prasad was the first President of independent India and served his term from 1950 to 1962. Dr. Rajendra Prasad was a lawyer and an ardent follower of Mahatma Gandhi.

Question 26. Who appoints the Governor of a State in India ?

a. The Chief Justice of the Supreme Court
b. The President of India
c. The Prime Minister of India
d. The Chief Minister

Answer: (b)

According to Article 155 of the Indian Constitution, the President of India appoints the Governor of a state in India. The President also removes the Governor of a state under the advice of the cabinet.

Question 27. In which year was the Right to Education Act enacted in India?

a. 2006
b. 2007
c. 2008
d. 2009

Answer: (d)

The parliament of India enacted the Right to Education Act on 4th August 2009. The Right to Education describes modalities for free and compulsory education for children between the ages of six and fourteen. It is enlisted under Article 21 (A) of India’s Constitution and hence recognised as a fundamental right.

Question 28. Sarkaria Commission was appointed in the year

a. 1980
b. 1981
c. 1982
d. 1983

Answer: (d)

The Sarkaria Commission was appointed by the Government of India in 1983 to scrutinise the centre-state relations and suggest recommendations within the constitutional framework. The commission was led by a retired Supreme Court judge Ranjith Singh Sarkaria as its Chairman.

Question 29. Which one of the following is the largest organ of UNO?

a. Security Council
b. General Assembly
c. The Economic and Social Council
d. Trusteeship Council

Answer: (b)

The United Nations General Assembly is the policy making and representative organ of the United Nations. The General Assembly has 193 member states and hence forms the largest organ of the United Nations.

Question 30. National Human Rights Commission was created in the year

a. 1990
b. 1991
c. 1992
d. 1993

Answer: (d)

The National Human Rights Commission was constituted on 12th October, 1993. It is a statutory body. The NHRC is responsible for promoting and protecting human rights and ensuring that individuals enjoy liberty, equality and dignity.

Question 31. Who is known as the Father of Economics?

a. Adam Smith
b. Chanakya
c. Marshall
d. None of the above

Answer: (a)

Adam Smith was an 18th-century Scottish economist and philosopher who is recognised as the father of economics. Adam Smith is known for his famous work “The Wealth of Nations”. He is also known as the “Father of Capitalism”.

Question 32. Which of the following is not a direct tax?

a. Sales Tax
b. Income Tax
c. Wealth Tax
d. Estate duty

Answer: (a)

Indirect taxes are called so because the point of levy and burden of payment are not on the same entity, unlike direct tax. For example, the government levies a tax on the seller of a particular good. But the burden of tax payment falls on the consumer who purchases that good. The consumer pays the respective tax amount with the product’s price. The seller in turn pays the respective tax amount to the government. Sales tax, excise duty and entertainment tax are some of the examples of indirect taxes.

Question 33. When was the Reserve Bank of India established?

a. 1925
b. 1935
c. 1945
d. 1955

Answer: (b)

The RBI is the central bank of India. It works as the official banker to the central and state governments. It is also a banker to banks as it maintains the banking accounts of other scheduled banks. The RBI was established on 1st April, 1935 in Kolkata based on the recommendations of the Hilton Young Commission.

Question 34. Which of the following is not a Cash Crop?

a. Jute
b. Groundnut
c. Jowar
d. Sugarcane

Answer: (c)

Cash crops are harvested for commercial purposes on a large scale in order to reap huge profits. Jute, groundnuts and sugarcane are cash crops whereas jowar is not. Jowar is a food and cereal crop.

Question 35. Planning Commission of India has been replaced by –

a. Finance Commission
b. NITI Aayog
c. GST Council
d. Monetary Policy Committee

Answer: (b)

NITI stands for National Institution for Transforming India which is the premier policy-making institution that is expected to foster the economic growth of the country. It was formed on 1st January, 2015 replacing the Planning Commission of India.

Question 36. Goods and Services Tax is

a. a direct tax
b. a central tax
c. a state tax
d. an indirect tax

Answer: (d)

The Goods and Services Tax or the GST is an indirect tax in India that has replaced other taxes like the Value-added tax (VAT), excise duty and service taxes.

Question 37. Which of the following comes under Horticulture?

a. Cotton
b. Jute
c. Fruits and Vegetable
d. Paddy

Answer: (c)

Horticulture refers to the cultivation of fruits and vegetables. After the Golden Revolution, India became the world’s second largest producer of fruits and vegetables. The Golden Revolution made a fruitful impact on the lives of workers involved in honey and horticultural production in India.

