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

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Uttarakhand NTSE 2020 Stage 1 SAT Paper

Uttarakhand 2020-21 NTSE Stage 1 - Question Paper With Solutions

Paper: MAT

Directions: (Question 1 to 10) In the following questions there is a relationship between the two words/ letters/ numbers and figures given to the left of the proportionality (: :) sign. The same relationship exists between the words/ letters/ numbers/ figures given to the right of the sign (: :) of which one is missing. Choose the missing one from the given alternative.

Question 1. 8 : 9 : : 64 : ?

1. a. 16
2. b. 36
3. c. 25
4. d. 20

Solution:

1. Answer: (b) or (c)

Option b, 23 : 32 :: 43 : 62

Option c, 23 : 32 :: 43 : 52

Question 2. SWZ : XTA : : DGM : ?

1. a. JEO
2. b. IDN
3. c. HCM
4. d. NDI

Solution:

Question 3. 6 : 18 : : 4 : ?

1. a. 2
2. b. 10
3. c. 8
4. d. None of these

Solution:

6 : 62/2 = 6 : 18

4 : 42/2 = 4 : 8

Question 4. Centimeter : Meter : : Paise : ?

1. a. Rupee
2. b. Coin
3. c. Wealth
4. d. Currency

Solution:

100 cm = 1 m (Units of length)

100 paise = 1 rupee (Unit of currency)

Question 5. Choose the missing one from the given alternative.

Solution:

Question 6. Choose the missing one from the given alternative.

Solution:

The image of the number is rotated by 180°.

Question 7. Entrance : Exit : : Loyalty: ?

1. a. Treachery
2. b. Patriotism
3. c. Clarity
4. d. Fidelity

Solution:

Solution:

Exit is the antonym of entrance. Similarly, treachery is the antonym of loyalty.

Question 8. Choose the missing one from the given alternative.

Solution:

If each component in the image is given a number, you can see how the order changes.

Question 9. TPNX : XNP : : BUCW : ?

1. a. WUC
2. b. CUW
3. c. WCU
4. d. COW

Solution:

Question 10. EIGHTY : GIEYTH : : OUTPUT : ?

1. a. UTOPTU
2. b. VOTUPT
3. c. TUOUTP
4. d. TUOTUP

Solution:

Directions: (Question 11 to 20) In the following questions numbers/ letters/ figures are arranged in a sequence on the basis of some logic. Find out the logic and select the correct answer from the given alternatives.

Question 11. 97, 90, 76, 55, ?

1. a. 28
2. b. 27
3. c. 26
4. d. 25

Solution:

Question 12. BDAC FHEG ?

1. a. JLIK
2. b. IKJL
3. c. JKLI
4. d. KLIJ

Solution:

Question 13. 17, 19, 23, 29, ?, 37

1. a. 33
2. b. 36
3. c. 31
4. d. 35

Solution:

The given series represents the series of consecutive prime numbers starting from 17. Therefore, the missing prime number in the series is 31 after 29.

Question 14. Z, X, ?, N, F

1. a. T
2. b. R
3. c. Q
4. d. O

Solution:

Question 15. 31, 34, 71, 216, 867, 4338, ?

1. a. 26028
2. b. 26031
3. c. 21690
4. d. 23150

Solution:

Question 16. Find out the logic and select the correct answer from the given alternatives.

Solution:

By observation it can be determined that the image rotates by 90° in the clockwise direction.

Question 17. Find out the logic and select the correct answer from the given alternatives.

Solution:

The three symbols circled in the first image are moving in clockwise direction.

Question 18. aac__bba__cc__baa__cb__

1. a. acbac
2. b. bacbc
3. c. abaac
4. d. cabcb

Solution:

Solution:

Repeating group of letters: aaccbb

Series: aaccbb | aaccbb | aaccbb

Question 19. Find out the logic and select the correct answer from the given alternatives.

Solution:

The symbols move to the next row and interchange their position. The bottom rows shift to the top without interchanging their position

Question 20. AZY, BYX, CXW, DWV, ?

1. a. EVA
2. b. EVU
3. c. VEU
4. d. VUE

Solution:

Directions: (Question 21 to 30) In the following questions four items are given. Find the odd Item in these.

Question 21. Find the odd Item

1. a. Mars
2. b. Sun
3. c. Jupiter
4. d. Satum

Solution:

The Sun is a star and the rest are planets.

Question 22. Find the odd Item

1. a. LNJK
2. b. DFBC
3. c. XZVW
4. d. RUPQ

Solution:

All the options follow the same sequence except option d.

Question 23. Find the odd Item

Solution:

By observation, it can be determined that all of them represent a happy face whereas option B represents a sad face.

Question 24. Find the odd Item

1. a. L
2. b. Y
3. c. T
4. d. V

Solution:

1. Answer: (a) or (b)

For option (a); letters Y, T, and V have a vertical line of symmetry whereas letter L does not have such symmetry.

For option (b); letters L (12), T (20) and V (22) are in even position whereas letter Y is in odd position.

Question 25. Find the odd Item

1. a. 1111
2. b. 11
3. c. 121
4. d. 1211

Solution:

1. Answer: (c) and (d)

Option c; All numbers specified in the options 121 are not symmetric.

Option d; All numbers specified in the options except 1211 are divisible by 11.

Question 26. Find the odd Item

1. a. 6 : 14
2. b. 10 : 24
3. c. 4 : 10
4. d. 22 : 46

Solution:

6 : 14 = 6 : (6 X 2) + 2

4 : 10 = 4 : (4 X 2) + 2

22 : 46 = 22 : (22 X 2) + 2

10 : 24 = 10 : (10 X 2) + 4

Question 27. Find the odd Item

Solution:

All options except for option (d) have 7 squares in it.

Question 28. Find the odd Item

1. a. 12 - 21
2. b. 34 - 43
3. c. 23 - 32
4. d. 55 - 65

Solution:

If we will observe the pairs of numbers, we will see that:

12 - 21 (12+9)

34 - 43 (34+9)

23 - 32 (23+9)

55 - 65 (55+10)

So, the odd one out is 55 - 65.

Question 29. Find the odd Item

1. a. VWUX
2. b. SURT
3. c. BDAC
4. d. PROQ

Solution:

Except the option a, all other options follow the below pattern:

Question 30. Find the odd Item

1. a. 5
2. b. 23
3. c. 9
4. d. 29

Solution:

By observation it can be determined that all the numbers except the number 9 is a prime number.

Directions: Answer question No. 31 to 34 on the basis of the following diagram. The circle represents players. The triangle represents outdoor games. The hexagon represents Indoor games and the square represents National level players.

Question 31. Which letter in the section represents the players who play indoor games at the National level ?

1. a. f
2. b. i
3. c. j
4. d. g

Solution:

Question 32. The letter representing the section of outdoor as well as indoor game players who do not play at the national level?

1. a. c
2. b. f
3. c. i
4. d. k

Solution:

Question 33. The section representing national level players who do not play either outdoor or indoor games but still come under the category of players is -

1. a. k
2. b. g
3. c. c
4. d. h

Solution:

Question 34. Persons who play outdoor games but do not come under the category of players are represented in the section marked as-

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

Solution:

Directions: (Question No. 35 to 39): Study the following paragraph and answer the questions.

Rohit, Kunal, Ashish and John are students of a school. Three of them stay far from the school and one near it. Two study in class IV, one in class V and one in class VI. They study Hindi, Mathematics, Social Science and Science. One of them is good at all the four subjects while the performance of the other is low in all the subjects. Rohit stays far from the school and is good at Mathematics only while Kunal’s performance is low in Mathematics only and he stays close to the school. Neither of these two nor Ashish studies in Class VI. One who is good at all the subjects studied in class V.

Based on the information given above, the table can be made:

Kunal stays close to the school. Since only one person stays near the school this means that the rest stay far from the school.

1. Kunal stays close to the school. Since only one person stays near the school this means that the rest stay far from the school.
2. Rohit, Kunal and Ashish do not study in class VI. This implies that John studies in class VI.
3. Rohit is good at maths but weak in the rest so he cannot be in class V. Similarly, as Kunal is not good at maths so he cannot be in class V either. Hence, Ashish studies in class V. He is therefore good to all subjects.
4. Class IV has two students. So, Rohit and Kunal study in class IV.
5. Since John has not been good in any subject, therefore, he is weak in every subject.
6. a. Rohit
7. b. Kunal
8. c. Ashish
9. d. John

Solution:

From the solution table, it is clear that Ashish is good in every subject.

Question 36. Name the boy whose performance has been low in all the subjects?

1. a. Rohit
2. b. Kunal
3. c. Ashish
4. d. John

Solution:

From the solution table, the boy who has been low in all the subjects is John.

Question 37. Who are the two boys good at Hindi?

1. a. Rohit and Kunal
2. b. Kunal and Ashish
3. c. Ashish and John
4. d. John and Rohit

Solution:

From the solution table, it is clear that Kunal and Ashish are good at hindi.

Question 38. Who are the two boys good at Mathematics?

