Rajasthan 2020-21 NTSE Stage 1 – Question Paper With Solutions complete details

**Paper: MAT**

**PHYSICS**

**Questions (1 – 8) Instruction: In each of the Question Nos. 1 to 8 a letter series is given with one term missing shown by question mark (?). This term is one of the four alternatives given under it. Find the correct alternative.**

**Question 1. R, V, A, G, N, __?**

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

Solution:

- Answer: (b)

**Question 2. AC, FH, KM, PR, ____?**

- a. UX
- b. TV
- c. UW
- d. VW

Solution:

- Answer: (c)

**Question 3. NZ, OY, PX, QW, RV, ____?**

- a. FS
- b. UF
- c. TU
- d. SU

Solution:

- Answer: (d)

**Question 4. AEI, EIO, IOU, OUA, ____?**

- a. UXB
- b. UAE
- c. EUA
- d. AOU

Solution:

- Answer: (b)Pattern based on the cyclicity of the vowels AEIOU.

**Question 5. ABZ, DFX, GJV, JNT, ____?**

- a. MRR
- b. QRQ
- c. MRQ
- d. QVR

Solution:

- Answer: (a)

**Question 6. COVIDNINETEEN, VIDNINETEENCO, DNINETEENCOVI, ________?**

- a. IDNINETEENCOV
- b. NINETEENCOVID
- c. INETEENCOVIDI
- d. INETEENCOVIDN

Solution:

- Answer: (d)The first two letters of a term are shifted to the last to form the next term of the series.So after,
**DN**INETEENCOVI, the next term will be INETEENCOVI**DN**.

**Question 7. RADIUS, RADSIU, RADSUI, RADUIS, ______?**

- a. RASDIU
- b. RDAIUS
- c. RADUSI
- d. RAIDUS

Solution:

- Answer: (c)

**Question 8. H2J, K3N, O4S, _____?**

- a. T5Y
- b. T5Z
- c. T5X
- d. T5A

Solution:

- Answer: (a)

**Question 9. 2, 3, 5, 8, 13, __?, 34**

- a. 23
- b. 21
- c. 20
- d. 22

Solution:

- Answer: (b)The given series is a Fibonacci series starting from 2.So, the series is 2, (2 + 1), (3 + 2), (5 + 3), (8 + 5),
**(13 + 8)**, (21 + 13)

i.e. 2, 3, 5, 8, 13,**21,**34.

**Question 10. 3, 8, 15, 24, 35, __?**

- a. 52
- b. 50
- c. 48
- d. 46

Solution:

- Answer: (c)The series is 3, (3 + 5), (8 + 7), (15 + 9), (24 + 11), (35 + 13)So, the missing term is 35 + 13, i.e. 48.

**Question 11. 8, 24, 28, 140, 146, 1022, 1030, __?**

- a. 1040
- b. 8240
- c. 10300
- d. 9270

Solution:

- Answer: (d)The pattern is ×3, +4, ×5, +6, ×7, +8, ×9.So, 1030 × 9 = 9270.

**Question 12. 2, 9, 3, 28, 4, 65, 5, __?**

- a. 137
- b. 126
- c. 118
- d. 115

Solution:

- Answer: (b)The series has two alternate series in it.One series: 2, 2 + 1, 3 + 1, 4 + 1,…Another Series: 2
^{3 }+ 1, 3^{3 }+ 1, 4^{3}+ 1, 5^{3}+ 1,…So, the missing term is 5^{3}+ 1, i.e. 126.

**Question 13. 4, 17, 290, __?**

- a. 84100
- b. 84101
- c. 84102
- d. 84103

Solution:

- Answer: (b)4
^{2}+ 1 = 1717^{2}+ 1 = 290290^{2}+ 1 = 84101

**Question 14. 3, 3, 4.5, 9, 22.5, __?**

- a. 27.3
- b. 48
- c. 55
- d. 67.5

Solution:

- Answer: (d)The pattern is ×1, ×1.5, ×2, ×2.5, ×3,…So, 22.5 × 3 = 67.5

**Question 15. 4, 5, 12, 39, 160, __?**

- a. 225
- b. 695
- c. 805
- d. 790

Solution:

- Answer: (c)The pattern is ×1+1, ×2+2, ×3+3, ×4+4, ×5+5,…So, (160 × 5) + 5 = 805.

**Question 16. 2, 3, 7, 16, 32, __?**

- a. 57
- b. 39
- c. 56
- d. 55

Solution:

- Answer: (a)The pattern is +1
^{2}, +2^{2}, +3^{2}, +4^{2}, +5^{2},…So, 32 + 5^{2}= 57.