Question 38. Which of the following does not belong to the Primary Sector?

a. Forestry
b. Mining
c. Agriculture
d. Construction

Answer: (d)

The Primary sector contains activities that utilise natural resources on earth. Thus, it includes hunting and gathering, pastoral activities, fishing, forestry, agriculture, and mining and quarrying. The secondary sector refers to activities that involve the production of a finished product from the extracted raw materials like construction.

Question 39. Which one of the following organizations estimates the National Income of India?

a. National Income Committee
b. Central Statistical Organization
c. Planning Commission
d. Reserve Bank of India

Answer: (b)

The Central Statistical Organization renamed as the Central Statistics Office is an agency of the Government of India formed on 2nd May, 1951. It is responsible for estimating the National Income of India and maintaining other statistical accounts.

Question 40. The first bank of India was the:

a. State Bank of India
b. Bank of Hindustan
c. Bank of Calcutta
d. Reserve Bank of India

Answer: (b)

The Bank of Hindustan was founded in 1770 at Calcutta by an agency house known as Alexander and Company. Paper notes were issued by the Bank of Hindustan when the East India Company first introduced them in India. However, the bank went defunct in 1832.

Question 41. Which among the following is getting reduced in the following reaction?

Fe₂O₃ + 3CO → 2Fe + 3CO₂

a. CO
b. Fe
c. CO₂
d. Fe₂O₃

Answer: (d)

Reduction is the removal of oxygen or addition of hydrogen from a chemical entity or decrease in oxidation number. In the given equation, oxygen is removed from Fe₂O₃. Hence Fe₂O₃ got reduced to Fe.

Question 42. Exposure of Silver Chloride to Sunlight for a long duration turns grey due to –

a. Formation of silver
b. Sublimation of silver chloride
c. Evolution of Chlorine gas
d. Oxidation of silver chloride

Answer: (a)

Exposure of silver chloride to sunlight for a long duration turns grey due to the formation of silver. The reaction involved in the process is as follows:

Silver chloride is white in colour while silver metal is grey and chlorine evolved in the reaction has a yellowish-green colour.

Question 43. A solution turns red litmus blue, its pH is likely to be

a. 1
b. 4
c. 5
d. 10

Answer: (d)

Red litmus turns blue with a basic solution. Basic solutions have a pH of more than 7. Thus, the pH of the solution mentioned in the question will be 10.

Question 44. pH of rain water is ________ than distilled water.

a. More
b. Less
c. Cannot be compared
d. None of these

Answer: (b)

Distilled water has a pH of 7. The pH of rainwater is less than 7 as it combines with oxides of sulphur and nitrogen and other impurities while coming down the atmosphere and becomes a bit acidic.

Question 45. The non-metal which is a liquid at room temperature –

a. Oxygen
b. Fluorine
c. Sulphur
d. Bromine

Answer: (d)

The non-metal which is liquid at room temperature is Bromine. At room temperature, oxygen and fluorine exist as gas whereas sulphur is in solid form.

Question 46. An alloy is –

a. An element
b. A mixture
c. An isomer
d. A metalloid

Answer: (b)

An alloy is a mixture of metals or a mixture of metal and other elements. Alloys can be both homogeneous or heterogeneous.

Question 47. The composition of aqua-regia is –

a. Dil. HCl : Conc. HNO₃ – 3 : 1
b. Conc. HCI: Dil. HNO₃ – 3 : 1
c. Conc. HCI: Conc. HNO₃ – 3 : 1
d. Dil. HCI: Dil. HNO₃ – 3 : 1

Answer: (c)

Aqua regia is composed of conc. HCl and conc. HNO₃ in the ratio 3:1.

Question 48. Which of the following is not a Dobereiner triad?

a. Li, Na, K
b. Mg, Ca, Sr
c. CI, Br, I
d. S, Se, Te

Answer: (b)

According to Dobereiner, the atomic mass of the middle element was approximately equal to the arithmetic mean (average) of the atomic masses of the other two elements of that triad when they are arranged in their increasing order of atomic mass.

(Mass of Mg +Mass of Sr)/2 = (24.305u + 87.62u)/2 = 55.96 u, which is not equal to the actual atomic mass of calcium (40 u).

Question 49. Newland gave the idea of re-occurrence of properties of every –

a. 7th
b. 8th
c. 6th
d. 4th

Answer: (b)

According to Newland, when elements are arranged in the increasing order of their atomic masses, the properties of the eighth element (starting from a given element) are a repetition of the properties of the first element.