1. a. Rohit and Ashish
2. b. Kunal and Ashish
3. c. John and Ashish
4. d. Rohit and John

Solution:

From the solution table, it is clear that Rohit and Ashish are good at maths.

Question 39. Other than Rohit and the boy good at all the subjects, who else stays far from the school?

1. a. Rohit
2. b. Kunal
3. c. Ashish
4. d. John

Solution:

From the soluble table, it is clear that apart from Rohit and Ashish, even John stays far from the school.

Question 40. If Ram’s house is located to the south of Krishna’s house and govnda’s house is to the East of Krishna’s house, in which direction is Ram’s house situated with respect to Govinda’s house?

1. a. North - East
2. b. North - West
3. c. South - East
4. d. South - West

Solution:

Question 41. In a certain code language COMPUTER is written as RFUVQNPC. How will MEDICINE be written in that code language?

1. a. MFEDJJOE
2. b. EOJDJEFM
3. c. MFFJDJOE
4. d. EMJDJEFM

Solution:

Question 42. If Z = 52 and ACT = 48 then BAT = ?

1. a. 39
2. b. 41
3. c. 44
4. d. 46

Solution:

Z = 26 x 2 = 52

ACT = (1 + 3 + 20) x 2 = 48

BAT = (2 + 1 + 20) x 2 = 46

Question 43. Which of the following words cannot be formed using the letters given in the word Father?

1. a. Heater
2. b. Cheat
3. c. Fear
4. d. Tear

Solution:

When we see the word CHEAT the letter C is not present in the word FATHER.

Question 44. Eagles, Birds, Dogs

Solution:

Eagles are Birds. Dogs do not come under the birds category.

Question 45. Pen, Ink, Writing material

Solution:

1. Answer: (a) or (d)

Option a

Pen and Ink are different materials. But, both of them come under writing material.

Option d

Ink is present in pen and pen is a writing material.

Question 46. Pulses, Arhar, Moong

Solution:

Moong and Arhar are two different types of pulses.

Question 47. Arun is the father of Rohit. Rohit is the brother of Mala. Mala is the wife of Dalip. How is Dalip related to Rohit?

1. a. Brother-in-law
2. b. Father-in-law
3. c. Son
4. d. Uncle

Solution:

Question 48. Arrange the following words in alphabetical order-
Equal 2. Entire 3. Erase 4. Envelope 5. Entreat

1. Equal 2. Entire 3. Erase 4. Envelope 5. Entreat
2. a. 25431
3. b. 25143
4. c. 25413
5. d. 25134

Solution:

The alphabetical order of the words are: Entire, Entreat, Envelope, Equal and Erase.

Question 49. Aman is the son of Sameer. Alka is the daughter of Aman. Shaila is the wife of Aman. Mohan is the son of Shaila. How is Alka related to Mohan?

1. a. Sister
2. b. Uncle
3. c. Son
4. d. Father

Solution:

Aman and Mohan are the male members of the family. (Nothing is given about Sameer)

Question 50. In certain code language pic vic nic means winter is cold, to nic re means summer is hot. vic tho pa means nights are cold then what will be the code of cold?

1. a. to
2. b. nic
3. c. pic
4. d. vic

Solution:

 No. Statement Code Language 1. Winter is cold pic vic nic 2. Summer is hot to nic re 3. Nights are cold vic tho pai

Question 51. If CBE means BAD then GMBH means-

1. a. GOOD
2. b. FOOD
3. c. FLAG
4. d. FLOG

Solution:

We have to take the alphabet that lies before the alphabet of the first set of letters.

Question 52. How many triangles are there in the following figure?

1. a. 4
2. b. 16
3. c. 10
4. d. 12

Solution:

Question 53. In the morning at sunrise Munbahadur and Dhanbahadur are talking to each other face to face. If Munabahadur’s shadow is exactly to his left side, then which direction is Dhanbahadur facing?

1. a. East
2. b. West
3. c. North
4. d. South

Solution:

Sun rises in the East, so any shadow will be formed at the West during sunrise. As Manbahadur’s (M) shadow (formed at West) is exactly to his left, he must be facing North. Thus, Dhanbahadur (D) will be facing South as both are facing each other while talking.

Question 54. A family consists of a man, his wife and three sons. All three sons have their wives and three children. How many members are there in the family?

1. a. 17
2. b. 15
3. c. 12
4. d. 13

Solution:

Man + Wife = 2 members

Three sons = 3 members

Wives of three sons + three children each = 1 +1 + 1 + 3 + 3 + 3 = 12 members

Total members = 2 + 3 + 12 = 17

Question 55. If Republic day was celebrated on Sunday in the year 1997, then on which day Independence day would have been celebrated in that year?

1. a. Tuesday
2. b. Friday
3. c. Saturday
4. d. Wednesday

Solution:

There are 5 + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 201 days between Republic day and Independence day which consist of 28 weeks and 5 odd days. Thus, if Republic day was celebrated on Sunday, Independence day would have been celebrated after five days of Sunday i.e., on Friday.

Question 56. Five books are kept on a table. Economics book is above Maths. Sanskrit is below Hindi. Maths is above Hindi but Science is below Sanskrit, then which book is in the middle?

1. a. Hindi
2. b. Sanskrit
3. c. Science
4. d. Maths

Solution:

The order of books from top to bottom as per the sequence given in the question is:

English

Maths

Hindi

Sanskrit

Science

Hence, the Hindi book lies in the middle.

Question 57. If 'N' means '✕', 'M' means '÷', 'P' means '+' and 'Q' means '-', then what will be the value of the given equation?

16 P 24 M 8 Q 6 M 2 M 3 = ?

1. a. 13
2. b. 17
3. c. 24
4. d. 10

Solution:

By replacing the letters with the symbols, we get:

16 + 24 ÷ 8 - 6 ÷ 2 ÷ 3

By applying BODMAS to the given expression, we get,

16 + (24 ÷ 8) - 6 ÷ (2 ÷ 3) or 16 + (24 ÷ 8) - (6 ÷ 2 )÷ 3

16 + (24 ÷ 8) - 6 ÷ (2 ÷ 3) = 16 + 3 - 6 ÷ 23

= 16 + 3 - (6 32)

= 16 + 3 - 9 = 10

OR

16 + (24 ÷ 8) - (6 ÷ 2 )÷ 3 = 16 + 3 - 3 ÷ 3

= 16 + 3 - 1 = 18

So the answer for the given expression can be 10 or 18. From the given options it is 10.

Question 58. A, B, C and D are four buildings. A is higher than only D. B is shorter than C but higher than A. Which is the highest building?

1. a. A
2. b. B
3. c. C
4. d. D

Solution:

Given:

A > D

A < B < C

On combining: D < A < B < C

Hence, the highest building is C.

Question 59. If A means +, B means -, C means and D means ÷, then what will be the value of the given equation?

18 C 14 A 6 B 16 D 4 = ?

1. a. 254
2. b. 238
3. c. 188
4. d. 258

Solution:

By replacing the letters with the symbols we get:

18 14 + 6 - 16 ÷ 4

On applying BODMAS, we get:

(18 14) + 6 - (16 ÷ 4) = 252 + 6 - 4 = 254

Question 60. P is the father of R, but R is not his son. T is the daughter of R. U is the wife of P. Q is the brother of R. S is the son of Q. V is the wife of Q. W is father of V. Who is the sister-in-law of R?

1. a. S
2. b. V
3. c. U
4. d. T

Solution:

Since V is the wife of Q and Q is the brother of R. Hence, V is the sister-in-law of R.

Question 61. Which will replace the question mark (?)

1. a. 1007
2. b. 1105
3. c. 1309
4. d. 1307

Solution:

The pattern in clockwise direction is as follows:

11 = 5 x 2 + 1

25 = 11 x 2 + 3

55 = 25 x 2 + 5

117 = 55 x 2 + 7

243 = 117 x 2 + 9

497 = 243 x 2 + 11

1007 = 497 x 2 + 13

Question 62. Which will replace the question mark (?)

1. a. 3
2. b. 5
3. c. 7
4. d. 8

Solution:

Solution:

The pattern followed in first figure is:

5 + 3 + 8 = 16 ⇒ 162 = 256

Similarly, 11 + 7 + ? = 26 ⇒ 262 = 676

11 + 7 + 8 = 26

Question 63. Which will replace the question mark (?)

1. a. 18
2. b. 10
3. c. 36
4. d. 24

Solution:

Solution:

The pattern in first and second figure is as follows:

(5 - 3) ✕ (12 - 9) = 2 ✕ 3 = 6

(8 - 4) ✕ (2 - 1) = 4 ✕ 1 = 4

Similarly, for the third figure:

(18 - 10) ✕ (17 - 14) = 8 ✕ 3 = 24

Question 64. Which will replace the question mark (?)

By observation, it can be determined that in a particular row, the base of all the three figures is the same as figure one. Also, on going from the second figure to the third figure, the cross over the base figure gets replaced by four small exterior circles. So it is option (b).

Solution:

By observation, it can be determined that in a particular row, the base of all the three figures is the same as figure one. Also, on going from the second figure to the third figure, the cross over the base figure gets replaced by four small exterior circles. So it is option (b).