**Question 17. Statement: Unemployment is one of the main reasons for the poverty of the country.**

**Conclusions:**

**(I) To end poverty, it is required to create employment opportunities.**

**(II) All the people in the country are unemployed.**

- a. Only conclusion I follow.
- b. Only conclusion II follows.
- c. Both conclusions I and II follow.
- d. Neither conclusion I nor II follows.

Solution:

- Answer: (a)From the given statement on unemployment, it can be concluded that, to end poverty more employment opportunities need to be created. But the statement doesn’t convey that all people in the country are unemployed.So, the conclusion (I) follows but conclusion (II) doesn’t follow.

**Question 18. Statement: Morning walk is good for health.**

- a. Only conclusion I follow.
- b. Only conclusion II follows.
- c. Both conclusions I and II follow.
- d. Neither conclusion I nor II follows.

Solution:

- Answer: (d)The statement does not convey anything about all healthy people. Some healthy people might not go for morning walks.The statement does not convey anything on evening walks. So, it cannot be concluded that evening walk is harmful.

**Question 19. Statement: Animals live on Oxygen.**

**Conclusions:**

**(I) Plants do not live on Oxygen.**

**(II) Anything that needs Oxygen is bound to be an animal.**

- a. Only conclusion I follow.
- b. Only conclusion II follows.
- c. Both conclusions I and II follow.
- d. Neither conclusion I nor II follows.

Solution:

- Answer: (d)The statement doesn’t convey anything regarding plants. Also, it doesn’t convey that only animals live on oxygen. So, both conclusions do not follow.

**Question 20. Which one of the following Venn-diagrams correctly represents the relation between currency, Rupee and Dollar?**

Solution:

- Answer: (c)Rupee and Dollar are currencies for different countries. They do not have anything in common.

**Question 21. Which one of the following Venn-diagrams correctly represents the relation between Mumbai, Madhya Pradesh and Bhopal?**

Solution:

- Answer: (c)Bhopal is in Madhya Pradesh but Mumbai is not.

**Question 22. Which one of the following Venn-diagrams correctly represents the relation between Herbivorous, Lions and Animals?**

Solution:

- Answer: (a)Lions belong to animals but are not herbivorous animals.

**Question 23. In a coded language, ONLINE is written as LNOENI and SILENT is written as LISTNE; then in the same coded language, LISTEN will be written as.**

- a. ILSNET
- b. SILENT
- c. SILNET
- d. SILETN

Solution:

- Answer: (c)Word is divided into two halves and each half is reversed.ONLINE: Reverse of ONL and INE are LNO and ENI respectively. So, we get LNOENI.SILENT: Reverse of SIL and ENT are LIS and TNE respectively. So, we get LISTNE.LISTEN: Reverse of LIS and TEN are SIL and NET respectively. So, we get SILNET.

**Question 24. In a coded language, AVOID is written as 73564 and CHINA is written as 28617; then in the same coded language, COVID will be written as**

- a. 53246
- b. 25364
- c. 25346
- d. 25634

Solution:

- Answer: (b)Decoding AVOID = 73564 letter by letter we get,A=7, V=3, O=5, I=6, D=4Similarly, In CHINA = 28617; C=2, H=8, I=6, N=1, A=7.So, the code for COVID: C=2, O=5, V=3, I=6, D=4

i.e., COVID = 25364.

**Questions (25 – 27) Instruction: Read the following information carefully and answer question number 25 to 27 based upon it.**

**In a coded language, 461 means WHERE ARE YOU; 169 means ‘YOU ARE GOOD’ and 8652 means ‘EXAMS ARE NOT BAD’.**

**//**Decoding the language for Q25-27:

4 – WHERE

6 – ARE

1 – YOU

9 – GOOD

8 – EXAMS

5 – NOT

2 – BAD**//**

**Question 25. What is the code for ‘NOT’?**

- a. 6
- b. 9
- c. 5
- d. 1

Solution:

- Answer: (c)NOT is 5.

**Question 26. What is the code for ‘GOOD’?**

- a. 9
- b. 4
- c. 6
- d. 1

Solution:

- Answer: (a)Good is 9.

**Question 27. How will ‘WHERE ARE GOOD EXAMS’ will be written in coded language?**

- a. 1654
- b. 4619
- c. 1945
- d. 4698

Solution:

- Answer: (d)From the digits corresponding to the words, the code for WHERE ARE GOOD EXAMS is 4698.

**Question 28. The two positions of a single dice are given below. Which digit will be at the face opposite to the face having digit 2.**

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

Solution:

- Answer: (b)There are 6 numbers 1 to 6 on the faces of a dice. All numbers are visible except 4, which must be on the face opposite of 2.