Question 50. Which of the following element will form a bivalent anion?

a. Fluorine
b. Oxygen
c. Chlorine
d. Nitrogen

Answer: (b)

Oxygen has an atomic number 8. The electronic configuration of oxygen is 2, 6. It requires 2e^– to fulfil its octet and thus have a valency of 2. So it will form a bivalent anion O^2-.

Question 51. An element with atomic number 19 will most likely combine with the element with atomic number

a. 17
b. 11
c. 18
d. 20

Answer: (a)

The element with atomic number 19 (Potassium) has 1 valence electron and will most likely combine with an element having 7 electrons in its valence shell.

Z = 17: 2, 8, 7

Thus, an element with atomic number 19 will most likely combine with the element with atomic number 17.

Question 52. Which of the following shows an electronic configuration of 2, 8, 4?

a. Sodium
b. Silicon
c. Sulphur
d. Aluminium

Answer: (b)

Sodium: 2, 8, 1

Silicon: 2, 8, 4

Sulphur: 2, 8, 6

Aluminium: 2, 8, 3

Question 53. Rutherford’s experiment is related to the size of the –

a. Nucleus
b. Atom
c. Electron
d. Neutron

Answer: (a)

Rutherford’s alpha-particle scattering experiment is related to the size of the nucleus.

Question 54. Which species does not contain neutrons?

a. H
b. Li⁺²
c. C
d. O

Answer: (a)

Protium (Isotope of Hydrogen) has a mass number of 1 and contains one proton.

Question 56. Electronic configuration of an atom is 2, 8, 1. Which of the following elements is similar with it in chemical reactivity?

a. K
b. CI
c. N
d. Ar

Answer: (a)

The electronic configuration 2, 8, 1 belongs to the element having atomic number 11 (Sodium). Any other element which belongs to the same group as that of sodium will have a similar sort of chemical reactivity. Thus, potassium which belongs to the same group as that of sodium will have similar chemical reactivity.

Question 57. In diamond, the bonding between Carbon is –

a. Coordinate
b. Ionic
c. Covalent
d. Electrostatic

Answer: (c)

All the carbon atoms of diamond possess strong chemical bonds with that of the four other carbon atoms. And the bond lengths of the carbon-carbon atoms are equal. Hence, diamond forms a three-dimensional network of strong covalent bonds.

Question 58. Which of the following is not a saturated Hydrocarbon?

a. Cyclohexane
b. Benzene
c. Butane
d. Isobutane

Answer: (b)

Saturated hydrocarbon consists of only carbon-carbon single bonds. Among the given options, benzene is an unsaturated hydrocarbon.

Question 59. Buckminster fullerene is an allotropic form of

a. Phosphorus
b. Sulphur
c. Carbon
d. Tin

Answer: (c)

Buckminster fullerene (C₆₀) is an allotropic form of carbon.

Question 60. The compound containing both ionic and a covalent bond is

a. AlCl₃
b. CaO
c. MgCl₂
d. NH₄Cl

Answer: (d)

The compound containing both ionic and a covalent bond is NH₄Cl. The covalent bonds exist between nitrogen and hydrogen atoms while ionic bonds exist between NH₄⁺ and Cl^–.

Question 61. The LCM of two numbers is 1200. Which of the following cannot be their HCF?

a. 600
b. 500
c. 400
d. 200

Answer: (b)

Let the two numbers be A and B.

Given, LCM (A,B) = 1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

HCF of A and B should be a factor of LCM of A and B.

1200 = 600 x 2

1200 = 400 x 3

1200 = 200 x 6

But 1200 cannot be written as a product of 500 and another integer.

Hence, 500 cannot be their HCF.

Question 62. The number of decimal places after which the decimal expansion of the rational number 14587/1250 will terminate is

a. 1
b. 2
c. 3
d. 4

Answer: (d)

Hence, the decimal expansion of 14587/1250 terminates after 4 decimal places.

Question 63. The expression (2 + √3) (2 – √3) is

a. a rational number
b. a natural number
c. an integer
d. All the above

Answer: (d)

(2 + √3) (2 – √3) = 2² – (3)² = 4 – 3 = 1

1 is an integer, rational number and a natural number as well.