Question 65. Which will replace the question mark (?)

Solution:

By observation it can be determined that each row consists of three different types of triangles with different vertical lines count (1,2 and 3). Also, each row consists of three small circles: 2 black and 1 white. Now, in the third row, the only figure missing is a black triangle with three vertical lines and a black circle.

Question 66. Which will replace the question mark (?)

1. a. 40
2. b. 38
3. c. 45
4. d. 39

Solution:

The pattern in clockwise direction is followed as:

13 = 9 + 22

22 = 13 + 32

Similarly, 22 + 42 = 38

Question 67. Which will replace the question mark (?)

Solution:

For each row, the figure shown in 3rd column is the addition of non-common part of the figures shown in 1st and 2nd columns.

Question 68. Which will replace the question mark (?)

Solution:

The common portion of the figures in the first two columns is removed in the figure in the third column.

Question 69. Which will replace the question mark (?)

1. a. -12
2. b. 12
3. c. 9
4. d. 7

Solution:

The pattern followed in first, second, and third figure is:

2 ✕ 2 ✕ 3 = 12

2 ✕ 3 ✕ 5 = 30

5 ✕ 1 ✕ (-1) = -5

Similarly, for the third figure:

4 ✕ 3 ✕ (-1) = -12

Question 70. Which will replace the question mark (?)

1. a. 30
2. b. 20
3. c. 10
4. d. 40

Solution:

The pattern in the first figure is followed as:

√64 + √49 + √36 = 8 + 7 + 6 = 21

Similarly, for the second figure:

√121 + √100 + √81 = 11 + 10 +9 = 30

Question 71. In the following series only one number is wrong. Find out the wrong number.

8000, 3200, 1280, 512, 204.8, 84.92, 32.768

1. a. 512
2. b. 84.92
3. c. 204.8
4. d. 1280

Solution:

The pattern in the series is followed as:

8000 ✕ 0.4 = 3200

3200 ✕ 0.4 = 1280

1280 ✕ 0.4 = 512

512 ✕ 0.4 = 204.8

204.8 ✕ 0.4 = 81.92

81.92 ✕ 0.4 = 32.768

Thus, the wrong number in the series is 84.92.

Question 72. Five boys A, B, C, D, E are sitting in a park in a circle. A is facing South-West direction, D is facing South-East B is sitting exactly opposite to E and A is sitting exactly opposite to D. C is sitting equidistant between D and B. Which direction is C facing?

1. a. West
2. b. South
3. c. North
4. d. None of these

Solution:

The positioning of B and E in relation to A and D is not mentioned in the question. So, Position of C cannot be determined due to insufficient information.

Question 73. If 1 March 1997 was a Saturday, then what was the day on 1 March 2000?

1. a. Monday
2. b. Tuesday
3. c. Wednesday
4. d. Friday

Solution:

The year 2000 was a leap year. So there are 365 + 365 + 366 = 1096 days between 1 March 1997 and 1 March 2000, which consist of 156 weeks and 4 odd days. Thus, 1 March 2000 lies after 4 days of Saturday i.e., on Wednesday.

Direction: (Q.No. 74 to 75): In the following questions, if a mirror is placed on the line MN, then which of the answer figures will be the correct image of the given question figure?

Question 74. Question figure

Solution:

The figure provided in option (a) is the mirror image of the figure provided in the question.

Question 75. Problem figure

Solution:

The figure provided in option (d) is the mirror image of the figure provided in the question.

Question 76. Rahul put his timepiece on the table in such a way that at 6 PM the hour hand points to North, then in which direction will the minute hand point at 9.15 PM?

1. a. East
2. b. South
3. c. North
4. d. West

Solution:

As the hour hand at 6 PM is pointing in the North direction, we can say that the timepiece has been rotated by 1800 clockwise/anticlockwise.

Therefore, at 09:15 PM, the minute hand will point in the West direction.

Question 77. If + denotes ÷, - denotes , denotes -, and ÷ denotes + then, 35 + 7 - 5 ÷ 5 6 = ?

1. a. 36
2. b. 24
3. c. 20
4. d. 14

Solution:

According to the sign change, the given equation 35 + 7 - 5 ÷ 5 ✕ 6 becomes 35 ÷ 7 5 + 5 - 6

On applying BODMAS,

= 5 5 + 5 - 6

= 25 + 5 - 6

= 24

Question 78. Find the total number of e’s followed by a vowel in the following letter series.

Ebeabeacacbcbceedeeceaceaceace

1. a. 4
2. b. 6
3. c. 7
4. d. 8

Solution:

On counting the marked e’s, we get 7.

Question 79. If RUSH is coded as 66 then what will be the code for GIRL?

1. a. 74
2. b. 64
3. c. 47
4. d. 46

Solution:

Solution:

The alphabet’s positional values are added:

RUSH = 18 + 21 + 19 + 8 = 66

Similarly GIRL = 7 + 9 + 18 + 12 = 46

Question 80. Five senior citizens are living in a multi-storeyed building. Mr. Muan lives in a flat above Mr. Ashokan. Mr. Lokesh lives in a flat below Mr. Gaurav, Mr. Ashoka lives in a flat above Mr. Gaurav and Mr. Rakesh lives in a flat below Mr. Lokesh. Who lives in the topmost flat?

1. a. Mr. Lokesh
2. b. Mr. Gaurav
3. c. Mr. Muan
4. d. Mr. Rakesh

Solution:

According to the data given in the question, the flats starting from the top are in the following order:

Mr. Muan

Mr. Ashokan

Mr. Gaurav

Mr. Lokesh

Mr. Rakesh

Question 81. Six persons A, B, C, D, E and F are sitting in two rows. Three persons are sitting in each row. E is not sitting at the end of any row. D is second to the left of F. C, the neighbour of E, is sitting diagonally opposite to D. B is the neighbour of F. Which of the following are sitting in one of the two rows?

1. a. D, B and F
2. b. C, E and B
3. c. A, E and F
4. d. F, B and C

Solution:

From the information given in the question, the following arrangement can be made:

So the two rows are AEC and DBF.

Question 82. A dice has been marked with some letters and placed in three different positions. Which letter is opposite to Q?

1. a. P
2. b. R
3. c. S
4. d. None of these

Solution:

From the first two orientations of the dice, we can conclude that the letters P, T, U and S are adjacent to the letter R. Therefore the letter Q must be opposite to the letter R. Conversely, R is opposite to Q.

Question 83. How many 7’ s are there in the following series which are preceded by 6 which is not preceded by 8?

87678675679861677688697687

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

Solution:

Question 84. Study the letter series given below and answer the following question.

HDYSMWNBQPOCRTBLZVEGUF

Which letter has the same two neighbours as in the alphabetical order though

they have changed their places?

1. a. M
2. b. N
3. c. O
4. d. P

Solution:

P has the same neighbours (O and Q) though their places are interchanged.

Question 85. The time on two clocks is corrected at 10 AM on Sunday. One clock loses 3 minutes in an hour while the other gains 2 minutes in an hour. By how many minutes do the two clocks differ at 4 PM on the same day?

1. a. 25 minutes
2. b. 20 minutes
3. c. 35 minutes
4. d. 30 minutes

Solution:

Time difference between 10 AM and 4 PM = 6 hours

Now, in one hour the time difference between two clocks = 3+2 = 5 minutes.

Therefore, the time difference from 10 AM to 4 PM = (6 X 5) minutes = 30 minutes

Question 86. In 1980, Indian Republic Day was on Saturday. ‘X’ was born on March 3, 1980. If ‘Y’ is four days elder than ‘X’, then on which day was ‘Y’ born?

1. a. Thursday
2. b. Friday
3. c. Saturday
4. d. None of these

Solution:

Republic Day of India is on 26th January. In 1980 (leap year), the republic day was on Saturday.

Y is 4 days older than X, i.e., Y's birthday is 4 days before that of X, or 4 days before March 3, i.e. on February 28, 1980.

So, there is a gap of 5 days ( 27-31 Jan) + 28 days = 33 days (between 26 January and 28 February.)

Now, we know that a day repeats itself after every 7 days or a week.

Then, there will be 33/7 = 4 weeks + 5 odd days between them.

The 5th day from Saturday will be Thursday.

Question 87. How many squares are there in the given figure.

1. a. 12
2. b. 17
3. c. 16
4. d. None of these

Solution:

Directions: (Q. No. 88 to 89) : Identify the missing part of the Problem figure and select it from the answer figures.

Question 88. Problem figure

Solution:

Question 89. Problem figure

Solution:

Directions:s: (Q. No. 90 to 91) : Find the answer figure which has the problem figure hidden in it.

Question 90. Problem Figure.

Solution:

Question 91. Problem figure.

Solution:

Directions: (Q. No. 92 to 93) : In the following figure, a square transparent sheet of paper is given with some patterns. Find out the correct option from the given alternatives that shows the pattern would appear when the transparent sheet is folded at the dotted line.

Question 92. Problem Figure.

Solution:

When we will fold the sheet along the dotted line, the two triangles which are at the bottom will coincide with the two triangles at the top. So, the pattern will look as given in option A.