**Question 29. The two positions of a single cube are shown below. The six faces of this cube are coloured with Green, Yellow, Red, Black, Pink and White. If the Green coloured face is at top then what will be the colour at bottom’s face?**

- a. White
- b. Green
- c. Yellow
- d. Red

Solution:

- Answer: (a)The colours adjacent to Green are Yellow, Red, Pink and Black. The only colour remaining is White which will be on the opposite face to Green.

**Questions (30 – 33) Instruction: In Question numbers 30 to 33, find the correct mirror image of the given figure, when the mirror is placed on the right side of the figure.**

**Question 30. Find the correct mirror image for the following figure;**

Solution:

- Answer: (b)

**Question 31. Find the correct mirror image for the following figure;**

Solution:

- Answer: (d)

**Question 32. Find the correct mirror image for the following figure;**

Solution:

- Answer: (c)

**Question 33. Find the correct mirror image for the following figure;**

Solution:

- Answer: (d)

**Question 34. Which of the answer figures will complete the matrix figure?**

Solution:

- Answer: (b)By observation it can be determined that the figure will be completed by the mirror image of the left side. So, it is option (b)

**Question 35. Which of the answer-figures will complete the matrix-figure?**

Solution:

- Answer: (a)By observation it can be determined that the figure will be completed by the mirror image of the left side. So it is option (a).

**Question 36. If it was Tuesday on 24 ^{th} March, 2020 then what was the day on 24^{th} August, 2020.**

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

Solution:

- Answer: (c)Months between March and August are April (30 days), May (31 days), June (30 days), July (31 days).Total Days in these months = 30 + 31 + 30 + 31 = 122Number of Days from 24
^{th}March to 31^{st }March = 7Number of Days from 1^{st}August to 24^{th }August = 24Total number of days = 122 + 7 + 24 = 153 days153 = (21 × 7) + 6There are 21 weeks and 6 odd days from 24^{th }March to 24^{th }August. So 24^{th }August is Monday (Tuesday + 6 odd days).

**Question 37. How many numbers from 10 to 200 are there which are divisible by 2 as well 7?**

- a. 13
- b. 14
- c. 15
- d. 16

Solution:

- Answer: (b)For a number to be divisible by both 2 and 7 it should be divisible by 14.200/14 = 14.28So, the number of multiples of 14 between 10 and 200 are 14. Hence 14 numbers between 10 and 200 are divisible by both 2 and 7.
**Instruction: In each of the Question numbers 38 to 43, three alternatives are alike in a certain way but the rest one is different. Select the odd one.**

**Question 38. Select the odd one.**

- a. Chalk
- b. Pen
- c. Pencil
- d. Map

Solution:

- Answer: (d)Except for a map, all others are used for writing.

**Question 39. Select the odd one.**

- a. Taxi
- b. Bus
- c. Car
- d. Tanker

Solution:

- Answer: (d)Taxi, Bus and Car carry passengers but Tankers do not.

**Question 40. Select the odd one.**

- a. June
- b. August
- c. April
- d. November

Solution:

- Answer: (b)Only August of the given options has 31 days in the month.

**Question 41. Select the odd one.**

- a. Africa
- b. Europe
- c. Australia
- d. England

Solution:

- Answer: (d)England is a country whereas all others are continents.

**Question 42. Select the odd one.**

- a. Hand
- b. Leg
- c. Ear
- d. Neck

Solution:

- Answer: (d)Except Neck all other body parts given are in pairs.

**Question 43. Select the odd one.**

- a. Cone
- b. Triangle
- c. Rectangle
- d. Circle

Solution:

- Answer: (a)Except for Cone, all the other options given are 2D figures.

**Question 44. Identify the missing term (?) in the following figure.**

- a. 114
- b. 113
- c. 123
- d. 124

Solution:

- Answer: (b)(8 x 2) – 1 = 15(15 x 2) – 1 = 29(29 x 2) – 1 = 57(57 x 2) – 1 = 113(113 x 2) – 1 = 225So, 113 is the missing number.

**Question 45. Identify the missing term (?) in the following table.**

- a. 87
- b. 85
- c. 77
- d. 75

Solution:

- Answer: (c) or (d)11 + (14 x 2) = 3912 + (15 x 3) = 5713 + (16 x 4) = 77The missing number in the table will be 77.OrSo, a = 75.Here, the missing number in the table will be 75.