Question 64. If the graph of the polynomial y = f(x) intersects the x – axis at two points then the number of zeros of f(x) is

a. 0
b. 3
c. 1
d. 2

Answer: (d)

y = f(x) is a polynomial in x such that it intersects at two points on the x axis. I.e., at two different values of x, y = 0 or f(x) = 0. Hence, the polynomial f(x) has two zeros, ie., where y = f(x) becomes zero.

Question 65. If the sum of the zeroes of the polynomial f(x) = 2x³ – 3kx² + 4x – 5 is 6, then k = ?

a. 2
b. 4
c. -2
d. -4

Answer: (b)

Sum of zeroes of a cubic polynomial ax³ + bx² + cx + d is given by α + β + γ = -b/a

Where, α, β, and γ are roots of the cubic polynomial.

So, for 2x³ – 3kx² + 4x – 5, sum of roots = -(-3k)/2 = 6

k = 4

Question 66. If the system of equations 2x + 3y = 5 and 4x + ky = 10 has infinitely many solutions then k = ?

a. 1
b. ½
c. 3
d. 6

Answer: (d)

Two linear equations a₁x + b₁y = c₁ and a₂x+b₂y = c₂ have infinitely many solutions

when,

For the given set of equations, this can be written as

Question 67. The area of the triangle formed by the lines y = x, x = 6 and y = 0 is

a. 36 sq. units
b. 18 sq. units
c. 9 sq. units
d. 72 sq. units

Answer: (b)

When the three lines are plotted, they enclose a right angled triangle as shown.

The length of base made by y = 0, is 6 units.

The height of the triangle made by x = 6, is 6 units. x = y is the hypotenuse.

Area of triangle = ½ × 6 × 6 =18 sq. units

Question 68. If x = 1 is a common root of the equation ax² + ax + 3 = 0 and x² + x + b = 0 then the value of ab is

a. 3
b. 3.5
c. 6
d. -3

Answer: (a)

Let, f(x) = ax²+ax+3 and p(x) = x²+x+b

Given that, f(1) = 0 and p(1) = 0

I.e., a+a+3 = 0 and 1+1+b = 0

a = -1.5 and b = -2

ab = (-1.5)(-2) = 3

Question 69. The value of

a. 4
b. 3
c. -2
d. 3.5

Answer: (b)

Let the value of

Then,

Squaring both sides.

x² – x – 6 = 0

x² – 3x + 2x – 6 = 0

(x-3)(x+2) = 0

x= 3 or x = -2.

However, we know that a square root can never be negative. Hence, x = 3.

Question 70. The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36 then the number of terms will be –

a. 5
b. 6
c. 7
d. 8

Answer: (b)

Given that, a = 1, l = a + (n-1)d = 11

Also given S_n = 36 = n/2(a + l) = n/2(1 + 11) = 6n

n = 6

Question 71. If 18, a, b, -3 are in A.P. then a + b = ?

a. 19
b. 7
c. 11
d. 15

Answer: (d)

Given that, 18, a, b, -3 are in AP.

We also can assume 4 terms to be in AP as: p-2q, p-1, p+q, p+2q

Comparing these two we can say that: p-2q = 18, p-q = a, p+q = b and p+2q = -3

a+b = p-q+p+q = 2p

Also, 18+(-3) = (p-2q)+(p+2q) = 2p

Hence a+b = 18+(-3) = 15

Question 72. The sides of two similar triangles are in the ratio 4 : 9. The Areas of these triangles are in the ratio.

a. 2:3
b. 4:9
c. 81:16
d. 16:81

Answer: (d)

Let the triangles be ∆ABC and ∆PQR. So, ∆ABC ~ ∆PQR

Question 73. If ∆ABC and ∆DEF are similar triangles such that ∠A = 47^o and ∠E = 83^o then ∠F = ?

a. 50^o
b. 60^o
c. 70^o
d. 80^o

Answer: (a)

Since, ABC∼DEF

∠A = ∠D = 47^o, ∠B = ∠E = 83^o and ∠C = ∠F

∠A + ∠B + ∠C = 180^o

47^o + 83^o + ∠C = 180^o

∠C = 50^o = ∠F

Question 74. The perimeter a triangle with vertices (0,4), (0,0) and (3, 0)

a. 7 + √5
b. 6
c. 7.5
d. 12

Answer: (d)

(0,4) lies on the x-axis, (0,0) is the origin and (3,0) lies on the y-axis. Hence, the triangle formed is a right-angled triangle with two sides’ length equal to 3 units and 4 units lying on the y and x-axis respectively.

