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

Paper: MAT

Question 1. Analyze the statement and find the correct answer.

A + B > C + D and B+ C > A + D, then it is definite that:

a. D > B
b. C > D
c. A > D
d. B > D

Answer: (d)

Given that

A + B > C + D …(i)

B + C > A + D …(ii)

Adding (i) and (ii), we get A + 2B + C > C + 2D + A

Therefore, option (d) is correct.

Question 2. Gopu ranks sixth from the top and twenty seventh from the bottom in a class. How many students are there in the class?

a. 31
b. 32
c. 33
d. 34

Answer: (b)

Given that Gopu ranks 6^th from the top and 27^th from the bottom.

So, Total No. of students = (6 + 27) – 1 = 32

Question 3. If the first September 2019 is Sunday, then first October 2019 will be:

a. Sunday
b. Monday
c. Tuesday
d. Wednesday

Answer: (c)

1^st September 2019: Sunday (given)

September has 30 days. So, 7(4) + 2.

Hence, Sunday + 2 = Tuesday on 1^st October 2019.

Question 4. If P means ‘division’, T means ‘addition’, M means ‘subtraction’ and D means ‘multiplication’, then what will be the value of the expression

12 M 12 D 28 P 7 T 15 ?

a. –21
b. –15
c. 15
d. 45

Answer: (a)

P → ÷

T → +

M → –

D → ×

12 M 12 D 28 P 7 T 15

12 – 12 × 28 ÷ 7 + 15

⇒ 12 – 48 +15 = –21

Question 5. Arrange the given words in a meaningful sequence and then choose the most appropriate sequence from amongst the alternatives provided below.

(a) Doctor

(b) Fever

(c) Prescribe

(d) Diagnose

(e) Medicine

a. (a), (d), (c), (b), (e)
b. (b), (a), (c), (d), (e)
c. (b), (a), (d), (c), (e)
d. (b), (d), (c), (e), (a)

Answer: (c)

Fever → Doctor → Diagnose → Prescribe → Medicine

Question 6. Let a, b, c and d be natural numbers such that a – 3012 = b + 3013 = c + 3014= d – 3015. Which one of the following is the smallest natural number ?

a. a
b. b
c. c
d. d

Answer: (c)

a – 3012 = b + 3013 = c + 3014 = d – 3015

a – 3012 = b + 3013; a > b

a – 3012 = c + 3014; a > c

a – 3012 = d – 3015; d > a

b + 3013 = c + 3014; b > c

Among the four, c is the smallest natural number.

Question 7. Find the missing number, if the series of figures follow a certain pattern.

a. 15
b. 12
c. 18
d. 20

Answer: (b)

Directions (Questions 8 to 11): Study the given figure carefully and answer the questions that follow. The figures given are square, circle,triangle and rectangle.

Question 8. Which number belongs to all figures

a. 3
b. 4
c. 6
d. None of these

Answer: (d)

There is no number that belongs to all figures. Therefore, option (d) is correct.

Question 9. What is the sum of the numbers which belong to two figures only?

a. 6
b. 15
c. 20
d. None of these

Answer: (c)

4 + 2 + 6 + 8 = 20

Question 10. What is the product of the numbers which belong to three figures only?

a. 90
b. 540
c. 440
d. None of these

Answer: (a)

10 × 9 = 90

Question 11. What is the sum of the numbers which belong to one figure only?

a. 43
b. 39
c. 41
d. None of these

Answer: (b)

1 + 3 + 5 + 7 + 11 + 12= 39

Question 12. A two – digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder?

a. 45
b. 36
c. 27
d. 9

Answer: (a)

94/49, Remainder = 45

Question 13. See the number matrix given below. Row wise or column wise, these numbers follow a certain rule. Identify this rule and find the missing number.

a. 21
b. 48
c. 59
d. 73

Answer: (d)

2³ + 1³ + 3³ = 36 (1^st column)

0³ + 4³ + 3³ = 91 (3^rd column)

3³ + 1³ + 0³ = 28 (4^th column)

⇒ 4³ + 2³ + 1³ = 73 (2^nd column)

Question 14. Find the missing term in the series:4, 8, 16, ? , 44, etc.

a. 24
b. 28
c. 32
d. 36

Answer: (b)

Question 15.In the following number series one term is wrong. Find the wrong term. 2,5,10,17,26,37,50,64

a. 17
b. 26
c. 37
d. 64

Answer: (d)

65 should have been there instead of 64.

Directions (Questions 16 to 20): Study the information given below and answer the questions that follow:

There are five persons A, B, C, D and E. One is a football player, one is a cricket player and one is a hockey player. A and D are unmarried ladies. They do not participate in any game. None of the ladies plays cricket or football. There is a married couple in which E is the husband. B is the brother of C and is neither a cricket player nor a hockey player.

According to the given data:

A and D are unmarried ladies: Neither of them played any of three games.

Since B is the brother of C, C is married to E.

1 Hockey Player (Married Lady) ➝ C

1 Cricket Player (Husband of C) ➝ E

1 Football Player (Brother of C) ➝ B

Question 16. Who is the football player?

a. A
b. B
c. C
d. D

Answer: (b)

E: Cricket, C: Hockey, B: Football

B (Brother of C) is a football player.

Question 17.Who is the hockey player?

a. A
b. B
c. C
d. D

Answer: (c)

E: Cricket, C: Hockey, B: Football

C (Married Lady) is the hockey player.

Question 18. Who is the Cricket player?

a. B
b. C
c. D
d. E

Answer: (d)

E: Cricket, C: Hockey, B: Football

E (Husband of E) is the Cricket Player.

Question 19. Who is the wife of E?

a. A
b. B
c. C
d. D

Answer: (c)

According to the given data, C is the wife of E.

Question 20. The three ladies are:

a. A, B, C
b. B, C, D
c. A, B, D
d. A, C, D

Answer: (d)

The three ladies are A and D (Unmarried ladies) and C (Married lady).

Question 21. Adarsh travels 10 km towards the North. From there, he travels 6 km towards the South. Then, he travels 3km towards the East. How far and in which direction is he with reference to his starting point?

a. 5 km west
b. 7 km west
c. 7 km east
d. 5 km north-east

Answer: (d)

K=√(4²+3² ) (By Pythagoras theorem)

=√(16+9) =√25= 5 km

Question 22. Which of the following words will come first, if the words are arranged alphabetically as in a dictionary?

Spine, Spinal, Spindle, Spinet

a. Spine
b. Spinal
c. Spindle
d. Spinet

Answer: (b)

Dictionary order:

Spinal

Spindle

Spine

Spinet

Question 23. Which term will replace the question mark in the series?

ABD, DFI, GJN, JNS, (?)

a. MRX
b. MRW
c. MQW
d. NRX

Answer: (a)

Question 24. Levan and Kushan walk around a circular park. They start at 7 a.m, from the same point in opposite directions. Levan walks at a speed of 2 rounds per hour. Kushan walks at a speed of 3 rounds per hour. How many times shall they cross each other after 7.00 a. m and before 8.30 a.m ?

a. 7
b. 6
c. 5
d. 4

Answer: (a)

Time duration = 7:00 am to 8:30 am

= 1.5 hour

Relative speed is

3 + 2 = 5 round in 1 hour

So, rounds in 1.5 hour = 7.5

They will cross 7 times.

Directions (Questions 25 and 26): In each question, a letter-number series is given. Find the next two terms in the series.

Question 25. D-4, F-6, H-8, J-10, ?-?

a. K-12
b. L-12
c. L-11
d. K-11

Answer: (b)

Question 26. O-24, L-20, I-16, F-12, (?-?)

a. C-6
b. D-8
c. E-6
d. C-8

Answer: (d)

Directions (Questions 27 and 28): In each of the following letter series, some of the letters are missing. Find the missing letters in the proper sequence from the four alternatives given.

Question 27._nmmn_mmn_mmnn_

a.nmmn
b.mnnm
c.nnmm
d.nmnm

Answer: BONUS

None of the letters in the options makes a meaningful sequence.

Sequence could have been: nnmm/nnmm/nnmm/nnm

Question 28. a_bccb_ca_cca_baab_c

a. ababc
b. abcaa
c. accab
d. bacaa

Answer: (a)

aabcc / bbcaa / ccabb / aabcc

Directions (Questions 29 to 31):

There is a relationship between the two terms to the left of : : . Find the missing one in the next pair holding the same relationship.

Question 29.Circle : Diameter : : Square : ____?

a. Volume
b. Area
c. Diagonal
d. Perimeter

Answer: (c)

Longest distance between any two points in a circle is of diameter. Similarly, in square, diagonal covers the longest distance.

Question 30. Mango : Fruit : : Potato : ____?

a. Root
b. Fruit
c. Stem
d. Flower

Answer: (c)

Mango is a fruit while potato is a modified stem.