**Question 46. Ishant is taller than Sanjay, Ashok is taller than Ishant, Sachin is not as tall as Ashok but taller than Ishant. Who is shortest in height?**

- a. Sanjay
- b. Sachin
- c. Ishant
- d. Can’t be determined

Solution:

- Answer: (a)From the question, the heights can be compared as follows.Ashok > Sachin > Ishant > Sanjay

**Question 47. In a class of 39 students, Mukesh’s rank is 7 more than Gautam’s rank. If Gautam’s rank from end is 17 ^{th}, then what will be the rank of Mukesh from beginning?**

- a. 13
^{th} - b. 14
^{th} - c. 15
^{th} - d. 16
^{th}

Solution:

- Answer: (d)Since Gautm’s rank is 17th from the last there are 16 students after him.Gautam’s actual rank from the 1st rank = 39 – 16 = 23
^{rd }rankMukesh’s rank = 23 – 7 = 16th rank.

**Question 48. From 14 December, 2020, morning 4 O’ clock to 15 December, 2020, morning 4 O’ clock. How many times, the minute hand & hour hand of a clock will overlap.**

- a. 21
- b. 22
- c. 23
- d. 24

Solution:

- Answer: (b)Hours between 4.00 AM, 14 December 2020 to 4.00 AM, 15 December 2020 = 24In 12 hours, the hands of a clock overlap 11 times.In 24 hours, the hands of the clock would have overlapped 22 times.

**Question (49 – 53) Instruction: The following questions are based on the diagram given below, Study the diagram carefully and answer the questions based upon it.**

**In the diagram**

**(I) Circle represents unemployed**

**(II) Square represent Hard working**

**(III) Triangle represent Rurals**

**(IV) Rectangle represents intelligents.**

**Question 49. The rurals which are Hard-working and intelligent but not unemployed are represented in the diagram by.**

- a. 14
- b. 1
- c. 9
- d. 8

Solution:

- Answer: (a)The number in the intersection of triangle (Rural), square (Hardworking), and rectangle (Intelligents), but not in the circle (unemployed), i.e. 14.

**Question 50. The Rurals, which are neither Hard-working nor Intelligent but unemployed are represented by**

- a. 1
- b. 2
- c. 3
- d. 6

Solution:

- Answer: (d)The number in the intersection of triangle (Rural) and circle (Unemployed), but not covered by square (Hardworking), and rectangle (Intelligents), but not in the circle (unemployed), i.e. 6.

**Question 51. The unemployed, which are intelligent but neither Rurals nor Hard working are represented by**

- a. 1
- b. 8
- c. 9
- d. 11

Solution:

- Answer: (b)The number in the intersection of and circle (Unemployed) and rectangle (Intelligents), but not covered by triangle (Rural) and square (Hardworking), i.e. 8.

**Question 52. Those who are Rurals, Hard-working and unemployed and also intelligent, are represented by**

- a. 14
- b. 9
- c. 8
- d. 1

Solution:

- Answer: (d)The number in the intersection of circle (Unemployed), rectangle (Intelligents), triangle (Rural) and square (Hardworking), i.e. 1.

**Question 53. Those persons who are neither rurals, nor unemployed and nor intelligent but Hard working, are represented by**

- a. 5 and 7
- b. 12 and 17
- c. 10 and 19
- d. 15 and 16

Solution:

- Answer: (b)The numbers in the square (Hardworking) but not covered by circle (Unemployed), rectangle (Intelligents), triangle (Rural), i.e. 12 and 17.

**Question 54. As clay is related to pottery in the same way gold is related to which of the following.**

- a. Woman
- b. Goldsmith
- c. Ornaments
- d. Metal

Solution:

- Answer: (c)Clay is used to make pottery.Gold is used to make ornaments.

**Question 55. As birds are related to kites, in the same way fish is related to which of the following.**

- a. Crow
- b. Submarine
- c. Boy
- d. Thread

Solution:

- Answer: (b)Birds and kites fly in the sky.Fish and submarines are in seas.

**Question 56. As ‘gram’ is related to ‘mass’ in the same way, ‘Centimeter’ is related to**

- a. Area
- b. Volume
- c. Density
- d. Length

Solution:

- Answer: (d)Gram is a unit of mass.Centimeter is a unit of length.

**Questions (57 – 61) Instruction: Study the information given below carefully and answer the questions based on it. All the faces of a solid cube are coloured with red colour and then cut it into 64 small equal cubes.**

**Question 57. How many cubes are such with only one face is coloured?**

- a. 12
- b. 24
- c. 30
- d. 36

Solution:

- Answer: (b)A cube cut into 64 small cubes looks like the figure below.The small cubes are arranged in a 4 x 4 x 4 matrix.On each face of the big cube there are 4 small cubes that have only one of its face coloured red as highlighted in the figure.The total number of small cubes with only one face coloured is 6 x 4, i.e. 24.