The third side by Pythagoras theorem is (3²+4²)^½ = 5 units

Perimeter of the triangle = 3+4+5 = 12 units

Question 75. The point on the x-axis which is equidistant from points (-1,0) and (5,0) is

a. (0,2)
b. (2,0)
c. (3,0)
d. (0,3)

Answer: (b)

The points equidistant from A(-1,0) and B(5,0) will lie on a line.

A is on x axis, B is on x-axis as well.

The point exactly in the middle of them will also lie on the x-axis.

Hence, the point is

Question 76. If sin θ + sin² θ =1 then cos² θ + cos⁴ θ = 1

a. -1
b. 1
c. 0
d. 2

Answer: (b)

sin θ =1-sin² θ = cos² θ

Putting in cos² θ + cos⁴ θ

sin θ + sin² θ = 1, which is given in the question itself.

OR

Putting in cos² θ + cos⁴ θ

cos² θ + sin² θ = 1

Question 77. If sec q + tan q = x then tan q = ?

a.

Question 78. The ratio of the length of a rod and its shadow is 1 : √3. The angle of elevation of the Sun is

a. 30^o
b. 45^o
c. 60^o
d. 90^o

Answer: (a)

Given that

Also,

Hence, ∠ACB = 30^o, which is the elevation of the Sun.

Question 79. Which of the following is correct?

a. Mode = 2 Median – 3 Mean
b. Mode = 2 Median + 3 Mean
c. Mode = 3 Median – 2 Mean
d. Mode = 3 Median + 2 Mean

Answer: (c)

The correct relation between Mean, Median and Mode is given by:

Mode = 3 Median – 2 Mean

Question 80. Which of the following cannot be the Probability of an event?

a. ⅔
b. -1.5
c. 15%
d. 0.7

Answer: (b)

Probability of an event can never be negative, as it doesn’t have any practical meaning. Probability can be anything falling ≥ 0 and ≤1.

Hence, -1.5 cannot be the probability of an event.

Question 81. The particles in the nucleus of an atom are

a. electron and proton
b. electron and neutron
c. proton and neutron
d. electron, proton and neutron

Answer: (c)

The nucleus of an atom is made of protons (positively charged) and neutrons (electrically neutral). The nucleus does not contain negatively charged electrons.

Question 82. The heaviest particle in an atom is

a. proton
b. electron
c. neutron
d. neutron and proton

Answer: (c)

Mass of proton = 1.672 × 10^-27 kg

Mass of electron = 9.109 × 10^-31 kg

Mass of neutron = 1.675 × 10^-27 kg

There is a small difference between the mass of protons and neutrons. Neutrons have more mass, i.e. they are the heaviest particle in an atom.

Question 83. In the process of sublimation

a. Solid goes to gas state
b. Liquid goes to gas state
c. Solid goes to liquid state
d. Liquid goes to solid-state

Answer: (a)

The process of conversion of the solid-state to the gas state, without passing through the liquid state is called sublimation.

Question 84. Avogadro’s number is

a. number of atoms or molecules in 1 gm of any substance
b. number of atoms or molecules in 1 kg of any substance
c. number of atoms or molecules in 1 mole of any substance
d. number of electrons in 1 gm of any substance

Answer: (c)

Number of atoms or molecules in one mole of any substance = Avogadro’s number = 6.022 × 10²³

Question 85. Force

a. Causes Motion
b. Changes motion
c. Does not change motion
d. None of these

Answer: (a) and (b)

Force can cause a change in motion or even cause the motion. Every time the motion of an object changes it is because a force has been applied. Force can cause a stationary object to move or a moving object to change its speed or direction.

Question 86. A body with an initial velocity of 10 km/hour comes to rest after 15 minutes. Then the distance covered by the body is –

a. 2.5 km
b. 1.25 km
c. 5 km
d. 10 km

Answer: (b)

Given: Initial velocity = u = 10 km/h

Time = 15 min = 15/60 = ¼ h

Final velocity = v = 0 km/h

Now, acceleration is change in velocity per unit time = (v-u)/t

a = (v-u)/t

= (0-10)/(¼) = -40 km/h²

Using the equation of motion, v²-u² = 2as

s = (v²-u²)/2a

= (0-100)/(2× -40)

= -100/-80

= 100/80

= 5/4

= 1.25 km

Question 87. The mass of moon is 7.34 x 10²² kg and the radius of the moon is 1737 km. The escape velocity at moon is –

a. 1.25 km/sec
b. 2.37 km/sec
c. 11.29 km/sec
d. 5 km/sec

Answer: (b)