Question 93. Problem Figure.

Solution:

When we will fold the sheet along the dotted line, the right side will coincide with the left side. So, the pattern will look as given in option C.

Question 94. In the following figures two positions of one dice is given. Which number will be opposite to number 3 ?

1. a. 6
2. b. 4
3. c. 1
4. d. None of these

Solution:

Considering the two orientations of the dice we can see that 6 is opposite to 3.

Question 95. Reena said “The woman walking on the road is my father’s wife. “How is the woman related to Reena?

1. a. Sister
2. b. Aunt
3. c. Mother
4. d. Daughter

Solution:

Question 96. The ratio of the present age of Sameer and Milan is 8:5. After 6 years, the ratio of their ages will be 3:2. What will be the ratio between the sum of their present ages and the difference of their present ages?

1. a. 39 : 19
2. b. 33 : 9
3. c. 12 : 7
4. d. 13 : 3

Solution:

Let the present age of Sameer and Milan be 8x and 5x respectively.

After 6 years, their ages will be 8x + 6 and 5x + 6 respectively.

Now, (8x+6)/(5x+6) = 3/2

16x+12 = 15x+18

x = 18-12 = 6

Now, sum of present ages of Sameer and Milan = 8x + 5x = 13x = 13×6 = 78

Difference between their present ages = 8x -5x = 3x = 3 × 6 =18

Ratio = 78/18 = 13/3

Therefore, the required ratio is 13:3

Question 97. How many squares are there in the given figure?

1. a. 12
2. b. 13
3. c. 14
4. d. None of these

Solution:

Question 98. 10 years ago, Neha’s mother was four times older than Neha. After 10 years, Neha’s mother age will be twice of Neha’s age. How old is Neha now?

1. a. 10 Years
2. b. 15 Years
3. c. 17 Years
4. d. 20 Years

Solution:

Let the present age of Neha and her mother be x and y respectively.

10 years ago, Neha and her mother’s age would have been (x-10) and (y-10) respectively.

Thus, (y-10) = 4 (x-10)

y = 4x - 30 Equation 1

After 10 years, Neha and her mother’s age will be (x+10) and (y+10) respectively.

Thus, (y+10) = 2 (x+10)

y= 2x + 10 Equation 2

On solving the above two equations,

We get x = 20.

Question 99. Which two signs are to be interchanged to make the given equation true?

5 × 15 ÷ 7 - 20 + 4 = 77

1. a. - and ÷
2. b. × and ÷
3. c. + and ÷
4. d. + and ×

Solution:

On interchanging + and ÷, we get,

(5 × 15) + 7 - (20 ÷ 4) = 5 × 15 + 7 - 5 = 75 + 2 = 77

Question 100. A river flows west to east and on the way turns left and goes in a semi-circle around a hillock and turns left at right angles. In which direction is the river finally flowing?

1. a. West
2. b. East
3. c. North
4. d. None of these

Solution:

Based on the information given in the question, the following diagram can be made:

Now we can see that the final direction of the river is towards the east.

Uttarakhand NTSE 2020 Stage 1 SAT Paper

Paper: SAT

Social Science

Question 1. In the 18th century, which class of the French society had to pay taxes to the State?

1. a. The nobility
2. b. The clergy
3. c. The traders and the peasants
4. d. None of the above

Solution:

The French society was divided into 3 estates, the first, second, and third estates. The clergy and the nobility belonged to the first and second estates respectively. The traders and peasants belonged to the third estate and had to pay taxes to the state.

Question 2. Who sought to build a cooperative community called "New Harmony," in the United States of America?

1. a. Robert Owen
2. b. Louis Blanc
3. c. Karl Marx
4. d. Friedrich Engels

Solution:

Robert Owen was a Welsh industrialist and social reformer. In 1825, he built a cooperative community called ‘New Harmony’ in Indiana, United States of America. He was one of the most influential advocates of utopian socialism in the early nineteenth century.

Question 3. The book "Third Reich of Dreams written by-

1. a. Charlotte Beradt
2. b. Ernst Hammer
3. c. Der Sturmer
4. d. Elvira Bauer

Solution:

Charlotte Beradt was the author of ‘Third Reich of Dreams’. The book is a compilation of dreams and nightmares of Germans from 1933-1939.

Question 4. With which country the Bolsheviks made a treaty at Brest Litovsk?

1. a. Italy
2. b. France
3. c. Austria
4. d. Germany

Solution:

The Treaty of Brest-Litovsk was a peace treaty signed between the Bolsheviks and the Central Powers led by the German Empire. It was signed at the German-controlled area of Brest-Litovsk. The treaty ended Russia’s participation in World War I.

Question 5. Match the Column ‘A’ with Column ‘B’ and choose the correct option -

Solution:

The German Empire ended with the abdication of Kaiser Wilhelm II on 9th November 1918. The Weimar Republic was the government of Germany from 1919 to 1933. The Treaty of Versailles was signed on 28th June 1919. Hitler was appointed as the Chancellor of Germany on 30th January 1933. Germany invaded Poland on 1st September 1939. It marked the beginning of World War II.

Question 6. Choose incorrect statement-

1. a. Indian Forest Act was enacted in 1865
2. b. Indian Forest Act was amended in 1878 and 1927.
3. c. The 1878 act divided forests into three categories.
4. d. The villagers could take wood from all three categories.

Solution:

The Indian Forest Act was passed in 1865. It was amended in 1878 and 1927. The amendment in 1878 divided Indian forests into 3 categories- reserved, protected and village forests. The villagers had no access to reserved forests and limited access to protected forests. Only village forests were open for villagers to use.

Question 7. Who were called Junkers?

1. a. Land-owners
2. b. Workers
4. d. Artisans

Solution:

Question 8. 'Vietnam Cong San Dang’ Party was established by-

1. a.Liang Qichao
2. b. Phan Boi Chau
3. c. Phan chu Trinh
4. d. Ho chi Minh

Solution:

Ho Chi Minh established the Vietnam Cong San Dang Party in 1930. Also known as the Communist Party of Vietnam, it is the ruling communist party of Vietnam.

Question 9. In which session of Indian National Congress Non -cooperation programme was adopted?

1. a. Nagpur, 1920
2. b. Amritsar, 1919
3. c. Ahmedabad 1921
4. d. Gaya, 1922

Solution:

Question 10. Match Column 'A' with Column 'B' and choose the correct option-

Solution:

Industrialists hired jobbers to find recruits. The jobbers became figures of authority and began to demand bribes and started controlling the lives of workers.

Tenements are run-down houses and overcrowded apartment houses.

The Inquisition was a powerful Roman Catholic court which identified and punished heretics throughout Europe and the Americas. The Pickwick Papers was Charles Dickens’ first novel. It popularised serialised novels.

Question 11. In democracy

1. a. Freedom to oppose is necessary for the people.
2. b. People can not elect or change their representatives.
3. c. People do not have the right to freedom of expressing their ideas.
4. d. People's right to freedom of formation of association is not essential.

Solution:

Democracy empowers its citizens with rights to question and criticize the government when it makes unfavorable decisions affecting them. In a Democracy people have the right to oppose, show dissent and protest against the governments in a non-violent and peaceful manner.

Question 12. " I have fought against white domination and I have fought against black domination. I have cherished the ideal of a democratic and free society in which all persons live together in harmony and with equal opportunities. It is an

1. a. Nelson Mandela
2. b. Mahatma Gandhi
3. c. Subhash Chandra Bose
4. d. Lai Bahadur Shastri

Solution:

Nelson Mandela is known for his endeavour against racial discrimination and apartheid in South Africa. He was tried and imprisoned for the same at the Robben Island Prison between 1964 to 1982. Later, he went on to become the first black president of South Africa (1994-1999).

Question 13. Philosophy behind the Indian constitution is known through-

1. a. The Preamble
2. b. Fundamental Rights
3. c. Directive Principles of State Policy
4. d. Right to Constitutional Remedies

Solution:

The Preamble to the Constitution of India summarises the essence of the constitution and the principles and philosophies present in it. The Preamble declares India to be a Sovereign, Socialist, Secular and Democratic and Republic.

Question 14. Minimum condition /conditions of a democratic election is/are-

1. a. Everyone should be able to choose. This means that everyone should have the right to vote and every vote should have equal value.
2. b. There should be something to choose from. Parties and candidates should be free to contest elections and should offer some real choice to the voters.
3. c. The choice should be offered at regular intervals. Elections must be held regularly after a few years.
4. d. All of the above.

Solution:

Democracy is a form of government in which people choose their representatives through free and fair elections held at regular intervals. Free and fair elections means that the voters are free to choose between political parties in elections held at regular intervals and there would be no misuse of power by the political party in power and cases of corruption like bribing voters at the time of election.

Question 15. In India, the supreme power/powers Lok Sabha exercises over the Rajya Sabha is/ are:-

1. a.In a joint session, members of both the Houses sit together. Because of the larger number of members, the view of the Lok Sabha is likely to prevail in such a meeting.
2. b.Once the Lok Sabha passes the budget of the government or any other money-related law, the Rajya Sabha cannot reject it.
3. c.Only a person who enjoys the support of the majority of the members in the Lok Sabha is appointed the Prime Minister.
4. d.All of the above.