Question 31. Deuce: Tennis : : Googly : ___?

a. Cricket
b. Football
c. Hockey
d. Polo

Answer: (a)

Deuce is related to Tennis and Googly is related to bowling in cricket.

Directions (Questions 32 and 33): There is a certain relationship between two numbers on one side of : : . One number is given on the other side. Identify the number having the same relationship in the first case.

Question 32. 3 : 243 : : 5 : ___?

a. 425
b. 465
c. 625
d. 3125

Answer: (d)

3⁵ = 243

5⁵ = 3125

Question 33. 25 : 37 : : 49 : _____?

a. 41
b. 65
c. 56
d. 60

Answer: (b)

5² : 6² + 1 : : 7² : (8² + 1) ⇒ 65

Directions (Questions 34 to 36):Choose the odd word which is least like the other words in the group.

Question 34.

a. Copper
b. Zinc
c. Brass
d. Aluminium

Answer: (c)

Copper, zinc and aluminium are metals while brass is an alloy.

Question 35.

a. Calendar
b. Year
c. Date
d. Month

Answer: (a)

All three (Year, Month, Date) are in a calendar.

Question 36.

a. Trunk
b. Tree
c. Fruit
d. Leaf

Answer: (b)

Trunk, Fruit and Leaf are parts of a tree.

Directions (Questions 37 to 40): Read the following information carefully and answer the questions given below.

Rahul and Krishnan are good in Cricket and Volleyball. Sachin and Rahul are good in Cricket and Hockey. Ganesh and Krishnan are good in Kabaddi and Volleyball. Sachin, Ganesh and Michel are good in Kabaddi and Football.

According to the given data, the following can be inferred.

Question 37. Who is good in Cricket, Hockey and Volleyball?

a. Sachin
b. Krishnan
c. Rahul
d. Ganesh

Answer: (c)

Question 38. Who is good in Kabaddi, Cricket, Hockey and Football?

a. Sachin
b. Krishnan
c. Ganesh
d. Rahul

Answer: (a)

Question 39. Who is good in Kabaddi, Volleyball and Football ?

a. Sachin
b. Krishnan
c. Rahul
d. Ganesh

Answer: (d)

Question 40.Who is good in all the five games?

a. Rahul
b. Sachin
c. Krishnan
d. None of them

Answer: (d)

According to the given data, none of them are good in all the five games.

Directions (Questions 41 and 42):

Read the following information and answer the questions given below it.

‘A + B’ means ‘A is the daughter of B’;

‘A × B’ means ‘A is the son of B’;

‘A – B’ means ‘A is the wife of B’.

Question 41. If P × Q – S, which of the following is true ?

a. S is wife of Q
b. S is father of P
c. P is daughter of Q
d. Q is father of P

Answer: (b)

P × Q – S

Question 42. If T – S × B – M, which of the following is not true?

a. B is mother of S
b. M is husband of B
c. T is wife of S
d. S is daughter of B

Answer: (d)

T – S × B – M

Question 43. The average age of three students and the teacher is 24 years. All the three students are of the same age. The difference between the age of the teacher and each student is 28 years. What is the age of the teacher?

a. 35 years
b. 36 years
c. 40 years
d. 45 years

Answer: (d)

Let the age of the teacher be x.

Then,the age of student = x – 28

Average age = ((x-28)×3 + x)/4

⇒ 24=(3x-84 + x)/4

⇒ 96 = 4x – 84

⇒ 4x =180

x = 45

Directions (Questions 44 to 47): Read the following information carefully and answer the following questions.

In a certain coding system,

816321 means ‘the brown dog frightened the cat’

64851 means ‘the frightened cat ran away’

7621 means ‘the cat was brown’

341 means ‘the dog ran’

According to the given information,

1 → the

2 → brown

3 → dog

4 → ran

5 → away

6 → Cat

7 → was

8 → frightened

Question 44. What is the code for – ‘ the dog was frightened’?

a. 5438
b. 8263
c. 1378
d. None of these

Answer: (c)

The code for ‘The dog was frightened’ will be 1378.

Question 45. What is the code for – ‘ Frightened’?

a. 2
b. 3
c. 6
d. 8

Answer: (d)

According to the given information, the code for ‘Frightened’ will be 8.

Question 46. What is the code for – ‘away’ ?

a. 1
b. 5
c. 6
d. 7

Answer: (b)

According to the given information, the code for ‘away’ will be 5.

Question 47. What is the code for-‘ brown’?

a. 2
b. 4
c. 6
d. 8

Answer: (a)

According to the given information, the code for ‘brown’ will be 2.

Directions (Questions 48 and 49): Two statements followed by II or III conclusions are given below. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Question 48. Which of the given conclusions logically follows from the two given statements?

Statements :

All film stars are playback singers.

All film directors are film stars.

Conclusions:

I. All film directors are playback singers.

II. Some film stars are film directors.

a. If only conclusion I follows.
b. If only conclusion II follows.
c. If both conclusions I and II follow.
d. If neither conclusion I nor II follow.

Answer: (c)

Therefore, option (c) is correct.

Question 49. Which of the given conclusions logically follows from the two given statements?

Statements :

All politicians are honest.

All honest people are fair.

Conclusions:

I. Some honest are politicians.

II. No honest is a politician.

III. Some fair are politicians.

a. None follows.
b. Only I follows.
c. Only I and II follows.
d. Only I and III follows.

Answer: (d)

Therefore, option (d) is correct.

Directions (Questions 50 and 51): Study each of the following tables and choose the alternative which can best replace the ? mark.

Question 50. Choose the corrective alternative.

a. 5
b. 1
c. 8
d. 6

Answer: (a)

4 x 3 = 12

7 x 6 = 42

10 x 9 = 90

2 x 1 = 2

5 x 4 = 20

3 x 2 = 6

Question 51. Choose the corrective alternative.

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

Answer: (c)

1 + 2 + 1 = 4 (2²)

2 + 5 + 2 = 9 (3²)

3 + 12 + 1 = 16 (4²)

5 + 15 + 5 = 25 (5²)

6 + 25 + 5 = 36 (6²)

Sum of all entries of each column = Perfect square

So, 4 + 10 + 2 = 16

Directions (Questions 52 and 53): Study the information given below and answer the questions that follow.

There are 40 students admitted to a nursery class. Some students can speak only Malayalam and some can speak only English. 6 students can speak both Malayalam and English. The number of students who can speak English is 16.

Question 52. How many students can speak only English?

a. 6
b. 8
c. 10
d. 12

Answer: (c)

Total Students = 40

B = 6

A + B = 16

Thus, A = 10.

Students who speak only in English are 10.

Question 53.How many students can speak only Malayalam?

a. 30
b. 24
c. 34
d. 22

Answer: (b)

Total students = 40

Students who speak only Malayalam = Total students – Student who speak English

= 40 – 16

=24

Directions (Questions 54 and 55): Find the next figure in the series shown as Problem figures. Choose your answer from Answer figures.

Question 54.Problem figures

Answer: (b)

Question 55. Problem figures:

Answer: (c)

Question 56. Examine the pattern and find the missing one.

a. 12
b. 24
c. 10
d. 16

Answer: (d)

Question 57. Four figures are given below. Three of them are alike. One is different. Identify the different one.

Answer: (c)

All lines apart from diagonal are either vertical or horizontal,except in option (c)

Question 58. If HEALTH is written as GSKZDG, then how will NORTH be written in that code?

a. OSUI
b. GSQNM
c. FRPML
d. IUSPO

Answer: (b)

Question 59. If in a certain code LUTE is written as MUTE and FATE is written as GATE, then how will BLUE be written in that code?

a. CLUE
b. GLUE
c. FLUE
d. SLUE

Answer: (a)

Question 60. In a coding system A = 26, SUN = 27, then CAT = ?

a. 24
b. 27
c. 57
d. 58

Answer: (c)

A = 26 = Z (Value of A is reversed with the last letter)

Question 61. Five bells begin to toll together and toll respectively at intervals of 6,5,7,10 and 12 seconds. How many times will they toll together in one hour excluding the one at the beginning?

a. 7 times
b. 8 times
c. 9 times
d. 11 times

Answer: (b)

All the 5 bells toll together at the interval of 5, 6, 7, 10 and 12 seconds respectively.

LCM of these intervals comes out to be 420 seconds.

Hence, this implies that the total number of times they toll together in one hour excluding the one at the beginning is 8 times.

Question 62. How many squares are there in the figure?

a. 18
b. 14
c. 10
d. 9

Answer: (b)

Question 63. Find the correct mirror image of

Answer: (d)

Question 64. Choose the correct mirror image from the alternatives given below:

Answer: (c)

Question 65. Find out which of the answer figures completes the figure matrix.

Answer: (a)

All shapes are in cyclic manner, i.e. 1,2,3; 2,3, 1; 3,2,1.

Directions (Questions 66 to 69): A cube is coloured white on all faces. Then it is cut into 64 smaller cubes of equal size. Now, answer the following questions based on this statement.