Given: Mass of the moon = 7.34 x 10²² kg

Radius of the moon = 1737 km

We know that,

G = 6.67 × 10^-11 m³/kgs²

Using the formula for escape velocity,

Question 88. A boat can float and move in a river due to –

a. Archimedes principle and viscous force
b. Frictional force and Archimedes principle
c. Pascal’s law and Archimedes principle
d. Newton’s law and Pascal’s law

Answer: (a)

The upward force exerted on an object partially or fully immersed in fluids is called buoyant force. On the other hand, viscous force is the force between a body and fluid moving past it, so as to oppose the flow of the fluid.

Now, according to Archimedes principle, an object immersed in fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid.

Question 89. An iron ball of mass 2 kg is lifted by 2 m against the gravitational force. The work done in the process is –

a. 19.6 Joule
b. 39.2 Joule
c. 9.8 Joule
d. 78.4 Joule

Answer: (b)

Given: Mass of ball = 2 kg

Distance upto which it is lifted = 2 m

We know that,

Work done = Force × distance moved

W = Fs

Now, Force = mg

W = mgh (s = h = height upto which the ball is lifted)

= (2 kg)(9.8 m/s²)(2 m)

= 39.2 J

Question 90. To see the full image of an object the minimum size of a plane mirror should be-

a. half the size of the object
b. equal to the size of the object
c. double the size of the object
d. four times the object size

Answer: (a)

In order to see the full image of a person, the minimum size of the mirror should be half of the person’s height.

Question 91. Which of the following is responsible for the absorption of light energy during photosynthesis?

a. Chlorophyll
b. Stomata
c. Stem
d. Root

Answer: (a)

Chlorophyll is the light-absorbing pigment present in the chloroplasts which helps in the light reaction of the photosynthesis.

Question 92. Which part of a plant shows a negative response to light?

a. Leaf
b. Stem
c. Root
d. Bark

Answer: (c)

Roots are negatively phototropic and grow away from sunlight.

Question 93. In Bryophyllum, which plant part is used for developing a new plant?

a. Chlorophyll
b. Root
c. Bud
d. Leaf

Answer: (d)

In Bryophyllum, leaf is used as a vegetative propagule where adventitious buds originate from the margins of the leaf.

Question 94. Which of the following is an example of unisexual flower?

a. Hibiscus
b. Rose
c. Papaya
d. Mustard

Answer: (c)

Papaya has unisexual flowers that is, it contains either stamens or carpels only.

Question 95. Which of the following helps in the activation of enzyme pepsin M stomach?

a. HCl
b. NaCl
c. Potassium
d. Calcium

Answer: (a)

Hydrochloric acid (HCl) creates an acidic medium of pH about 1-2 during digestion which activates the enzyme pepsin which helps in the breakdown of proteins.

Question 96. In human muscle cells, which of the following is produced after breakdown of glucose in absence of Oxygen?

a. Ethanol
b. Starch
c. Lactic Acid
d. Pyruvate

Answer: (c)

In human muscle cells, in the absence of oxygen, pyruvate is converted into lactic acid via lactic acid fermentation.

Pyruvate → (lack of oxygen) → Lactic acid + energy

Question 97. The instrument which is used for the measurement of blood pressure is known

a. Oxymeter
b. Thermometer
c. Sphygmomanometer
d. Glucometer

Answer: (c)

A sphygmomanometer is used for the measurement of blood pressure.

Question 98. If a human Zygote, cell carries sex chromosomes XY, then it will develop into a –

a. Male
b. Female
c. Bisexual
d. Genetically abnormal child

Answer: (a)

The presence of the XY chromosome indicates male child, while the XX chromosome develops into a female.

Question 99. Which of the following is not an example of a bio-mass energy source?

a. Wood
b. Gobar Gas
c. Nuclear energy
d. Coal

Answer: (c)

Biomass is the dead remains of living organisms or organic substances. Wood, gobar gas (biogas) are produced from biomass. Coal is produced by the carbonization of the dead and decaying plant and animal remains over millions of years ago and hence is a biomass product as well. Nuclear energy is produced by radioactive elements by their fission and fusion properties.

Question 100. In energy flow diagram of ecosystem, which trophic level lies at the bottom?

a. Primary Consumer
b. Producer
c. Tertiary Consumer
d. Decomposer

Answer: (b)

Producers lie at the bottom of an energy flow diagram/pyramid.