Solution:

The Lok Sabha is known as the lower house of the parliament or the House of the people and the Rajya Sabha is known as the upper house of the parliament or the Council of states. The Lok Sabha enjoys certain powers than the Rajya Sabha because members of the Lok Sabha are elected directly by the people. The Constitution of Indiaalso mandates that the Council of ministers are directly responsible to the Lok Sabha

Question 16. The Supreme Court of India can take up any dispute

1. a. Between citizens of the country.
2. b. Between citizens and government.
3. c. Between the Union government and the state government.
4. d. All of the above.

Solution:

According to the Constitution of India, the original jurisdiction of the Supreme Court of India is to deal with disputes between the Central government and state governments. However, the Supreme Court of India can hear appeals in cases that deal with disputes between citizens of the country and between citizens and the government but cannot be approached directly on the same.

Question 17. Feature/features of a federal form of government is/are-

1. a. There are two or more levels of government.
2. b. Different tiers of government govern the same citizens.
3. c. A single level of government cannot amend the fundamental provisions of the constitution at its own.
4. d. All of the above.

Solution:

Federalism is a type of government in which the power is divided between the central government and other lower levels of government. Or in other words, power is not concentrated within a single level of government like the central government.

Question 18. Education is a subject of -

1. a. Union List
2. b. State List
3. c. Concurrent List
4. d. None of the above

Solution:

The Constitution of India enlists three lists under the seventh schedule, namely, Union list, state list and the concurrent list in order to divide power between the centre and states. Education is a subject under concurrent list which means both parliament of India and the state assembly can make laws on this subject.

Question 19. The third level (Local self-government) of the democratic government system was made more powerful and effective in-

1. a. 1992
2. b. 1993
3. c. 1994
4. d. 1996

Solution:

The 73rd Constitutional Amendment Act of 1992 introduced the Panchayati Raj system, a third tier to our federal structure. Local self-governments at the village level became more powerful and effective as it got constitutional backing to them.

Question 20. Match Column ’A’ with Column 'B' and choose the correct option-

Solution:

The President is the ceremonial head of our nation. Similarly, the Governor is the head of the Indian states. Mayor is responsible for the administration of municipal corporations and the sarpanch heads the gram panchayats.

Question 21. Which one of the following rivers flows through a rift valley?

2. b. Krishna
4. d. Tapi

Solution:

Tapi river flows through a rift valley. It originates near Multai reserve forest in Betul district of Madhya Pradesh. Flowing westward, Tapi enters Maharashtra and Gujarat before draining into the Arabian sea.

Question 22. A large proportion of children in a population is the result of-

1. a. High birth rate
2. b. High death rate
3. c. High life expectancy
4. d. None of the above

Solution:

Birth rate and death rate determine the population growth. A high birth rate results in a large population of children. Likewise, a high death rate may cause a decline in population.

Question 23. Which one of the following characterises the cold-weather season in India?

1. a. Warm days and warm nights
2. b. Warm days and cold nights
3. c. Cold days and cold nights
4. d. Cold days and warm nights

Solution:

The cold season in India is characterised by warm days and cold nights. This season usually starts during November and ends by the end of February. The weather is normally marked by clear sky, low temperatures, low humidity and feeble winds.

Question 24. Which one of the following causes rainfall during winters in the north-west region of India?

1. a. Cyclonic depression
2. b. Western disturbances
3. c. Retreating monsoon
4. d. Southwest monsoon

Solution:

Western disturbances is a type of extratropical cyclone originating over the Mediterranean region. It carries moisture towards the Indian subcontinent due to westerlies. This causes sudden rainfall during the winter in the northwestern parts of India.

Question 25. Which of the following conservation strategies does not directly involve communities ?

1. a. Joint forest management.
2. b. Beej Bachao Andolan.
3. c. Chipko Movement.
4. d. Demarcation of Wildlife sanctuaries

Solution:

A wildlife sanctuary is an area where animal habitats and their surroundings are protected from any sort of disturbance. The capturing, killing and poaching of animals is strictly prohibited in these regions.The government notifies such areas. Demarcation of such sanctuaries are done by the government, thus communities are not directly involved in this process.

Question 26. The tropic of cancer does not pass through-

1. a. Rajasthan
2. b. Odisha
3. c. Chhattisgarh
4. d. Tripura

Solution:

The tropic of Cancer passes through eight states in India. These states include Rajasthan, Gujarat, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura and Mizoram. The tropic of Cancer doesn't pass through the state of Odisha.

Question 27. What is' The Himalayan Yew'?

1. a. Medicinal plant
2. b. Himalayan animal
3. c. Himalayan bird
4. d. None of these

Solution:

The Himalayan Yew is a medicinal plant. This evergreen plant is found in the high altitude areas of Himalayan region.

Question 28. The finest type of Iron ore is -

1. a. Magnetite
2. b. Haematite
3. c. Limonite

Solution:

Iron can be extracted from various types of ores. These include hematite, limonite, Magnetite, siderite etc. Magnetite is the finest type of Iron ore.

Question 29. Match Column ‘A’ with Column ‘B’ and choose the correct option

Solution:

Question 30. In which field ' School Bhuvan Portal' is providing map based learning to the students to bring awareness about their role.

1. a. Country's natural resources environment and sustainable development.
2. b. About the educational institutions of the country.
3. c. To provide career guidance to the students.
4. d. None of the above.

Solution:

School Bhuvan portal provides map-based learning to the students. This initiative aims to bring awareness among the students about the country's natural resources, environment, and their role in sustainable development.

Question 31. Main purpose of buffer stock scheme is

1. a. To save food grains from pest attack
2. b. To stop price fluctuations
3. c. To meet the crisis of low production
4. d. Both (b) and (c)

Solution:

The price of food grains fluctuates with deviating harvest. To stop such price fluctuations, food grains are bought and stocked during a good harvest season under the buffer stock scheme. It helps to prevent prices falling below a target level. During a poor harvest season, stocks are released to avoid a food crisis and prices rising above a target level.

Question 32. Antyodaya Anna Yojana and Annapurna Scheme are linked with-

1. a. Public Distribution system
2. b. Mid-day Meal
3. c. Special Nutrition Programme.
4. d. None of these

Solution:

Antyodaya Anna Yojna and Annapurna Scheme are linked with the Public Distribution System. To make the Public Distribution System beneficial, Antyodaya Anna Yojna was launched to provide highly subsidized food to one crore poorest of the poor families. Similarly, under the Annapurna Scheme, food grains are distributed at free of cost to senior citizens regularly.

Question 33. The two components of Indian government food security system are-

1. a. Buffer Stock and Public Distribution system
2. b. Mid day meal and Antyodaya Anna Yojna
3. c. Integrated Child Development Services and Food for Work Programme.
4. d. None of the above

Solution:

Buffer stock and Public Distribution system are two main components of the food security system of the Indian government. Buffer stock is maintained for essential commodities like food grains, pulses etc. Under the Public Distribution System, commodities like wheat, rice, sugar are allocated to the States/UTs for distribution. The public distribution system is operated under the joint responsibility of the Central and the State Governments.

Question 34. MGNREGA is associated with -

1. a. Creation of employment in rural areas
2. b. Creation of employment in urban areas
3. c. Creation of employment for the minorities
4. d. All of the above

Solution:

MGNREGA (Mahatma Gandhi National Rural Employment Guarantee Act) is associated with the creation of employment only in rural areas. Passed in 2005, this act aims to provide guaranteed wage employment to rural unskilled labour on-demand basis and increase their economic and social security.

Question 35. On which basis public and private sectors are categorised?

1. a. Conditions of employment
2. b. Nature of economic activities
3. c. Ownership of enterprises
4. d. Number of workers

Solution:

The public and private sector are categorized on the basis of ownership of enterprises. The public sector enterprise is owned and operated by the state. Whereas, the private sector enterprise is owned and operated by an individual or group of individuals.

Question 36. Which is not a feature of the organized sector?

1. a. Pension facility
2. b. Leave with pay facility
3. c. Entitled to medical benefits
4. d. Unsafe employment

Solution:

In the organized sector, the terms of employment are fixed and regular. Employees are provided with pension facilities, medical benefits, paid leaves and also a safe working environment. In India more number of people are employed under the unorganized sector.

Question 37. The most common way for the investment of Multinational companies (MNC) between countries all over the world is-

1. a. Buy existing local companies
2. b. Setup new factories
3. c. Form partnership with local companies
4. d. None of the above

Solution:

To expand their business, Multinational companies (MNC) look for various investment options worldwide. The most common way is acquiring or buying existing local companies. It helps them to gain access to the market and existing operational activities. While setting up new factories or forming partnerships may incur a higher operating cost or limited access to the market.