**Question 58. How many cubes are such with two opposite faces are red coloured?**

- a. 0
- b. 4
- c. 6
- d. 8

Solution:

- Answer: (a)There can be no cube whose opposite faces are coloured. The faces opposite to painted faces of each painted small cube are hidden in the interior side of the bigger cube.

**Question 59. How many cubes are such that two adjacent faces are red coloured and the remaining faces are not coloured?**

- a. 8
- b. 12
- c. 16
- d. 24

Solution:

- Answer: (d)As highlighted in the image, on each edge of the big cube there are 2 edge cubes that have only 2 adjacent faces painted. The big cube has 12 edges. So total number of edge cubes = 2 x 12 = 24.

**Question 60. How many cubes are such with three faces red coloured?**

- a. 0
- b. 6
- c. 8
- d. 12

Solution:

- Answer: (c)The small cubes at the 8 vertices of the bigger cube have 3 painted faces.

**Question 61. How many cubes are such that any of the faces is not coloured?**

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

Solution:

- Answer: (b)The 64 cubes obtained by cutting the big cube are arranged in a 4 x 4 x 4 matrix.If the outer layer of small cubes are left, there will be 2 x 2 x 2 small cubes that are left. So, the total number of small cubes that have no painted face is 8 (2 x 2 x 2).

**Question 62. In numbers 5 8 1 3 2 7 6 4, how many digits are such that they are at the same distance from the beginning as if arranged in descending order?**

- a. Three
- b. Two
- c. One
- d. None

Solution:

- Answer: (d)Original order: 5 8 1 3 2 7 6 4Descending order: 8 7 6 5 4 3 2 1From the arrangement of numbers, it can be seen that there is no such digit.

**Question 63. If the unit place and hundreds place digit of every number is interchanged then what will be the sum of the unit place digit and Tens place digit of greatest number?**

- a. 7
- b. 11
- c. 12
- d. 14

Solution:

- Answer: (b)The numbers after interchanging unit place and hundreds place digit of every number is 683, 257, 169, 375, 938. The greatest number is 938.The sum of unit place digit and tens place digit = 3 + 8 = 11

**Question 64. If the unit place digit and tens place digit of every number is interchanged then what will be the second greatest number?**

- a. 893
- b. 863
- c. 961
- d. 725

Solution:

- Answer: (a)The numbers are 368, 725, 916, 537, 893.The second greatest number is 893.

**Question 65. If the digits of every number are rearranged in such a way that if form the smallest possible number by the digits then what will be the biggest number out of them?**

- a. 368
- b. 527
- c. 691
- d. 389

Solution:

- Answer: (d)The numbers are 368, 257, 169, 357, 389.The greatest of them is 389.

**Question 66. In the arithmetic expression given below, if the digit 4 and 3 are interchanged then what will be the solution?**

- a. 10
- b. 10/3
- c. 18
- d. 12

Solution:

- Answer: (d)The expression becomes 3 x 2 + 8 – 4
**÷**2 = 6 + 8 – 2 = 12

**Question 67. In the arithmetic expression given below, if the sign X and ÷ are interchanged then what will be the solution? 8 x 3 – 2 + 3 ÷3**

- a. 29 / 3
- b. 9
- c. 23
- d. 23 / 3

Solution:

- Answer: (a)8 ÷ 3 – 2 +3 x 3 = 8 / 3 – 2 + 9 = 8 / 3 + 7 = 29 / 3

**Question 68. After interchanging the sign + and ÷ and also interchanging the digits 2 and 3, which of the following is given with the correct solution?**

- a. 4 x 3 + 8 – 3 ÷ 2 = 17
- b. 4 + 3 x 8 – 3 ÷ 2 = 17
- c. 4 + 3 x 8 ÷ 2 x 3 = 17
- d. 4 + 3 + 8 ÷ 2 – 3 = 17

Solution:

- Answer: (b)Rewriting the options by interchanging operators + and ÷ and digits 2 and 3 in the options:a. 4 x 2 ÷ 8 – 3 + 2 = 4 x 025 – 3 + 2 = 0b. 4 ÷ 2 x 8 – 2 + 3 = 2 x 8 – 2 + 3 = 16 + 1 = 17c. 4 ÷ 2 x 8 + 3 x 2 = 8 + 6 = 22d. 4 ÷ 2 x 8 ÷ 3 – 2 = 2 x 8 / 3 – 2 = 10 / 3

**Question 69. If 50% books in a library are in English language and 7 ^{th} / 10 of the rest in Hindi language which of the following shaded parts approximately represent books in Hindi language.**

Solution:

- Answer: (b)Let us say that the total number of books are a.Number of English books = 0.5aNumber of Hindi books = 7/10 (a – 0.5a) = 0.7 × 0.5a = 0.35aThe shaded portion, that represents the number of books in Hindi, should be more than quarter and less than half, i.e. the option (b).

**Question (70 – 72) Instruction: In an open ground Ranu, Shaifu and Charvi are standing at the corner of an equilateral triangle. Study the questions 70 to 72 carefully which are based on the following diagram and select the correct answer.**

**Question 70. From the positions shown in above figure, Ranu, Shaifu and Charvi run along the sides of equilateral triangle in clockwise direction for sides of triangle. Now which of the following statements is true?**

- a. Charvi is in the West of Shaifu.
- b. Ranu is in the South-West of Charvi.
- c. Ranu is in the South-West of Shaifu.
- d. Shaifu is in the North-East of Ranu.

Solution:

- Answer: (b)After they have run along 1.5 sides of the triangle in clockwise direction their positions are as shown.From the figure it can be clearly seen that Ranu is South-West of Charvi.

**Question 71. From the positions shown in above figure, Ranu, Shaifu and Charvi run along the sides of equilateral triangle in anti-clockwise direction for sides of triangle. Now Shaifu is in which direction of Ranu?**

- a. In East
- b. In South
- c. In North-West
- d. In North-East

Solution:

- Answer: (c)After they have run along 1.5 sides of the triangle in an anti-clockwise direction their positions are as shown.From figure it can be clearly seen that Shaifu is in the North-West of Ranu

**Question 72. From the position shown in above figure, Ranu, Shaifu and Charvi run along the sides of the equilateral triangle in clockwise direction for 1 side of the triangle. Now Charvi is in which direction of Shaifu?**

- a. South-West
- b. South-East
- c. North-West
- d. North-East

Solution:

- Answer: (d)After they have run along 1 side of the triangle in clockwise direction their positions are as shown.From the figure it can be clearly seen that Charvi is in the North-East of Shaifu.

**Question 73. In this question, ‘∆’ means “Greater than” ‘❏’ means “Less than”, ‘ϕ’ means, “equal to” and ‘⊕’ means “not equal to”. If C∆A, A∆B, DϕB, AND B⊕C, then choose the correct option in the following.**

- a. D❏C
- b. D∆C
- c. A∆C
- d. B⊕D

Solution:

- Answer: BONUSThe decoded relations as given are: C > A, A < B, D = B and B ≠ CThe decoded options are:D < C, D > C – Relationship between C and D is not defined. So, these options cannot be concluded.A > C – From the given, A cannot be greater than C.B ≠ D – From the given, B is equal to D and so this option cannot be true.None of the options is correct.

**Question 74. Darshan walked 4 meters in the East, then he turned right and walked 7 meters, then he turned left and walked 5 meters again he turned left and walked 7 meters. Then finally before stopping he turned right and walked 3 meters. How far is Darshan from his initial poin**t?

- a. 10 meter
- b. 11 meter
- c. 12 meter
- d. 13 meter

Solution:

- Answer: (c)The image shows the path walked by Darshan.So, distance from the initial point to final point = 4 + 5 + 3 = 12 m.

**Questions (75 – 77) Instruction: The following table shows the record of surgery done in a hospital. This record shows the data from January to July. Study the table carefully and answer the following questions.**

**Question 75. As per the above table, what is the percentage of successful surgery?**

- a. 32%
- b. 29%
- c. 58%
- d. 21%

Solution:

- Answer: (c)Total successful surgeries = 5 + 4 + 5 + 6 + 4 + 3 + 2 = 29Total unsuccessful surgeries = 3 + 4 + 2 + 3 + 2 + 3 + 4 = 21Total number of surgeries = 21 + 29 = 50Percentage of successful surgeries = 100 x 29/50 = 58%

**Question 76. In which month the percentage of successful surgery was highest in the hospital?**

- a. January
- b. April
- c. July
- d. March

Solution:

- Answer: (d)The percentage of successful surgery is highest in the month of March.

**Question 77. In which month the percentage of unsuccessful surgery was highest in the hospital?**

- a. July
- b. June
- c. February
- d. March

Solution:

- Answer: (a)The percentage of unsuccessful surgeries is highest in the month in which the percentage of successful surgeries is at the lowest, i.e. July.