According to the given information:

Total cubes = 64

Three white face coloured cubes = 8

Two white face coloured cubes = 24

One white face coloured cubes = 24

Question 66. How many cubes have no face coloured?

a. 24
b. 16
c. 8
d. 4

Answer: (c)

Cubes with no face coloured = Total Cubes – [Cubes with coloured faces]

= 64 – [8 + 24 + 24]

= 64 – 56

= 8

Question 67. How many cubes are there which have only one face coloured?

a. 4
b. 8
c. 16
d. 24

Answer: (d)

Total one face coloured cubes = 4 x 6 = 24

Question 68. How many cubes have two white opposite faces?

a. 0
b. 8
c. 16
d. 24

Answer: (a)

There is no cube which has two white opposite faces.

Question 69. How many cubes have 3 faces coloured?

a. 24
b. 16
c. 8
d. 4

Answer: (c)

Cubes with three faces coloured = 8 (Present at the edges of the bigger cube)

Question 70. Three persons A,B,C are standing in a queue. There are 5 persons between A and B and 8 persons between B and C. If there are 3 persons ahead of C and 21 behind A, what could be the minimum number of persons in the queue?

a. 27
b. 28
c. 40
d. 41

Answer: (b)

So, minimum number of persons in queue = 28

Question 71. In the table, the numbers in rows follow a rule. Identify the rule and find the missing number.

a. 5
b. 9
c. 10
d. 11

Answer: (b)

Directions (Questions 72 to 75): Three different positions X, Y, Z of a dice are shown in the figures. Answer the following questions which are based on these figures.

According to the given information,

6 is opposite to 1.

4 is opposite to 2.

3 is opposite to 5.

Question 72. Which number lies at the bottom face in position (X)?

a. 2
b. 3
c. 6
d. Cannot be determined

Answer: (b)

From the figure, we can infer that 4, 1, 6 and 2 lie adjacent to number 5. Hence, the only number left is 3. Therefore, we can conclude that number 3 lies at the bottom face in position ‘X’.

Question 73. Which number lies at the bottom face in position (Y)?

a. 1
b. 2
c. 5
d. Cannot be determined

Answer: (b)

2 is opposite to 4. Thus, 2 is at the bottom face in position (Y).

Question 74. Which number lies opposite 6?

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

Answer: (a)

According to the given information, 1 lies opposite to 6.

Question 75. Which numbers are opposite to the numbers 6 and 5 in position (Z)?

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

Answer: (b)

From figure X and Y, we can infer that 6 is adjacent with 4, 3, 2 and 5. Hence, number 1 is opposite to 6. Similarly, 4,1,6 and 2 lie adjacent to number 5. Therefore, 3 is the opposite face of 5.

Question 76. With reference to the figure (X), the number of different routes from A to B without retracing from C and D is:

a. 3
b. 6
c. 9
d. 18

Answer: (d)

Possible different routes if one takes [1] Path:

Similarly, there will total 6 different paths each if one takes [2] and [3] paths.

Thus, in total, there will be 18 different routes.

Question 77. The elements of the problem figures given below are changing with certain- rules as we observe them from left to right. Find the next figure from the answer figures.

Problem figures:

Answer: (a)

Triangles vertically flip and move anti-clockwise along the corners.

Directions (Questions 78 to 82): Read the given information carefully. Then answer the questions that follow.

Video classes on 5 subjects – Malayalam, English, Maths, Social Science and Science have to be arranged in a week from Monday to Friday. Only one class can be arranged in a day. Malayalam cannot be scheduled on Tuesday. English teacher is available only on Tuesday. Maths class has to be scheduled immediately after the day of Malayalam class. Social Science class has to be scheduled immediately before the day of Malayalam class.

According to the given information, the following data can be interpreted.

Question 78. Which class is scheduled for Monday?

a. Maths
b. Malayalam
c. Science
d. Social Science

Answer: (c)

Question 79. Which class is scheduled between Maths and Social Science?

a. Malayalam
b. Science
c. English
d. No class

Answer: (a)

Question 80. Which class is the last one in the week?

a. Social Science
b. Science
c. Malayalam
d. Maths

Answer: (d)

Question 81.Which class is scheduled on Wednesday?

a. Malayalam
b. Maths
c. Social Science
d. Science

Answer: (c)

Question 82.Which class is scheduled before Maths class?

a. Malayalam
b. Social Science
c. English
d. Science

Answer: (a)

Question 83. Consider the following figure and answer the question that follows.

A square is divided into four rectangles as shown. The length of the sides of rectangles are natural numbers. The areas of two rectangles are 30 sq.cm and 72 sq.cm as marked in the figure. Then what is the length of each side of the square in cm?

a. 15
b. 14
c. 17
d. 12

Answer: (b)

Let l and b be the length and breadth of the rectangle with area 32 sq. cm.

Let l’ and b’ be the length and breadth of the rectangle with area 72 sq. cm.

l x b = 30

l’ x b’ = 72

Now, l + l’ = b + b’ ( Since sides of the square are equal)

Thus, the values can be:

5 x 6 = 30

9 x 8 = 72

(5 + 9) = (6 + 8)

So, side of square = 14 cm

Question 84. Four cardboard pieces of specific shapes are shown in the following figure.

Which of the following figures given can be formed by joining these pieces together?

Answer: (d)

Directions (Questions 85 to 87): In each of the following questions, various terms of an alphabet series are given with one term missing as shown by (?). Choose the missing term from the alternatives.

Question 85. K, N, Q, T, (?)

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

Answer: (c)

Question 86. Y, B, T, G, O, (?)

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

Answer: (b)

Question 87. p s r t w v x ? z

a. y
b. b
c. u
d. a

Answer: (d)

Question 88. Choose the odd number pair which is different from others.

a. 5, 13
b. 2, 17
c. 3, 8
d. 7, 11

Answer: (c)

All pairs are prime except (3, 8).

Question 89. Choose the odd word which is different from others.

a. IMF
b. SAARC
c. UNICEF
d. WHO

Answer: (b)

All except SAARC are world organisations.

Directions (Questions 90 to 92): There is a certain relationship between two given numbers on one side of : : . Identify this relationship and find the missing number on the other side.

Question 90. 7:56 : : 9 : ?

a. 63
b. 81
c. 90
d. 99

Answer: (c)

Question 91. 26 : 5 : : 65 : ?

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

Answer: (c)

Question 92. 5 : 36 : : 7 😕

a. 64
b. 55
c. 63
d. 56

Answer: (a)

Question 93. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?

a. 5
b. 11
c. 12
d. 13

Answer: (c)

Set of all integer between 1 and 100, which have 4 as a digit but not divisible by 4:

{14,34,54,74,94,41,42,43,45,46,47,49}

So, number of elements in set = 12

Question 94. If × means –, + means ÷, – means × and ÷ means +, then 15 – 2 ÷ 900 + 90 × 100 = ?

a. 60
b. –60
c. 90
d. –90

Answer: (b)

Given that

× → –

– → ×

÷ → +

+ → ÷

15 – 2 ÷ 900 + 90 × 100

= (15 × 2) + (900 ÷ 90) – 100

= 30 + 10 – 100

= –60

Question 95. If ‘when’ means ‘×’,’you ‘ means ‘÷’, ‘come’ means ‘–’ and ‘will’ means ‘+’, then what will be the value of”8 when 12 will 16 you 2 come 10″ ?

a. 94
b. 45
c. 112
d. 96

Answer: (a)

Given that when → x, you → ÷, come → –, will → +

‘ 8 when 12 will 16 you 2 come 10’

⇒ 8 × 12 + 16 ÷ 2 –10

= 8 × 12 + 8 –10

= 96 + 8 – 10

=104 –10

= 94

Question 96. There are Deer and Peacocks in a Zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?

a. 60
b. 50
c. 30
d. 20

Answer: (a)

Let the no. of deer = x and no. of peacocks = y

x + y = 80 …(1)

4x + 2y = 200 …(2)

Solving 1 and 2, we get:

4x + 2 (80 – x) = 200

4x + 160 – 2x = 200

2x = 40

x = 20

Putting the value of x, in (1), we get y = 60.

Thus, the total number of peacocks are 60.

Directions (Questions 97 and 98): Read the information carefully and answer the questions that follow:

A, B, C, D and E are sitting around a circular table. C is to the immediate right of A and is second to the left of D. E is not between A and D. Then:

According to the given, the sitting arrangement will be as shown:

Question 97. Who is between C and D?

a. A
b. B
c. E
d. Cannot be determined

Answer: (c)

According to the given data, E is between C and D.

Question 98. Who is second to the left of C?

a. A
b. B
c. D
d. E

Answer: (b)

According to the given data, B is second left to C.

Question 99. What is the correct mirror image of

Answer: (a)

Question 100. If 18^th February 2005 falls on Friday, then what will be the day on 18^th February, 2007?

a. Sunday
b. Monday
c. Tuesday
d. Wednesday

Answer: (a)

18/02/2005 → Friday

↓ +1

18/02/2006 → Saturday

↓ +1

18/02/2007 → Sunday

Kerala NTSE 2021 Stage 1 SAT Paper

PAPER – SAT

Question 1. Which of the following is regarded as a political contrivance intended to reconcile National Unity with the maintenance of State’s right?

a. Panchayati Raj
b. Secularization
c. Federalism
d. Bicameralism

Answer: (c)

Federalism is an institutional mechanism to accommodate two sets of polities—one at the regional level and the other at the national level. It ensures the rights of the state while maintaining national unity.

Question 2. Identify the right bank tributary of River Ganga.

a. Gomati
b. Gandek
c. Kosi
d. Son

Answer: (d)

The Ganga is one of the main rivers that flow in the northern plain of India. Multiple tributaries join Ganga through its course. The right bank tributaries of Ganga river are the Yamuna, Son, Punpun and Damodar.

Question 3. Sort out the wrong statement, on the impact of an increase in the irrigation credit facilities in the agriculture sector.

a. It can remove the underemployment in the same sector
b. Can stimulate commercial activities
c. It can stimulate industries in the urban centres
d. Can revive small scale village industries

Answer: (c)

Irrigation plays a vital role in agricultural and allied activities. Increase in the irrigation credit facilities provides capital to develop irrigation facilities, thus positively impacting the production. Eventually, it can help in the growth of employment in the agricultural sector and it will boost other commercial activities in the region. It can also help in the revival of other small scale village industries. But, it may have limited direct impact on the industries in urban centres.

Question 4. Who was Not a member of the States Reorganisation Commission constituted in 1953 ?

a. H. N. Kunzru
b. K.M. Panicker
c. V.P. Menon
d. Fazl Ali

Answer: (c)

In 1953, then Prime Minister of India, Jawaharlal Nehru, constituted a State Reorganisation Commission to recommend the reorganisation of state boundaries. It was a three-member commission having H. N. Kunzru, K.M. Panicker and Fazl Ali as its members. V.P. Menon was not a member of this commission.

Question 5. HDI is indexed on the basis of :

a. Health, Education status and GDP
b. Per Capita Income, Environment and Health status
c. Average Income, Health and Educational status
d. None of the above

Answer: (c)

The Human Development Index (HDI) is a statistical tool used to measure individual human development in each country. It was developed and compiled by the United Nations Development Programme. It is calculated or indexed on the basis of average income, health and educational status of a country’s population.

Question 6. The name of some leaders of the Revolt of 1857 and the places where they led the revolt are noted below.

Match them correctly.

Leaders Places

1) Nana Sahib i) Awadh

2) Birjis Qadr ii) Bareilly

3) Maulvi Ahmadullah iii) Kanpur

4) Khan Bahadur khan iv) Faizabad

1. 2. 3. 4.

a. (iii) (ii) (iv) (ii)
b. (iii) (iv) (ii) (i)
c. (iv) (i) (iii) (ii)
d. (iii) (i) (iv) (ii)

Answer: (d)

There was a widespread uprising across India against the British in 1857. It is popularly known as the Revolt of 1857. Nana Sahib of Kanpur, Birjis Qadr of Awadh, Maulvi Ahmadullah of Faizabad, Khan Bahadur Khan of Bareilly were some of the leaders of the revolt.

Question 7. Who is the founder of the self Respect Movement ?

a. C.R Das
b. E. V. Ramaswami Naicker
c. Vaikunda Swamikal
d. Veeresalingam

Answer: (b)

E. V. Ramaswami Naicker founded the Self-Respect Movement in Tamil Nadu in 1925. He was against Brahmanical supremacy and caste system.

Question 8. Indian Parliament consists of :

a. Indian President, Lok Sabha and Rajya Sabha
b. Lok Sabha, Rajya Sabha and Cabinet Ministers
c. Indian President, Prime Minister and Lok Sabha
d. Lok Sabha and Rajya Sabha

Answer: (a)

The Constitution of India provides for a bicameral Parliament consisting of the President and the two Houses. The two Houses are known as the Council of States (Rajya Sabha) and the House of the People (Lok Sabha).

Question 9. The Net attendance ratio can be obtained when :

a. The total number of children in the age group of 14-15 years is divided by the total number of children attending school in the same age group.
b. The total number of children attending school in the age group of 14-15 years is divided by the total number of children in the same age group.
c. The total number of children attending school in the age group of 15-16 years is divided by the total number of children in the same age group.
d. None of the above

Answer: (b)

The Net attendance ratio is used to understand the educational status of a country. It is used to calculate the number educated individuals in the same age category. It can be obtained when the total number of children attending school in the age group of 14-15 years is divided by the total number of children in the same age group.

Question 10. State in India with the lowest density of population as per 2011 census:

a. Sikkim
b. Arunachal Pradesh
c. Rajasthan
d. Mizoram

Answer: (b)

According to the census of 2011, Arunachal Pradesh has the lowest population density in India. The state has 17 persons per square kilometre.

Question 11. In a topographical map of scale 1 : 50000, each square grid with 2 cm length and 2 cm breadth represents an actual area :

a. 4 sq. km
b. 16 sq. km
c. 2 sq. km
d. 1 sq. km

Answer: (d)

2 x 2 x 5000= 10000 sq. cm which is 1 sq.km

Question 12. Identify the Fourteenth point of the ‘Fourteen points’ of woodrow Wilson.

a. Division of Germany
b. Disarmament of Italy
c. Creation of the League of Nations
d. Division of Austria

Answer: (c)

Fourteen Points of the U.S. President Woodrow Wilson’s was the proposal for a post-war peace settlement. It was outlined for peace negotiations to end World War I. Wilson’s fourteenth point suggested the formation of a general association of nations.

Question 13.The average income of Kerala is less than that of Haryana. But Haryana’s social indices are below than Kerala. This can be reasoned on the fact that :

a. Kerala employ more people in the organised sector
b. Foreign remittance of Kerala is higher
c. Private consumption goods are cheaper in Kerala
d. Collective goods are cheaper in Kerala

Answer: (d)

Although the average income of Kerala is less than that of Haryana, the latter’s social indices are below than the former’s. This can be attributed to the fact that collective goods are cheaper in Kerala. Collective goods, also known as public goods, comprise health, education and other public services. Availability to collective goods help improve the social indices of a state.

Question 14. Total Geographical area of India is :

a. 3.28 million sq. km
b. 32.8 million sq. km
c. 3.28 lakh sq. km
d. 328 lakh sq. km

Answer: (a)

The mainland of India, extends from Kashmir in the north to Kanyakumari in the south and Arunachal Pradesh in the east to Gujarat in the west. It is the seventh-largest country in the world with its area of 3.28 million sq. km.

Question 15. The typical soil type found in the Deccan trap region in India :

a. Black soil
b. Red Soil
c. Alluvial soil
d. Laterite soil

Answer: (a)

The Deccan Traps region, which covers parts of Maharashtra, Madhya Pradesh, Gujarat, Andhra Pradesh, and some portions of Tamil Nadu, has black soil. These soils are also known as the ‘Regur Soil’ or the ‘Black Cotton Soil’.

Question 16. The Fundamental Right which B.R. Ambedkar considered as the heart and soul of Indian Constitution

a. Right to Equality
b. Right to Freedom
c. Right to Constitutional Remedies
d. Cultural and Educational Rights

Answer: (c)

Article 32 of the Indian Constitution provides the Right to Constitutional Remedies. Ambedkar termed this right as ‘the heart and soul of the Constitution’. It highlights this provision’s significance, as the mere declaration of the fundamental right without guaranteed remedial right to enforce the fundamental rights would have been meaningless. It allows people the right to approach the Supreme Court for the protection of their fundamental rights.

Question 17. Some events that happened after the First World War are given below. Identify the correct chronological order of them.

1. Attack on Pearl Harbour

2. D Day

3. The Munich Pact

4. The Soviet -German Non-Aggression Pact

(a) 4, 3, 1, 2
(b) 3, 4, 1, 2
(c) 3, 1, 4, 2
(d) 3, 1, 2, 4

Answer: (b)

Question 18. Who were ‘Dhangars’ ?

a. Zamindars of Bengal
b. Pastoral community of Maharashtra
c. Peasants of Bengal
d. Peasants of Punjab

Answer: (b)

The Dhangars are Pastoral community of Maharashtra, who live mostly in Western Maharashtra and Marathwada. The population is estimated to be around one crore – or about 9% of Maharashtra’s population.

Question 19. Pick out the true pair from the statements on the ‘Debt trap’ Situation.

1. Credit pushes a person to the situation in which recovery is not possible

2. The loan is taken from a village moneylender at an exorbitant rate of interest.

3. Earnings are not enough to cover the repayment

4. It happens due to heavy crop failures in the current year

(a) 1, 2

(b) 2, 4

(c) 1, 3

(d) 1, 4

Answer: (c)

A ‘Debt trap’ is a situation in which the borrower is stuck in a cycle of borrowing and re-borrowing to an extent where recovery is not possible. This is because his earnings are not sufficient to repay the debt, so he chooses to re-borrow and enter the trap.

Question 20. Which among the following is not a characteristic feature of the Hot weather season in India?

a. Hot dry winds called Loo
b. Mango Showers
c. Kalbaisakhi
d. Inflow of temperate cyclones

Answer: (d)

The hot weather season is characterised by ‘loo’, a strong, gusty, hot, dry winds blowing during the day over the north and northwestern India. Localised thunderstorms, associated with violent winds, torrential downpours, often accompanied by hail, are also common. In West Bengal, these storms are known as the ‘Kaal Baisakhi’. By the end of the hot weather season, pre-monsoon showers are common especially, in Kerala and Karnataka. It helps in the ripening of mangoes, thus often referred to as ‘mango showers’.

Question 21. Identify the capital of the Abbasids.

a. Baghdad
b. Damascus
c. Medina
d. Cairo

Answer: (a)

The Abbasids were one of the two great dynasties of the Muslim Empire of the caliphate. They deposed the Umayyad caliphate in 750 CE. The capital was also shifted from Damascus to Baghdad.

Question 22. Which among the following is the correct pair ?

a. Bhilai steel Plant – Britain
b. Rourkela steel plant – Soviet Union
c. Bokaro Steel plant – Soviet Union
d. Durgapur Steel plant – West Germany

Answer: (c)

Within a few decades of independence, India established four integrated steel plants with foreign countries’ collaboration. The Rourkela Steel plant in Orissa in collaboration with Germany in 1959. Bhilai Steel Plant in Chattisgarh was established in the same year with the Soviet Union’s collaboration. In 1962, Durgapur Steel Plant in West Bengal in collaboration with the United Kingdom. Another steel plant came up with the Soviet Union’s collaboration in Bokaro, Jharkhand, in 1964.

Question 23. Evaluate the statements regarding sugarcane cultivation in India and choose the correct statements

(1) Requires hot and humid climate

(2) India is the second largest producer

(3) Gujarat is the largest producer in India

(a) (1), (2) and (3) are correct
(b) (1), (2) and (3) are wrong
(c) (1) and (3) are correct but (2) is wrong
(d) (1) and (2) are correct but (3) is wrong

Answer: (d)

Sugarcane is a tropical as well as a subtropical crop. It requires a hot and humid climate with a temperature of 21°C to 27°C and annual rainfall between 75 cm. and 100cm. India stands in second place in sugar production after Brazil. In India, Uttar Pradesh is the largest sugarcane producing state.

Question 24. Bhakra dam is built on :

a. Satluj river
b. Mahanadi river
c. Kosi river
d. Narmada river

Answer: (a)

Bhakra Dam is the 2nd highest dam in India after the Tehri dam. It is also the tallest straight gravity dam in the world. It is constructed on the Satluj river and located in Himachal Pradesh and Punjab border near Nangal city.

Question 25. Which one of the statements is applicable to Rigid Constitution?

a. It contains no provision for amendment
b. It is easy to make amendments
c. It must be an unwritten constitution
d. It requires special procedure for amendments

Answer: (d)

The rigidity of constitutions is based on Amenability. If the constitutional laws and ordinary laws are amended in separate ways, it is a rigid constitution. A rigid constitution requires a special procedure for amendments. An example of a rigid constitution is the Constitution of the United States of America.

Question 26. Pick out the appropriate answer from the statements given, on the nature of employment in the unorganised sector.

a. Regular employment but low paid
b. Low paid but secured
c. Better working environment
d. None of the above

Answer: (d)

Unorganised sector does not provide regular employment. The jobs in this sector are also low paid. It does offer any job security or benefits. Working environments in the unorganised sector are mostly unhealthy and sometimes pose a threat to the life of the workers. This sector also faces the challenges of migration.

Question 27. The power of Judicial Review originated in :

a. India
b. Britain
c. U.S.A
d. Switzerland

Answer: (c)

Judicial review refers to the judiciary’s power to examine the actions of the legislative, executive, and administration to determine whether such actions are consistent with the constitution. The constitutional judicial review began in the United States during 1801–35, in the Marbury vs Madison case.

Question 28. The southern most hilly ranges of Northern mountains

a. Karakoram
b. Himadri
c. Shiwaliks
d. Zaskar

Answer: (c)

The northern mountain range, which includes the Himalayan range, is divided into three ranges from north to south. The outer or southernmost range of the Himalayas is called the Shiwaliks. These ranges are formed of unconsolidated sediments brought down by rivers.

Question 29. An important mineral largely obtained from the beach sands of Kerala:

a. Uranium
b. Dolomite
c. Lignite
d. Monazite

Answer: (d)

Thorium, a radioactive metal, is mainly obtained from monazite sands. Monazite is a crucial mineral largely obtained from the beach sands of Kerala.

Question 30. Mandal commision Report is related to :

a. Reservation to Backward classes
b. Centre-State relations
c. Panchayati Raj
d. Monazite

Answer: (a)

The Mandal Commission was set up on January 1, 1979, under the chairmanship of BP Mandal. In its report submitted on December 31, 1980, it recommended the reservation to Backward Classes in employment and central educational institutions.

Question 31. The First Lokpal of India :

a. Justice Y.V. Chandrachud
b. Justice Pinaki Chandra Ghose
c. Justice Ranjan Gogoi
d. Justice Pradip kumar Mohanty

Answer: (b)

Shri Justice Pinaki Chandra Ghose is the first Lokpal of India. He is a former Judge of India’s Supreme Court and was a sitting member of the National Human Rights Commission.

Question 32. The first Round Table conference was held in :

a. New Delhi
b. Calcutta
c. Paris
d. London

Answer: (d)

The First Round Table Conference was held in London. It was convened from November 12, 1930 to January 19, 1931. It was orchestrated by the Labour Party led British government to ponder and bring about constitutional reforms in India.

Question 33. Which among the following is wrongly related ?

a. East India association – Dadabhai Naoroji
b. Forward Bloc – Subhash Chandra Bose
c. Poona Sarvajanik sabha – Justice Ranade
d. Ghadar Party – Khan Abdul Gaffer khan

Answer: (d)

Ghadar Party was a political movement founded by expatriate Indians in the United States to overthrow the British rule in India in the early twentieth century. Its founders were Lala Har Dayal, Sant Baba Wasakha Singh Dadehar, Baba Jawala Singh, Santokh Singh and Sohan Singh Bhakna.

Khan Abdul Gaffer Khan is also known as the ‘Frontier Gandhi’. He was a devout disciple of Mahatma Gandhi.

Question 34. Identify the planetary wind from the given hints.

Hints :

• Blows from sub-trophical high to sub polar lows
• Known as Roaring forties, Furious fifties or shrieking sixties

a. Trade winds
b. Westerlies
c. Polar winds
d. Monsoon winds

Answer: (b)

Westerlies are the winds that blow from the west to east in the mid-latitudes between 30° and 60°, they blow from subtropical high to subpolar lows. These winds are known by the names of the latitudes where they blow, the Roaring forties, Furious fifties or shrieking sixties.

Question 35. Which was the first country in Asia to industrialize ?

a. Japan
b. China
c. Vietnam
d. Singapore

Answer: (a)

Japan was the first country in Asia to industrialize. At present, it is one of the largest national economies in the world.

Question 36. Pick out the false pair from the statement on the working of SHGS, given below.

(1) Provides credit without collateral securities

(2) Concerned of health and family welfare activities.

(3) SHG loans cannot be used for the release of mortgaged land.

(4) No interest rate is charged on loans.

a. (3), (4)
b. (1), (2)
c. (1), (3)
d. (1), (4)

Answer: (a)

SHGs stand for Self Help Groups. These are informal small associations of people with similar socio-economic backgrounds who come together to help each other. Members of the group are provided credit without any collateral securities. These groups also help in conflict resolution and prove effective in the collective advancement of the poor and marginalised.

Question 37. The finest iron ore with nearly 70% iron content being mined in India

a. Siderite
b. Hematite
c. Magnetite
d. Limonite

Answer: (c)

India has good quality iron ore reserves which include Magnetite, Hematite etc. Magnetite is the finest iron ore with very high iron content, up to 70 per cent. It has excellent magnetic qualities and is used in the electrical industry.

Question 38. In Saudi Arabia voting right was extended to women in the year :

a. 2005
b. 2015
c. 2016
d. 2019

Answer: (b)

Prior to 2015, the Saudi women were not allowed to vote. In the country’s history, Saudi women casted their first ever votes during the municipal elections held in 2015.

Question 39. The Gross Domestic product of a country is :

a. The sum total of values of all primary intermediate and final goods and services
b. The sum total of values of all primary and final goods and services
c. The sum total of values of all final goods and services produces during the current year
d. The sum total of values of all goods produces during the current year

Answer: (c)

The Gross Domestic Product (GDP) of a country is the sum total of values of all final goods and services produces during the current year. It is a tool used to estimate the growth rate and size of the economy.

Question 40. The loans provided by the Mughal state was known as

a. Zat
b. Taccavi
c. Sawar
d. Jama

Answer: (b)

The loans provided by the Mughal state were known as the Taccavi. These loans were advanced to the villagers following a disastrous famine or other natural calamities.

Question 41. In a hall there are 10 doors in how many ways can a man enter the hall through one door and come out through a different door?

a. 100
b. 110
c. 80
d. 90

Answer: (d)

No. of ways to enter = 10

No. of ways to exit = 9

So, total no. of ways = 10 x 9 = 90.

Therefore, option (d) is correct.

Question 42. In a parallelogram the length of two sides and one diagonal are 7 cm,√23 cm and 6 cm respectively. Find the length of the other diagonal.

a. 8
b. 6 √3
c. 6√2
d. 7√2

Answer: (b)

Let the sides of the parallelogram be l, b and diagonals be d₁, d₂.

Using formula:

2(l₂ + b₂) =d₁² + d₂²

⇒2[7² + (√23) ²] = 6² + d₂²

⇒2[49+23]=36+d₂²

⇒ 144 – 36 = d₂²

⇒d₂² = 108

⇒ d₂ = 6√3

Question 43. If one root of a quadratic equation is 2 +√5, then the equation is :

a. x²+ 4x +1= 0
b. x² – 4x –1= 0
c. x² – 4x +1= 0
d. x² + 4x –1= 0

Answer: (b)

Since, Rational roots are come is pair, if one root is a + √b then another is a –√b.

So, root are (2+√5) and (2–√5).

Now, Sum of root = 2 + √5+ 2 – √5 = 4

And, product of roots = (2+√5)(2–√5)=4 – 5 = – 1

Hence, required equation is x² – 4x – 1 = 0.

Question 44. The first ten natural numbers are squared, each is then multiplied by 2 and 1 is added to each. Find the average of the resulting number.

a. 38.5
b. 78
c. 78
d. 39

Answer: (b) and (c)

Sum of squares of first 10 natural number

⇒n(n+1)(2n+1) / 6

⇒10(10+1)(2×10+1) / 6

⇒10×11×21 / 6

⇒ 5 × 11 × 7 ⇒ 385

Now,

Mean = [2×385+10]/ 10 ⇒ 78

Therefore, option (b) and (c) are correct, since both are given as 78

Question 45.The figure given below has a square of 1 unit and equal sector centred at each vertex. What is the diameter of the shaded circle ?

a.√2–1
b.√3– 1
c.0.41
d.0.732

Answer: (a)

In ΔADC

AD² + DC² = AC² (By Pythagoras theorem)

⇒ 1² + 1² = AC²

⇒ AC=√2

⇒ AC = AP + PQ + QC = √2

⇒1/2+PQ +1/2 = √2

⇒ PQ = √2–1

Question 46. The first two digits of a three digit number are 3 and 2 ; and the first two digits of another three digit numbers are 2 and 5. The sum of the number is 584 and the difference is 66. What is the ratio of the last digits of the numbers ?

a. 11 : 15
b. 1 : 1
c. 7 :11
d. 5 : 9

Answer: (d)

Let numbers are 32x and 25y.

So, 300 + 20 + x + 200 + 50 + y = 584 (given)

⇒ 570 + x + y = 584

⇒ x + y = 14 …..(1)

(300 + 20 + x) – (200 + 50 + y) = 66 (given)

⇒ (320 – 250) + x–y = 66

⇒ x – y = 66 – 70

⇒ x – y = 66 – 70

⇒ x – y = – 4 …..(2)

From (1) & (2), we get

⇒ x = 5 and y = 6

So, digits are 325 and 259

Required ratio x/y=5/9⇒5:9

Question 47. Which are the last two digits of the number 7²⁰²⁰ ?

a. 01
b. 11
c. 71
d. 61

Answer: (a)

7²⁰²⁰ = (7⁴)⁵⁰⁵⇒ (2401)⁵⁰⁵

⇒ Last two digits of the number (2401)⁵⁰⁵ is 01.

Question 48. The figure show a triangle ABC with AC=2, ∠A =60° ,∠C = 75° . Find the length of the side BC.

a. √3
b. √5
c. √2
d. √6

Answer: (d)

By sum of angles property

∠A + ∠B + ∠C = 180°

⇒ 60° + ∠B + 75° = 180°

⇒ ∠B = 45°

By using sine rule

sin B / AC = sin A / BC = sin C / AB

⇒ sin 45 / 2 = sin 60 / BC

⇒ 1 / 2√2 = √3 / 2BC

⇒ BC = √6

Question 49. If 2x/3y = 1/2, then find the value of(x–y)/(x+y) + 1/7

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

Answer: (c)

2x/3y = 1/2 (given)

⇒ x/y = 3/4

(x+y) / (x–y )= (3+4)/ (3–4) = 7/–1 (By Componendo-Dividendo Rule)

⇒(x–y)/ (x+y)= –1/7

Adding 1/7 both side, we get

⇒(x–y)/ (x+y) +1/7 = –1/7 + 1/7 = 0

Question 50. A certain amount of money was invested for 3 years paying simple interest. If the rate of interest had been 2% higher. It would have fetched Rs 5,100 more. What was the amount deposited ?

a. Rs. 75,000
b. Rs. 60,000
c. Rs. 85,000
d. Rs. 62,500

Answer: (c)

Simple interest = (P×R×T)/100; P → Principal, R → Rate of interest, T → Time (in years)

⇒(P(R+2)×3)/100–(PR×3)/100=5100(given)

⇒P(R + 2) × 3 – PR × 3 = 510000

⇒6P = 510,000

⇒P = 85,000

Question 51. If 1/a + 1/b = 1 then which of the following can be the quadratic equation whose roots are a and b?

a. x²+ 4x + 4 = 0
b. x²– 3x – 3 = 0
c. x²– 2x + 2 = 0
d. x²+ 5x –10 = 0

Answer: (c)

Given 1/a+1/b=1

⇒ a + b = ab

And if roots are a and b then quadratic equation is

⇒x² – (a + b)x + ab = 0

⇒a + b = ab

⇒a + b = ab = K (say)

⇒x² – kx + k = 0

Comparing this with option we get,

x² – 2x + 2 =0

Question 52. If A(–2,1), B(1,4) and C(–2, –4) are three points, then find the angle between AB and BC.

a. 100°
b. 115°
c. 135°
d. 145°

Answer: BONUS

Question 53. Find the remainder of

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

Answer: (a)

Question 54. The figure shows a unit circle with centre O and AB, AC are tangents. If ∠A = 60°, find the area of the quadrilateral ABOC.

a. √6
b. 3√3–3
c. √3
d. 2√3

Answer: (c)

In ΔOBA, ∠B=90°

tan 30° = OBAB(∵ tanθ = P/B)

⇒ 1 /√3 = 1 / AB

⇒ AB = √3

Now, Area of ΔABO = 1/2 × 1 × √3 = √3 / 2

Area of ΔBACO = 2 × [Area of ΔABO]

= 2 × √3/2

= √3

Question 55. The salary of a worker is first increased by 10% and thereafter decreased by 10%. What is the change in his salary?

a. Increased by 1%
b. Increased by 2%
c. Decreased by 1%
d. Decreased by 2%

Answer: (c)

Let the salary be y.

Increased by 10% = y + (10% of y)

= y + (10/100×y)

⇒ y + 0.1 y = 1.1y …….(1)

And then decreased by 10%

= [1.1y – 10% of 1.1y]

=[ 1.1y – 10/100× 1.1y]

= [1.1y – 0.11y]

= 0.99 y

Now, change in salary = y – 0.99 y

= 0.01y (decreases)

% change in salary =(1/100)×(0.01y)

= 1% (decreases)

Question 56. 6³+ 7³+ 8³+ 9³+10³ is equal to :

a. 2800
b. 1925
c. 2925
d. 1800

Answer: (a)

Question 57. The ratio of the areas of circumcircle and incircle of square is :

a. 1: √2
b.√2 :1
c.√3: 2
d. 2 :1

Answer: (d)

Let, radius of inscribed circle = BO = r

So, radius of circumcircle be =AO = √2r (By Pythagoras theorem in ΔABO)

(Area (circum circle))/(Area (Incircle))=(π(√2 r)²)/(πr² ) = 2/1

Question. 58. Find the smallest 3 – digit number, which when divided by 3,4 and 5 leaves the remainder 2.

a. 115
b. 122
c. 124
d. 134

Answer: (b)

Number which is divisible by 3, 4 and 5

= LCM (3, 4, 5)

= 60

Smallest three number

⇒ 60 × 2 = 120

which gives remainder 2

= 120 + 2 = 122

Question 59. A fruit seller buys lemons at 2 for a rupee and sells them at 5 for three rupees. What is his profit?

a. 15%
b. 20%
c. 10%
d. 25%

Answer: (b)

Cost price of one lemon = Rs 1/2

Selling price of one lemon = Rs 3/5

Profit (%) = (3/5–1/2)/(1/2) × 100

⇒ 0.6 – 0.5 / 0.5 × 100

⇒15 × 100

⇒ 20%

Question 60. If 777x + 666y =1332 and 666x + 777y =111, then the value of x + y is:

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

Answer: (a)

777x + 666y = 1332 …(1)

666x + 777y = 111 …(2)

Adding equation (1) & (2), we get

1443x + 1443y = 1443

1443(x +y) = 1443

Divide both side by 1443

x + y = 1

Question 61. An object approaches a plane mirror with a speed of 5 m/s. The speed with which the image moves with respect to the object will be:

a. 5 m/s
b. 2.5 m/s
c. 10 m/s
d. 20 m/s

Answer: (c)

Given :

Speed of object = 5m/sec

When the object moves towards the mirror, its image will also move with the same speed but in the opposite direction.

∴ Speed of image = 5m/sec

Now speed of image with respect to object.

V_IO = V_I – V_O

= 5 – (–5)

V_IO = 10 m/sec

Question 62. A car moving on a circular path of radius 10 m completes three – fourth of the circular path. The distance travelled and displacement will be respectively:

a. 47.1 m and 14.1 m
b. 31.4 m and 10 m
c. 47.1 m and 10 m
d. 31.4 m and 14.1 m

Answer: (a)

Given :

Radius of circle R = 10m

Distance = OA + AB + BC = OAB + BC

= πR + (2πR/4) = 3/2 × πR

= 3/2 π × 10 = 15π = 47.1 M

Displacement = OC ⇒

By the Pythagoras theorem in ΔODC,

OC² = OD² + DC²

OC = √[OD²+DC²] = √[R² + R²]

= √2R = 14.1  m

Question 63. A wire of resistance 16Ω is bent in the form of a circle as shown. The effective resistance between the diametrically opposite points A and B will be :

a. 16Ω
b. 4Ω
c. 32Ω
d. 8 Ω

Answer: (b)

Given :

R = 16Ω

When the wire is bent to form a circle, the resistance of half wire is 8Ω

So, R₁ = R₂ = 8Ω

R_eq = (R₁ R₂)/(R₁+R₂ ) = (8×8)/(8+8)

R_eq = 4Ω

Question 64. The lowest possible temperature, when expressed in Fahrenheit scale is :

a. – 485°F
b. 0°F
c. –273°F
d. –459°F

Answer: (d)

Least possible temperature is 0 Kelvin i.e. Absolute zero.

°C = K – 273

°C = 0 – 273 = – 273

Now relation between °C and °F,

(°C)/100=(°F–32)/180

(–273)/100=(°F–32)/180

Thus, the lowest possible temperature will be –459°F.

Question 65. When light enters from one medium to another medium of different optical densities which of the following remains unchanged?

a. Speed
b. Wavelength
c. Frequency
d. None of these

Answer: (c)

Frequency of the light remains the same when it passes from one medium to the another because it depends on the source of light. Whereas wavelength and velocity depends on medium.

Question 66. Choose the organism which does not reproduce through fission:

a. Plasmodium
b. Hydra
c. Amoeba
d. Bacteria

Answer: (b)

Plasmodium, amoeba, and bacteria reproduce through fission. Hydra reproduces through budding.

Question 67. Which one of the following is not a part of first level defense?

a. Wax in the ear
b. Keratin in skin
c. Neutrophils in the blood
d. Lysozyme present in tears

Answer: (c)

The first line of defense against infection are the surface barriers that prevent the entry of pathogens into the body. These include your skin, lysozyme present in tears, and wax in the ear. On the other hand, neutrophils in the blood is not the first line of defense against infection.

Question 68. Which of the following statements is correct?

a. A concave mirror always produces inverted image
b. A convex mirror always produces enlarged image
c. Both convex mirror and concave mirror can produce enlarged image
d.A concave mirror can produce enlarged image

Answer: (d)

A convex mirror produces virtual, small and inverted image whereas concave mirror can produce, virtual/Real, small / enlarged, inverted / upright.

Question 69. Identify the ammonotelic organism.

a. Frog
b. Fish
c. Insect
d. Lizard

Answer: (b)

The process of excreting ammonia is ammonotelism. Fishes are ammonotelic in nature.

Question 70. Two identical balls are thrown vertically up with velocities u and 2u. The ratios of maximum heights reached by them and time taken to reach the maximum heights are respectively:

a. 1 : 2 and 1 : 2
b. 1 : 4 and 1 : 2
c. 1 : 2 and 1 : 4
d. 1 : 4 and 1 : 4

Answer: (c)

From 1st equation of motion, V = u + at

0 = u + gt

t = u/g or t ∝ u

∴t₁ / t₂= u₁ / u₂ = u / 2u = 1/2 

From 3rd equation of motion, v² = u² + 2as

O = u² – 2gh

h = u² / 2g or h ∝ u²

∴ h₁ / h₂ = u²₁ / u²₂ = u² / (2u)² = 1/4

Question 71. Which among the following does not contain an aluminium atom?

a. Alumina
b. Bauxite
c. Carnallite
d. Cryolite

Answer: (c)

Molecular formula of the following compounds are:

Alumina: Al₂O₃

Bauxite: Al₂H₂O₄

Carnallite: Cl₃H₁₂KMgO₆

Cryolite: Na₃AlF₆

Question 72. Fountain experiment of HCl gas demonstrates:

a. The high reactivity of the gas with water
b. The high solubility of the gas in water
c. The oxidising nature of the gas
d. The reducing nature of the gas

Answer: (b)

Fountain experiment demonstrates the solubility of HCl gas in water. The HCl gas present inside the flask dissolves in water due to its high solubility.

Question 73. Nephrons are involved in :

a. Digestion
b. Impulse transmission
c. Excretion
d. Transportation

Answer: (c)

Nephrons are involved in excretion. They are the basic filtering units of kidneys.

Question 74. Choose the statement which is not true about glaucoma.

a. Reabsorption of aqueous humor does not occur
b.Lens of the eyes become opaque
c. Can be rectified by laser surgery
d. Pressure inside the eyes increases

Answer: (b)

In glaucoma, pressure inside the eyes increases and resorption of aqueous humor does not occur. It can be rectified by laser surgery. Whereas the lens of the eyes become opaque in cataract.

Question 75. Choose the correct statement from the following :

a. Chloroplast is a single membrane bound organelle.
b. Vacuoles are absent in plant cell.
c. Ribosomes are involved in lipid synthesis.
d. Mitochondrion is a double membrane bound organelle.

Answer: (d)

Mitochondria as well as chloroplasts both are double membrane bound organelle.

Vacuoles are present in plant cells. Ribosomes are involved in protein synthesis whereas smooth endoplasmic reticulum is responsible for lipid synthesis.

Question 76. Lichen is the association between:

a. Alga and Bacteria
b. Fungus and Roots
c. Fungus and Bacteria
d. Alga and Fungus

Answer: (d)

Some organisms live together and share both shelter and nutrients. This relationship is called symbiosis. Lichen is the symbiotic relationship between a fungi and an algae. The fungi provide shelter, water and minerals to the algae and, in return, the algae prepare and provide food to the fungi.

Question 77. If the speed of sound in air is 340 m/s, the wavelength range audible to human:

a. 20 m to 20,000 m
b. 17 mm to 17,000 mm
c. 20 Hz to 20,000 Hz
d. 1.7 m to 170 m

Answer: (b)

Given :

Speed of sound in air V = 340m/sec.

As we know that the audible range of human is

20Hz to 20,000 Hz

∴ Speed V = distance / time= λ / T = λf

Or λ = v / f

∴ for 20 Hz λ₁ = 340 / 20 = 17m = 17 × 10³ / 10³ m = 17000mm

∴ for 20,000 Hz λ₂ = 340 / 20,000 = 17 × 10^-3 m = 17mm

Range of wavelength = 17 mm to 17000 mm

Question 78. The IUPAC name of the alkane (CH₃)₃ C – CH₂ – CH₂ – CH (C₂H₅) – CH₃ is :

a. 2,2,5-trimethylheptane
b. 5-ethyl-2,2-dimethylhexane
c. 2-ethyl-5,5-dimethylhexane
d. 1,1,1-trimethyl-4-ethyl-pentane

Answer: (a)

Question 79. The metal present in the ions, CrO₄^2–, MnO₄^– and VO₄^3–, when arranged in the decreasing order of their oxidation states follows the order:

a. Mn > Cr > V
b. V > Cr > Mn
c. V > Mn > Cr
d. Mn > V > Cr

Answer: (a)

The oxidation states of the various transition elements are:

V (+5); Cr (+6); Mn (+7)

Therefore, the order will be: Mn > Cr > V

Question 80. Which among the following ions is divalent?

a. Dichromate
b. Manganate
c. Oxalate
d. All of the above

Answer: (d)

A divalent cation is a cation with valence of 2+. This type of ion may form two chemical bonds with anions. Therefore, Oxalate, Manganate and Dichromate are divalent.

Dichromate: Cr₂O₇^2-

Manganate: MnO₄^2-

Oxalate: C₂O₄^2-

Question 81. Choose the correctly matched pairs from the options given.

(a) Hypothalamus – Controls involuntary actions

(b) Aorta – Carries blood to various parts of the body

(c) Axon – Receives impulses from the adjacent neuron

(d) Renal artery – Carries blood to the kidney

a. (b) and (d)
b. (b) and (c)
c. (a) and (c)
d. (a) and (b)

Answer: (a)

The aorta is the largest artery in the body. It carries blood away from the heart to different parts of the body. Renal arteries carry a large portion of total blood flow to the kidneys.

Question 82. A bulb marked 100 W, 220 V is connected to a 110 V power supply. The power consumed by the bulb will be:-

a. 100 W
b. 50 W
c. 25 W
d. 200 W

Answer: (c)

Given,

Power of bulb P = 100 watt

Voltage of bulb V = 220 volt

Supplied voltage Vs = 110 volt

Now, Resistance of bulb ∴ P = V² / R

R = V² / P = 220 × 220 / 100

R = 22 × 22 ohm

Now power consumption by bulb,

P = V² / R = V_s² / R

= 110 × 110 / 22 × 22 = 25 watt

Question 83. Structurally AC generator and DC generator differ only in:

a. Shape of field magnets
b. Shape of armature coil
c. Rings attached to armature coils
d. Carbon brushes

Answer: (c)

AC generators have slip rings whereas DC generators have split rings.

Question 84. 60 g of sodium hydroxide is dissolved in water and made upto 1000 mL in a standard flask. The molarity of the resulting solution is:

a. 0.6 M
b. 1.2 M
c. 1.5 M
d. 2 M

Answer: (c)

Given weight = 60g; Volume = 1000mL (1L)

∴Molarity=(mole of NaOH)/(V(L))

Number of moles of NaOH = Given weight / molecular mass

= 60 / 40 = 1.5

Molarity=(60/40)/1=1.5M

Question 85. Which gas is liberated when calcium carbide reacts with water?

a. Acetylene
b. Ethane
c. Hydrogen
d. Carbon dioxide

Answer: (a)

Calcium carbide (CaC₂) reacts with water to produce acetylene (C₂H₂).

CaC₂(s) + 2H₂O(g) → Ca(OH)₂(s) + C₂H₂(g)

Question 86. The amount of calcium oxide obtained by heating 25 kg of calcium carbonate (80% pure) is:

a. 14 kg
b. 11.2 kg
c. 7 kg
d. 5.6 kg

Answer: (b)

CaCO₃ → CaO + CO₂ (↑)

25 kg (80% solution)

20 kg (Pure CaCO₃)

Molecular mass of CaCO₃ = 40 + 12 + (16 ｘ3) = 100 g

Moles of CaCO₃ = 20 x 10³ / 100 = Moles of CaO

Weight of CaO = (20×10³)/100x 56

=11200 g = 11.2 kg

Question 87. In which of the following cases, matter is converted into energy?

a. Burning of charcoal
b. Burning of kerosene
c. Nuclear reactor
d. All of the above

Answer: (c)

In a nuclear reactor, splitting of atoms is done where a particle (neutron) is bombarded at an atom, which then splits into two smaller atoms (neutrons). This process is called fission. Some of the neutrons that are released then hit other atoms, causing them to split and in turn release more atoms.

This continuous fission process releases a certain amount of energy in the form of heat. So, atoms (matter) are split and energy is released in the form of heat.

Question 88. Which among the following is an example for physical change?

a. Burning of candle
b. Adding water to calcium oxide
c. Photosynthesis
d. Sublimation of iodine

Answer: (d)

A physical change is a process in which the physical state of the substance is changed.

Therefore, sublimation of Iodine is a physical change as there is a transition from solid to gas state.

Question 89. Which among the following has the maximum number of atoms?

a. 24g of CH₄
b. 28g of CO
c. 34g of NH₃
d. 36g of H₂O

Answer: (c)

Number of moles in 34 g of NH₃ = 2 moles

Number of atoms in a molecule= 4 x 2 N_A = 8 N_A

Number of atoms in 24 g of CH₄ = 1.5 x 5 N_A

Number of atoms in 28g of CO = 1 x 2 N_A

Number of atoms in 36g of H₂O = 2 x 3 N_A

Question 90. Certain elements have fractional atomic mass. This is due to the:

a. Difference in atomicity
b. Formation of ions by the atoms
c. Existence of isobars of the element
d. Existence of isotopes of the element

Answer: (d)

The atomic masses of most elements are fractional because they exist as a mixture of isotopes of different masses. Most elements occur as a mixture of isotopes of different masses.

Question 91. The deficiency of thyroxine during the foetal stage or infancy leads to a condition called:

a. Goitre
b. Graves disease
c. Cretinism
d. Myxoedema

Answer: (c)

The deficiency of thyroxine during the fetal stage or infancy leads to a condition called cretinism. Myxoedema is another term for severely advanced hypothyroidism. Graves’ disease is an autoimmune disorder that causes hyperthyroidism. A goitre is a swelling in the neck resulting from an enlarged thyroid gland.

Question 92. A respiratory pigment which has high affinity for oxygen is:

a. Globulin
b. Haemoglobin
c. Carotene
d. Rhodopsin

Answer: (b)

Haemoglobin is a respiratory pigment which has high affinity for oxygen. It binds with oxygen to form oxyhaemoglobin.

Question 93. The chemical formula of cyclobutane is:

a. C₄H₄
b. C₄H₆
c. C₄H₈
d. C₄H₁₀

Answer: (c)

Cyclobutane, C₄H₈, is a four-membered carbocycle.

Question 94. Which of the following does not represent the mean distance between the earth and the sun?

a. 1 angstrom unit
b. 1.5×10¹¹m
c. 1 astronomical unit
d. 500 light second

Answer: (a)

1 Angstrom = 10^–10 m

This is the size of an atom, so it cannot represent the mean distance between the earth and the sun.

Question 95. Identify the group which includes water borne diseases.

a. Cholera and Typhoid
b. Tetanus and Typhoid
c. Cholera and Malaria
d. Tetanus and Tuberculosis

Answer: (a)

Cholera and typhoid are water borne diseases. These are illnesses caused by microscopic organisms, like viruses and bacteria that are ingested through contaminated water or by coming in contact with feces.

Question 96. The opening and closing of stomata is regulated by:

a. Lenticels
b. Chloroplast
c. Complimentary cells
d. Guard cells

Answer: (d)

Guard cells are specialized plant cells in the epidermis of leaves that regulate the opening and closing of stomata.

Question 97. Choose the correct pathway of impulses in a reflex action.

a. Stimulus → Sensory neuron → Motor neuron → Interneuron → Receptor →Related muscle
b. Stimulus → Receptor → Sensory neuron → Interneuron → Motor neuron →Related muscle
c. Stimulus → Motor neuron → Related muscle → Sensory neuron → Receptor → Interneuron
d. Stimulus → Related muscle → Sensory neuron → Motor neuron →Interneuron → Receptor

Answer: (b)

Correct pathway of impulses in a reflex action is :

Stimulus → Receptor → Sensory neuron → Interneuron → Motor neuron → Related muscle

Question 98. Which one of the following is an example of chemotropism?

a. Growth of climbers towards a support
b. Growth of stem away from water
c. Growth of root away from light
d. Growth of pollen tube towards the ovary

Answer: (d)

Chemotropism is the movement of a part of the plant in response to a chemical stimulus. Growth of the pollen tube towards the ovary is an example of chemotropism.

Question 99. Haber process is associated with the industrial preparation of:

a. Teflon
b. Ammonia
d. Nitric acid
d. Sulphuric acid

Answer: (b)

In Haber’s process, the atmospheric nitrogen (N₂) is converted to ammonia (NH₃) by reacting it with hydrogen (H₂).

N₂ + 3H₂ → 2NH₃

Question 100. A passenger inside a bus throws a stone vertically up. In which of the following situations the stone returns to his own hands?

(a) When the bus is at rest

(b) When the bus is moving with uniform speed in a straight line

(c) When the bus is moving with uniform acceleration

(d) When the bus is moving in a curved path with uniform speed

a. (a) only
b. (a) and (b) only
c. (a), (b) and (c) only
d. (a), (b) and (d) only

Answer: (b)

The stone will return to the passenger’s hand when either bus is at rest or moving with uniform speed; otherwise due to pseudo force it will deflect.