Question 38. Which of the following factors is responsible for poverty according to social scientists-

1. a. Less Income
2. b. Less Consumption
3. c. Social Exclusion
4. d. All of the above

Solution:

Poverty is the result of various socio-economic factors like the absence of employment opportunities, inadequate infrastructure, inequality, etc. Additionally, Social scientists identify social exclusion as a factor responsible for poverty. Less Income would lead to a lower standard of living. Less consumption of nutritious food, health and educational services would put them in a vicious cycle of poverty.

Question 39. The price that is announced before the sowing season is called -

1. a. Issue price
2. b. Fair price
3. c. Market price
4. d. Minimum support price

Solution:

Minimum support price is announced before the sowing season for certain crops. It aims to prevent losses suffered by the farmers, in case of a price fall. If the open market prices are less than the cost incurred, the government buys the farmers' harvest directly at the announced MSP.

Question 40. Which sector includes agriculture and animal husbandry?

1. a. Primary sector
2. b. Secondary sector
3. c. Tertiary sector
4. d. None of the above

Solution:

The primary sector of the economy includes activities related to the extraction and production of raw materials by utilising natural resources. Agriculture and animal husbandry, forestry, fishing, poultry farming are few activities that are included in this sector.

Question 41. What kind of Decimal Expansion has the number 4 ⅛ ?

1. a. Non terminating recurring
2. b. Terminating
3. c. Non terminating non-recurring n
4. d. None of the above

Solution:

Converting the mixed fraction into decimal form shows that the number is terminating.

4 ⅛ = 4 + ⅛ = 4 + 0.125 = 4.125

Question 42. If sin x = 3/5, cos y = 12/13, then the value of tan x + tan y will be

1. a. 7/6
2. b. 5/6
3. c. 11/6
4. d. 6/7

Solution:

Question 43. The mean of prime numbers between 20 and 30 is-

1. a. 21
2. b. 26
3. c. 25
4. d. 27

Solution:

The prime numbers between 20 and 30 are 23 and 29.

Mean of 23 and 29 = 23 + 29 / 2= 52 / 2 = 26

Question 44. In the given figure, if line PQ and line RS intersect at a point T such that PRT = 40o, and RPT = 95o and TSQ = 75o, then the value of SQT will be

1. a. 45o
2. b. 75o
3. c. 60o
4. d. 40o

Solution:

Since PQ and RS are two straight lines intersecting at T, therefore, ∠RTP = ∠QTS (Vertically opposite angle property).

Question 45. . In the given fig. AM⊥BC and AN is the bisector of A. If B = 650 and C = 33o, then the value of MAN will be

1. a. 33o
2. b. 25o
3. c. 16o
4. d. 41o

Solution:

In ΔABC,

∠ABC+ ∠BAC + ∠BCA = 180o (Using the angle sum property of a triangle)

65o + 33o + ∠BAC = 1800

∠BAC = 180o - 98o = 82o

Now, AN is the angle bisector of the angle BAC.

∠BAN = ∠NAC = 82o / 2 = 41o

In ΔBAM,

∠MBA + ∠BAM + ∠BMA = 180o (Using the angle sum property of a triangle)

65o + 90o + ∠BAM = 180o

∠BAM = 180o - 155o = 25o

Now, ∠MAN = ∠BAN - ∠BAM = 41o - 25o = 16o

Question 46. In the given figure AB = AC and DB = DC, Then ABD : ACD will be

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

Solution:

An easy way to solve this question is to draw a line AD in the figure.

Question 47. In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the value of vertex angle will be

1. a. 126o
2. b. 124o
3. c. 128o
4. d. 120o
5. a.deg; + a° + 4a° = 180°

6a° = 180°

a.deg; = 30°

4a° = 120°

Solution:

Let the value of base angle be a° .

Now based on the conditions in the questions and applying angle sum property we get:

∠PQR +∠PRQ + ∠QPR = 180°

a.deg; + a° + 4a° = 180°

6a° = 180°

a.deg; = 30°

4a° = 120°

Question 48. In the given figure OCDE is a rectangle inscribed in a quadrant of a circle of 10 cm radius. If OE = 2√5 cm, then the area of rectangle will be

1. a. 38 cm2
2. b. 40 cm2
3. c. 42 cm2
4. d. 44 cm2

Solution:

Radius of the circle = Diagonal of the rectangle = 10 cm

OE = CD = 2 √5 (Opposite sides in a rectangle are equal)

Now, in triangle OCD, using the pythagorean theorem,

OD2 = CD2 + OC2

(102) = (CD)2 + (2√5)2

CD2 = 100 - 20 = 80

CD = 4√5 cm

Now, area of the rectangle OEDC = OC X CD = 2√5 × 4√5 = 8 × 5 = 40cm2

Question 49. The length of a chord which is at a distance of 4 cm from the centre of a circle of radius 6 cm will be-

1. a. 4√5 cm
2. b. 3√5 cm
3. c. 2√5 cm
4. d. 5√5 cm

Solution:

Let the image given below be a representation of the condition given in the question.

Let the cord be AC.

In ΔAOB, by applying pythagoras theorem.

OA2 = AB2 + OB2

62 = AB2 + 42

AB2 = 20

AB = 2√5

Since, AB is half of AC, the length of chord will be 2AB.

AC = 4√5

Question 50. The radius and slant height of the cone are in the ratio 4 : 7. If its curved surface area is 792 cm2, then its radius will be-

1. a. 12 cm
2. b. 4 cm
3. c. 9 cm
4. d. 7 cm

Solution:

Ratio of the radius of the cone and its slant height is 4:7

Let the radius and the slant height of the cone be 4x and 7x respectively.

Curved surface area of a cone = πrl = 22/7 × 4x × 7x = 792 cm2

88x2 = 792

x2 = 9

x = 3

Therefore, the radius of the cone = 4x = 4 × 3 = 12 cm

Question 51. A cone and a hemisphere have equal bases and equal volumes. Then the ratio of their heights will be-

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

Solution:

The bases of cones and hemispheres are equal. Hence, their radii are equal.

Given: Volume of cone = Volume of hemisphere

1 / 3 𝜋r2h = 2 / 3 𝜋r3

⇒ h = 2 r

⇒ h / r= 2 / 1

Hence, the ratio of their heights is 2:1.

Question 52. The mean of marks Scored by 100 students was found to be 40. Later on it was discovered that a Score of 53 was misread as 83. Then the correct mean will be-

1. a. 39 .7
2. b. 39.9
3. c. 39.6
4. d. 39.8

Solution:

Mean of marks = 40

Total Students = 100

Hence, Total Marks = Mean ✕ Total students = 40 ✕ 100 = 4000

Corrected Total Marks = 4000 - 83 + 53 = 3970

Now, the correct mean = Corrected Total marks/ Total students = 3970/100 = 39.7

Question 53. If α, β and γ are the zeroes of a cubic polynomial ax3 + bx2 + cx + d = 0, then the value of α + β + γ will be

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

Solution:

Sum of roots of the cubic equation ax3 + bx2 + cx + d = 0 is given by -b / a.

Hence, α + β + γ = -b / a

Question 54. For what value of p the points (11,4), (1, –1) and (p, 1) are collinear?

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

Solution:

Given: A (11, 4), B (1, -1), and C (p, 1) are collinear.

If these points are collinear, then the slopes of the lines made using any two pairs are equal.

Slope of AB =

$$\frac{-1-4}{1 - 11} = \frac{-5}{-10} = \frac{1}{2}$$

Slope of AC =

$$\frac{1-4}{p - 11} = \frac{-3}{p-11}$$

Slope of AB = Slope of AC

$$\frac{1}{2} = \frac{-3}{p-11}$$

⇒ 1(p - 11) = -6

⇒ p - 11 = -6

⇒ p = -6 +11

⇒ p = 5

Question 55. The sum of probability of an event E and Probability of the event not E' is always equal to

1. a. -1
2. b. 1
3. c. 0
4. d. ½

Solution:

The sum of the probability of all events in an experiment is 1.

P(E) + P(E’) = 1

Question 56. Two consecutive positive even integers, the sum of whose squares is 164, will be

1. a. 6 and 8
2. b. 8 and 10
3. c. 10 and 12
4. d. 4 and 6

Solution:

Let two consecutive positive even integers be y and y+2.

Given: y2 + (y + 2)2 = 164

⇒ 2y2 + 4 + 4y = 164

⇒y2 + 2y - 80 = 0

⇒(y + 10) (y - 8) = 0

⇒ y = -10 or 8

y = 8 and y + 2 = 8 + 2 =10 (∵positive even integers)

Hence, two consecutive positive even integers are 8 and 10.