**Question 78. If a and b are natural numbers. If A +B = 2020 then what will be the value of (-1) ^{a} +(-1)^{b}?**

- a. 1 or -1
- b. 2020 or -2020
- c. 1010 or -1010
- d. 2 or -2

Solution:

- Answer: (d)When a + b = 20202020 is an even number. So, if a is even, b is also even (to make the sum even). Similarly, if a is odd, b is also odd to make the sum even.When a and b are even,
**(-1)**When a and b are odd,^{a}+ (-1)^{b}= 2**(-1)**^{a}+ (-1)^{b}= -2

**Question 79. How many integers are in between 1 and 100 which satisfies all the following conditions?**

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

Solution:

- Answer: (b)The 7 multiples that leave a remainder of 1 when divided by 3 and 5 are to be counted.In other words, the 7 multiples that leave a remainder of 1 when divided by 15 are to be counted.Between 1 and 100:7 multiples are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 and 98.15 multiples between 1 and 100 are 15, 30, 45, 60, 75, 90.(Multiples of 15) +1 are, 16, 31, 46, 61, 76, 91.91 is the only multiple of 7 which is 1 more than a multiple of 3 and 5.

**Question 80. A square is divided into four identical rectangles. The perimeter of each of these rectangles is 20 cm. What is the perimeter of the square?**

- a. 80 cm
- b. 50 cm
- c. 48 cm
- d. 32 cm

Solution:

- Answer: (d)Let l and b be the sides of the rectangle.2(l + b) = 20 cml + b = 10 cmFrom the image, l = 4bSo, 2(4b + b) = 20b = 2 cml = 8 cmPerimeter of the square = 4l = 32 cm

**Question 81. What is the difference between the biggest 3-digit number having 8 as tens place and divisible by 4 and smallest 3-digit number having 8 as tens place and divisible by 4?**

- a. 888
- b. 808
- c. 708
- d. 788

Solution:

- Answer: (b)The greatest 3-digit number having 8 in tens place and divisible by 4 is 988.The smallest 3-digit number having 8 in tens place and divisible by 4 is 180.So, the difference is 808.

**Question 82. 20 : 11 : : 102 😕**

- a. 49
- b. 52
- c. 61
- d. 96

Solution:

- Answer: (b)(20 + 2)/2 = 11(102+2)/2 = 52

**Question 83. 6 : 35 : : 7 : ?**

- a. 48
- b. 42
- c. 34
- d. 13

Solution:

- Answer: (a)6
^{2}– 1 = 357^{2}– 1 = 48

**Question 84. 9 : 162 : : 8 : ?**

- a. 96
- b. 112
- c. 128
- d. 162

Solution:

- Answer: (c)2 × 9
^{2}= 1622 × 8^{2}= 128

**Question 85. 64 : 100 :: 144 😕**

- a. 121
- b. 169
- c. 180
- d. 196

Solution:

- Answer: (d)64 = 8
^{2}100 = 10^{2}144 = 12^{2}:So, the missing number = 14^{2}= 196

**Question 86. 0.01 : 0.0001:: 0.05 😕**

- a. 0.00025
- b. 0.0025
- c. 0.025
- d. 0.25

Solution:

- Answer: (b)0.01
^{2}= 0.00010.05^{2}= 0.0025

**Question 87. Arrange the following in a meaningful sequence:**

**(1) Crop (2) Root (3) Stem (4) Seed (5) Flower**

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

Solution:

- Answer: (d)The sequence is based on the growth of a crop from a seed.The sequence will be: Seed, Root, Stem, Flower, Crop, i.e. 4, 2, 3, 5, 1.

**Question 88. Arrange the following in a meaningful sequence:**

**(1) Rain (2) Cloud (3) Ocean (4) River (5) Monsoon**

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

Solution:

- Answer: (a)In the monsoon season, the clouds rain and the water flows from the river and finally enters the ocean. So, the sequence is Monsoon, Cloud, Rain, River, Ocean, i.e. 5, 2, 1, 4, 3.

**Question (89 -92) Instruction: Read the information given below and answer the question numbers 89 to 92 based on it.**

**Kriti and Amit are two children of Smt and Shri Mittal. Amit, married to Ananya, who is daughter of Smt. Goyal. Shri Goyal had married Rita. Sonu and Rakesh are children of Sumer and Rita. Urvi and Poorvi are daughters of Ananya and Amit.**

**Family tree based on the directions given:**

**Question 89. What is the surname of Rakesh?**

- a. Goyal
- b. Mittal
- c. Amit
- d. Kriti

Solution:

- Answer: (a)From the family tree, Surname of Rakesh is Goyal

**Question 90. What is the relation of Sumer with Poorvi?**

- a. Brother
- b. Uncle
- c. Maternal Grandfather
- d. Father

Solution:

- Answer: (c)From the family tree, Sumer is the maternal grandfather of Poorvi.

**Question 91. What is the relation of Urvi with Kriti?**

- a. Sister
- b. Niece
- c. Aunty
- d. Daughter

Solution:

- Answer: (b)From the family tree, Urvi is the niece of Kriti.

**Question 92. What is the relation of Sonu with Shri Goyal?**

- a. Sister
- b. Brother
- c. Son/Daughter
- d. Father

Solution:

- Answer: (c)From the family tree, Sonu is the son/daughter of Shri Sumer Goyal.

**Questions (93 -95) Instruction: Read the sequence given below and answer question number 93 to 95.**

**7, 6, 3, 2, 3, 5, 4, 3, 5, 2, 7, 6, 4, 5, 2, 3, 6, 2, 7, 5, 2, 5, 2, 3, 6, 5, 2, 6, 3, 7, 4, 2, 5**

**Question 93. How many times 5 is followed by 2 but 4 does not occur just before it?**

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

Solution:

- Answer: (c)7, 6, 3, 2, 3, 5, 4,
**3, 5, 2**, 7, 6, 4, 5, 2, 3, 6, 2,**7, 5, 2, 5, 2**, 3,**6, 5, 2**, 6, 3, 7, 4, 2, 5There are four such instances.

**Question 94. How many times 2 is followed by odd numbers?**

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

Solution:

- Answer: (d)7, 6, 3,
**2, 3**, 5, 4, 3, 5,**2, 7**, 6, 4, 5,**2, 3**, 6,**2, 7**, 5,**2, 5**,**2, 3**, 6, 5, 2, 6, 3, 7, 4,**2, 5**There are seven instances of 2 being followed by an odd digit.

**Question 95. How many times has number 5 been used just before or after 4?**

- a. 1
- b. 2
- c. 3
- d. 5

Solution:

- Answer: (b)7, 6, 3, 2, 3,
**5, 4**, 3, 5, 2, 7, 6,**4, 5**, 2, 3, 6, 2, 7, 5, 2, 5, 2, 3, 6, 5, 2, 6, 3, 7, 4, 2, 5There are two instances of 5 being followed or preceded by 4.

**Question 96. What will be the angle between minute hand and hour hand of a watch at 12:30?**

- a. 180
^{o} - b. 150
^{o} - c. 175
^{o} - d. 165
^{o}

Solution:

- Answer: (d)The angle between two divisions in a clock is 30°.At 12.30 the hour hand would be 15° away from 12.So, the angle between minute hand and hour hand at 12:30 is 180° – 15°, i.e. 165
^{0}.

**Question (97 – 100) Instruction: Read the information given below carefully and answer the questions that follow:**

**A, B, C, D, E, F and G are seven students of a school, who are studying in seven different Classes V, VI, VII, VIII, IX, X and XI. Every one of them likes a particular subject viz. English, Hindi, Physics, Chemistry, Mathematics, History and Geography. Students, Classes and subjects can always be in different order as given.**

**B likes History and does not study in Class VII. The one who likes English studies in Class IX. The one who studies in Class V, likes Chemistry. F likes Physics. C is studying in Class VI and doesn’t like Geography. E is studying in Class X and likes Mathematics. D likes Chemistry. G doesn’t like English and G is not in Class VII or VIII. F is not in Class VIII**

Table based on the instructions given:

**Direction on How the table was filled for the cells for which the information is not given directly:**

**D likes chemistry, so he is in class V.**

**The information on who is studying in VII, VIII, IX and XI is not given directly.**

**G is not in VIII and VII. Since he doesn’t like English, he is not in IX. So, G is in XI.**

**Now grades of B and F are to be determined and VII and VIII are the only grades left without students mapped. So B is in VIII (Since it’s given that B is not in VII) and F is in VII.**

**A is the remaining one without a grade mapped and so he is in class IX.**

**C doesn’t like geography, so, G likes geography and C likes Hindi.**

**Question 97. F is in which Class?**

- a. VII
- b. IX
- c. XI
- d. Data inadequate

Solution:

- Answer: (a)As can be seen from the table, F is in VII class.

**Question 98. G is in which Class?**

- a. VI
- b. VII
- c. XI
- d. IX

Solution:

- Answer: (c)As can be seen from the table, G is in XI class.

**Question 99. Which subject does A like?**

- a. Hindi
- b. Geography
- c. English
- d. Chemistry

Solution:

- Answer: (c)As can be seen from the table, A likes English.

**Question 100. Who studies in Class – 8?**

- a. B
- b. C
- c. A
- d. E

Solution:

- Answer: (a)As can be seen from the table, B is in VIII class.