Question 57. Let ∆ABC ∼ ∆DEF and their areas be respectively, 64 cm2 and 121 cm2, If EF = 15.4 cm, then the value of BC is

1. a. 11.2 cm
2. b. 11.6 cm
3. c. 11.4 cm
4. d. 11.8 cm

Solution:

Given: ∆ABC ∼ ∆DEF

Question 58. How many terms of the A.P. 9, 17, 25…… must be taken to give a sum of 636

1. a. 13
2. b. 11
3. c. 14
4. d. 12

Solution:

For the given AP series:

First term, a = 9

Common difference, d =17-9 = 8

Sn = 636

∴ 636 = n/2 [2 × 9 + (n-1) × 8]

⇒ 636 = n/2 [18 + 8n - 8]

⇒ 636 = n[9 + 4n - 4]

⇒ 636 = 5n + 4n2

⇒ 4n2 + 5n - 636 = 0

⇒ 4n2 + 53n - 48n - 636 = 0

⇒ n (4n + 53) - 12 (4n + 53)= 0

⇒ (n - 12) (4n + 53) = 0

⇒ n = 12 or -53 / 4

⇒ n = 12 (∵ terms can’t be negative)

Question 59. If the points A (6, 1), B (8, 2), C (9, 4) and D (p, 3) are the vertices of a parallelogram, taken in order, then the value of p will be -

1. a. 6
2. b. 9
3. c. 8
4. d. 7

Solution:

Given: A(6,1), B(8,2), C(9,4), D(p,3) are vertices of parallelogram.

AC and BD bisects each other at point E. (Property of parallelogram)

∴ Midpoint of AC = Midpoint of BD

Question 60. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes will be

1. a. 51 ½ cm2
2. b. 51 ⅓ cm2
3. c. 51 ¼ cm2
4. d. None of these

Solution:

From the image given below it is clear that the minute hand covers 30° in 5 minutes.

Given: The length of the minute hand of the clock, r = 14 cm

Now, the area of sector of a circle of angle 𝜃 and radius r is given by πr2 ✕ θ / 360o

Area swept by minute hand in 5 minutes will be:

⇒ 22 / 7 ✕ (14)2 ✕ 30o / 360o

⇒ 22 / 7 ✕ 196 ✕ 1/12 = 154 / 3 = 51

Thus, the area swept by a minute hand in 5 minutes will be 51 ⅓ cm2.

Question 61. If a cell is placed in hypertonic solution it will

1. a. Shrink
2. b. Show plasmolysis
3. c. Swell up
4. d. No change in shape and size

Solution:

A cell placed in hypertonic solution loses water by exosmosis and it shrinks.

Question 62. A plant hormone which inhibits plant growth is

1. a. Auxin
2. b. Cytokinin
3. c. Gibberellin
4. d. Abscisic Acid

Solution:

Abscisic acid (ABA) is a plant growth inhibiting hormone. It causes wilting of leaves, helps in closure of stomata, abscission of fruits, seed dormancy, etc.

Question 63. The disease caused due to deficiency of iron in the human diet is

1. a. Anaemia
2. b. Goitre
3. c. Scurvy
4. d. None of the above

Solution:

Anaemia is the disease caused due to the deficiency of iron. Goitre and scurvy is caused due to the deficiency of iodine and vitamin C respectively.

Question 64. Oxygen-rich blood from the lungs comes to which chamber of the heart

1. a. Right atrium
2. b. Left atrium
3. c. Both (a) and (b)
4. d. None of the above

Solution:

The pulmonary vein carries oxygenated blood from the lungs to the left atrium.

Question 65. The enzyme that is responsible for break down of starch into simple sugar in human mouth is

1. a. Amylase
2. b. Pepsin
3. c. Lipase
4. d. Trypsin

Solution:

Salivary amylase is the enzyme that helps breakdown starch into simple sugar maltose in the mouth.

Question 66. The mode of nutrition in fungi is -

1. a. Only saprotrophic
2. b. Saprotrophic or parasitic
3. c. Only parasitic
4. d. None of the above

Solution:

Majority of the fungi basically have a saprotrophic mode of nutrition. Although many disease causing parasitic fungi are also found.

Question 67. Which organelle of a cell contains its own DNA besides the nucleus?

1. a. Endoplasmic Reticulum
2. b. Golgi bodies
3. c. Mitochondria
4. d. Lysosome

Solution:

Mitochondria is a semi-autonomous cell organelle. It has its own genetic material in the form of a double-stranded circular DNA.

Question 68. Which one of the following is not a bacterial disease?

1. a. Cholera
2. b. COVID-19
3. c. Tuberculosis
4. d. Anthrax

Solution:

COVID-19 is a viral disease caused by coronavirus. Whereas cholera, tuberculosis and anthrax are bacterial diseases.

Question 69. Which of the following has an open circulatory system?

1. a. Arthropoda
2. b. Porifera
3. c. Annelida
4. d. Coelenterata

Solution:

Arthropods have an open circulatory system. The blood flows without blood vessels directly into the haemocoel.

Question 70. Which of the following is not a component of phloem?

1. a. Stone cell
2. b. Sieve plate
3. c. Sieve tube
4. d. Phloem parenchyma

Phloem consists of sieve plates, phloem fibres, sieve tubes, and phloem parenchyma. Stone cells are also called sclereids and constitute sclerenchymatous tissue.

Solution:

Phloem consists of sieve plates, phloem fibres, sieve tubes, and phloem parenchyma. Stone cells are also called sclereids and constitute sclerenchymatous tissue.

Question 71. The function of centrosome is-

1. a. Formation of spindle fibres
2. b. Protein synthesis
3. c. Osmoregulation
4. d. Secretion

Solution:

Centrosome helps in the formation of spindle fibres during cell division.

Question 72. Which of the following juice is secreted by pancreas?

1. a. Trypsin
2. b. Pepsin
3. c. Bile juice
4. d. Both (a) and (b)

Solution:

Trypsin is an enzyme secreted by pancreas which helps in the digestion of proteins.

Question 73. A person suddenly spots a snake. His heart beat increases and blood pressure also goes up. Which hormone is being released in his body at that time?

1. a. Parathormone
3. c. Corticoid
4. d. Thyroxine

Solution:

Adrenalin is a hormone synthesized by stimulation of the sympathetic nervous system in response to fight, flight and fright/fear.

Question 74. When ice melts at the same temperature 0o C (273 Kelvin) , which one of the following has more energy?

1. a. Energy of water particles
2. b. Energy of ice particle
3. c. Both water and ice particles have same energy
4. d. None of these

Solution:

Energy possessed by the particles of water is maximum as ice melts into water by absorbing the latent heat of fusion.

Question 75. In order to balance a chemical equation, it is necessary to satisfy the law of

1. a. Conservation of motion
2. b. Conservation of momentum
3. c. Conservation of energy
4. d. Conservation of mass

Solution:

In order to balance a chemical reaction, law of conservation of mass needs to be satisfied. The process of balancing chemical equations makes the number and type of atoms equal on both sides of the chemical equation.

Question 76. Which of the following phenomena occurs when a small amount of acid is added to water?

1. a. I and II
2. b. I and III
3. c. II and III
4. d. II and IV

Solution:

Ionization of a compound refers to a process in which a neutral molecule splits into charged ions when exposed in a solution. According to Arrhenius theory, acids are the compounds that dissociate in an aqueous medium to generate hydrogen ions (H+). Addition of acid to water leads to decrease in concentration of H+ ions per unit volume leading to dilution of the acid.

Question 77. Which of the following statements is usually correct for carbon compounds?

1. a. I and III
2. b. II and III
3. c. I and IV
4. d. II and IV

Solution:

The compounds of carbon are poor conductors of electricity due to the absence of free electrons in the compounds and also they are bonded by covalent bonds which is a weak force of attraction compared to ionic bonds.

Question 78. Which one of the following is the weakest acid?

1. a. H2SO4
2. b. HNO4
3. c. H2SO3
4. d. HCl

Solution:

H2SO3 is the weakest acid amongst all of them. A strong acid dissociates completely in aqueous medium to give H+ ions. H2SO3 on the other hand partially dissociates in water.

Question 79. A milkman adds a very small amount of baking soda to fresh milk, why?

1. a. To increase the rate of fermentation
2. b. To decrease the rate of fermentation
3. c. To increase the quality of milk
4. d. To make paneer

Solution:

The milkman adds a very small amount of baking soda in fresh milk to increase the pH of the milk which in turn slows down the process of curdling by reducing the rate of fermentation.

Question 80. Read carefully the following statements regarding the ions Na+, Mg2+, F- and O2-

1. a. I and II
2. b. I,II and III
3. c. I,III and IV
4. d. All are correct

Solution:

The number of valence electrons in Na+, Mg2+, F- and O2- is 8. They have attained the stable octet configuration of the nearest noble gas “Neon”. Thus, they have the same electronic configuration and electron shells.

Question 81. Two elements P and Q have 5 and 7 electrons in their outermost shell respectively. Atomic number of P and Q will be

1. a. 5 and 7
2. b. 9 and 11
3. c. 23 and 25
4. d. None of the above

Solution:

Atomic number = number of protons = number of electrons

Z (5) = 2, 3

Z (7) = 2, 5

Z(9) = 2, 7

Z (11) = 2, 8, 1

Z (23): 2, 8, 11, 2

Z (25): 2, 8, 13, 2

Thus, none of the options have 5 and 7 electrons in their outermost shell, respectively.

Question 82. In which reaction the addition and removal of oxygen take place simultaneously?

1. a. Oxidation reaction
2. b. Reduction reactions
3. c. Redox reactions
4. d. Precipitation reactions

Solution:

The addition of oxygen to a chemical entity is called oxidation and removal of oxygen from a chemical entity is called reduction. The reaction where both the processes happen simultaneously is known as a redox reaction.

Question 83. A piece of charcoal was heated over the flame of the burner. When it starts burning it is immediately dipped into a boiling tube containing water. Now this solution is transferred to another boiling tube and a piece of litmus paper is dipped into it. What will be the observation?

1. a. Blue litmus turns to red
2. b. Red litmus turns to blue
3. c. No change in the colour of litmus
4. d. None of the above

Solution:

The burning of charcoal over the flame of the burner produces carbon dioxide.

C + O2 → CO2

When carbon dioxide is mixed with water, it produces carbonic acid. Carbonic acid turns blue litmus red.

CO2 + H2O → H2CO3

Question 84. At a refinery petroleum is separated into several components by a process called fractional distillation using a fractionating column. Which of the following statements is incorrect about the process?

1. a. I only
2. b. I and II
3. c. II only
4. d. II and IV

Solution:

The statements II, III and IV are incorrect.

The most volatile compounds get collected at the top of the column. The fraction with the lowest boiling point condenses first at the top of the fractional distillation column due to its lower density and molecular weight. At each level of a fractionating column a mixture of hydrocarbons can also be produced which are then processed to obtain different products.

Question 85. Which of the following sets contains all the possible combustion products of methane?

1. a. C, CO2, CO and H2O
2. b. C, CO and H2
3. c. CO2, CO, H2 and water
4. d. CO and water

Solution:

Complete combustion of methane produces carbon dioxide and water.

$$CH_{4}(g) + 2O_{2}(g)\rightarrow CO_{2}(g) + 2H_{2}O(g)+energy$$

Incomplete combustion of methane, on the other hand, produces carbon monoxide, water and some unburnt carbon.

$$4CH_{4}(g) + 5O_{2}(g)\rightarrow 2CO(g) + 8H_{2}O(g) + 2C (s)$$

Question 86. Strips of metal X were dipped into the solution of silver nitrate and zinc nitrate separately. A greyish metallic deposit was found on both the strips. Metal X could be

1. a. Cu
2. b. Mg
3. c. Pb
4. d. Fe

Solution:

Since both silver and zinc got displaced from their nitrate solutions, it can be said that the metal which displaces them is more reactive than that of silver and zinc. Thus, the only possible metal capable of performing the reaction is magnesium.

2AgNO3(aq) + Mg (s) → Mg(NO3)2(aq) + 2Ag(s)

Zn(NO3)2(aq) + Mg (s) → Mg(NO3)2(aq) + Zn(s)

Question 87. Some gases evolved during different tests are given in column A. Column B shows their characteristics. Match column A with column B and choose the correct option-

Solution:

Chlorine is a gas having greenish-yellow colour and it turns moist starch iodide paper blue.

Hydrogen is a colourless and odourless gas which burns with a pop sound.

Sulphur dioxide has a suffocating smell and turns acidified potassium dichromate solution green.

Hydrogen sulphide is a colourless gas and it turns lead acetate paper black.

Question 88. A boy moving along a circular path of radius 10 m completes ¾ th of the circle in 10 sec. The magnitude of speed and velocity are

1. a. 4.71 m/s and 47.1 m/s
2. b. 4.71 m/s and 1.41 m/s
3. c. 1.41 m/s and 4.71 m/s
4. d. 1.41 m/s and 1.41 m/s

Solution:

Question 89. Two objects have masses in the ratio 1:2. If the forces acting on them are in the ratio 2:1 then the ratio of their acceleration is -

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

Solution:

Question 90. The given graph shows the displacement versus time relation for a disturbance travelling with velocity 1500 m/s. The wavelength of the disturbance will be

1. a. 3 × 10-3m
2. b. 15 × 10-4m
3. c. 3 × 103m
4. d. 15 × 104m

Solution:

Wavelength = speed × time

Speed = 1500 m/s and time = 2µs = 2 × 10-6s

Wavelength = 1500 × 2 × 10-6 = 3 × 10-3

Question 91. ρ1and ρ2. Two wires of equal length and equal cross section area with resistivity and r2 are connected in a series. The equivalent resistivity of combination is -

1. a. (ρ1 + ρ2)
2. b. ½ (ρ1 + ρ2)
3. c. √ρ1 ρ2
4. d. 2(ρ1 + ρ2)

Solution:

R = ρL / A and in series Req = R1 + R2

ρeq(L+L) / A = ρ1L / A + ρ2L / A; 2ρeqL = ρ1L + ρ2L

ρeq = ½ (ρ1 + ρ2)

Question 92. A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. The catching process is completed in 0.1 second. The force exerted by the ball on the hand of the player is

1. a. 3 Newton
2. b. 30 Newton
3. c. 300 Newton
4. d. 150 Newton

Solution:

F = ma = mx (change in velocity) / change in time

Mass = 150g = 150 × 10⁻³

F = 0.15 × (0-20) / 0.1 = -30 N

Force exerted by the ball on the hand of the player is 30N.

Question 93. The energy produced by converting 1 micro gram of matter completely into energy will be-

1. a. 9 × 1014 Joule
2. b. 9 × 1010 Joule
3. c. 9 × 102 Joule
4. d. 9 × 104 Joule

Solution:

E = (change in mass) x c²

E = 1 x 10⁻³ x 10⁻⁶x (3 x 10⁸)² = 9 x 10⁷ Joule

Question 94. The danger signals installed at the top of tall buildings are red in colour. These can be easily seen from a distance because among all other colours, the red light-

1. a. is scattered the most by smoke or fog.
2. b. is scattered the least by smoke or fog.
3. c. is absorbed the most by smoke or fog.
4. d. is absorbed the least by smoke or fog.

Solution:

Red light is least scattered by smoke, fog or particles since it has the highest wavelength.

Question 95. A wire of Resistance R is coiled in the form of a circle. Then the equivalent resistance between points A and B is-

1. a. R/16 Ω
2. b. 3R/16 Ω
3. c. 3R/4 Ω
4. d. 4/3 Ω

Solution:

Question 96. The ratio of the present age of Sameer and Milan is 8:5. After 6 years, the ratio of their ages will be 3:2. What will be the ratio between the sum of their present ages and the difference of their present ages?

1. a. 39 : 19
2. b. 33 : 9
3. c. 12 : 7
4. d. 13 : 3

Solution:

Let the present age of Sameer and Milan be 8x and 5x respectively.

After 6 years, their ages will be 8x + 6 and 5x + 6 respectively.

Now, (8x+6)/(5x+6) = 3/2

16x+12 = 15x+18

x = 18-12 = 6

Now, sum of present ages of Sameer and Milan = 8x + 5x = 13x = 13×6 = 78

Difference between their present ages = 8x -5x = 3x = 3 × 6 =18

Ratio = 78/18 = 13/3

Therefore, the required ratio is 13:3

Question 96. For a concave mirror of focal length 10 cm. to form twice magnified image, distance of object from its pole is/are

1. a. -5 cm
2. b. -15 cm
3. c. -10 cm
4. d. Both (a) and (b)
5. a. 12 × 6.673 × 10-11 N -m2 / kg2
6. b. 6.673 / 12 × 10-11 N -m2 / kg2
7. c. 6.673 × 10-11 N -m2 / kg2
8. d. 6.673 / 6 × 10-11 N -m2 / kg2

Solution:

Magnification = image distance/object distance = +2 or -2

1 / v + 1 / u = 1 / f

Taking m = 2

2 = -v / u

v = -2u

Now,

1 / v + 1 / u = 1 / f

-12 / u + 1 /u = -1 / 10

1 / f = 1 / 2u

u = -5 cm

Taking m = -2; v = 2u

Now,

1 / v + 1 / u = 1f

1 / 2u + 1 / v = -110

3 / 2u = -1 / 10

u = -15 cm

Question 97. Value of G on surface of earth is 6.673 × 10-11 m2/kg2, then value of G on surface of Jupiter will be

Value of the universal constant G remains the same everywhere.

G = 6.673 × 10-11 m2/kg2

Question 98. A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistance and respectively. Which of the following is true?

1. a. R1 = R2 = R3
2. b. R1 > R2 > R3
3. c. R3 > R2 > R1
4. d. R2 > R3 > R1

Solution:

V = IR; R = V/I

In a V-I graph, the resistance is directly proportional to the slope of the graph.

But in a I-V graph, resistance and slope is inversely proportional.

Thus, R3 > R2 > R1.

Question 99. A light and a heavy object have same momentum, then

1. a. The kinetic energy of heavy object will be more.
2. b. The kinetic energy of heavy object will be less.
3. c. The kinetic energy of both objects will be same.
4. d. None of the above.

Solution:

K.E = p² / 2m

Kinetic energy is inversely proportional to mass. Since momentum p is the same for both objects, the lighter object will have higher kinetic energy compared to the heavier object.

Question 100. The unit of mass among the following is

1. a. AU
2. b. Light year
3. c. Chandrashekhar limit (CSL)
4. d. Å

Solution: