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

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Bihar NTSE 2020 Stage 1 SAT Paper

### Bihar 2020-21 NTSE Stage 1 - Question Paper With Solutions

Paper: MAT

Direction Question (1 to 4): Mark at the following information and answer the question based on it. Seven students J,K, L, M, N, O and P are standing in a row from left to right in random order such that:

(1) P, O, K and N do not stand at either end.

(2) M is not in the middle.

(3) J stands to the left of P and to the right of O.

(4) K stands on the right side of N and on the left side of L.

Question 1. Who is in the middle of the line?

1. a. N
2. b. J
3. c. P
4. d. K

Solution:

According to the given conditions, M and L occupy either end. Since there are members to the left of L, L is at the right end of the row and M is on the left end of the row. The final arrangement is MOJPNKL.

Question 2. Who is standing fifth from the left side of the row?

1. a. K
2. b. P
3. c. N
4. d. J

Solution:

The final arrangement is MOJPNKL

Question 3. Who is standing to the left of O?

1. a. L
2. b. J
3. c. M
4. d. P

Solution:

Final arrangements is MOJPNKL

Question 4. K travels a certain distance with L at a speed of 3 km/hr. He then completes a total of 27 km with M at a speed of 6 km/hr in 7 hours. Find the distance travelled with M.

1. a. 15 km
2. b. 12 km
3. c. 10 km
4. d. 9 km

Solution:

Let distance with L be x.

x/3+(27-x)/6= 7

(2x+27-x)/6= 7

x + 27 = 42

x = 15

Travelled distance along with M = 27 – x = 27–15 = 12 km.

Direction Questions (5 to 7): Study the following information and answer the questions given below:

• P is the father of A whose son is S.

• L is K's mother who is also the sister of S.

Question 5. How is A related to L?

1. a. Brother
2. b. Husband
3. c. Wife
4. d. Sister

Solution:

From the above family tree, it can be concluded that A is the husband of L.

Question.6. How is A related to K?

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

Solution:

From the above family tree, it can be concluded that A is the father of K since L is the mother of K and also A and L are couples.

Question 7. How is P related to L?

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

Solution:

P is A’s father and L is A’s wife, hence, P is the father-in-law of L as can be seen from the family tree above.

Direction Questions 8 to 10: In each of the following questions, the numbers have been arranged according to thepattern shown in the sample figure given below. Find the missing figure. Replace question mark (?) as a missing character with correct option.

The pattern can be represented as below for the given set of numbers

Question 8. Find the missing figure.

1. a. 11
2. b. 13
3. c. 15
4. d. 17

Solution:

The arrangement of numbers follows the pattern as given below.

Question 9. Find the missing figure.

1. a. 125
2. b. 90
3. c. 105
4. d. 225

Solution:

According to the given pattern above, the numbers are:

152 = 225

Question 10. Find the missing figure.

1. a. 33
2. b. 81
3. c. 243
4. d. 42

Solution:

According to the given pattern above, the numbers are:

3x27 = 81

Direction Questions 11 to 15: Find the missing character in each of the following: In place of question mark (?). Choose the correct option as the answer and mark it on answer sheet as directed.

Question 11. Choose the correct option as the answer.

1. a. 190
2. b. 221
3. c. 236
4. d. 255

Solution:

The rule is being followed clockwise, hence, (127×2) + 1 = ? = 255

Question 12. Choose the correct option as the answer.

1. a. 5
2. b. 9
3. c. 11
4. d. 13

Solution:

Difference between W, T = 3

Difference between S, D = 5

Difference between J, T = 10

So, difference between G, P = 9

Question 13. Choose the correct option as the answer.

1. a. E12
2. b. E10
3. c. F12
4. d. F10

Solution:

Each row has alternate letters either ascending or descending according to their positions. So, the missing letter of the second row is E.

The numbers in the columns are 4, 5, 6, 2, 3, 4 are in AP so, 9, 12, 15 are also in AP.

Hence, the missing character is E12.

Question 14. Choose the correct option as the answer.

1. a. 18
2. b. 33
3. c. 135
4. d. 145

Solution:

Question 15. Choose the correct option as the answer.

1. a. 5
2. d. 6
3. c. 8
4. d. 9

Solution:

Direction Question 16 to 20: In each of the following questions, a set of figure carrying certain characters is given. Assuming that the character in each set follows a similar pattern, find the missing character in each case. Mark the correct selected options as the answer on the answersheet as instructed.

Question 16. Choose the correct option as the answer.

1. a. 8
2. b. 9
3. c. 7
4. d. 21

Solution:

Question 17. Choose the correct option as the answer.

1. a. 6
2. b. 8
3. c. 9
4. d. 12

Solution:

(15–8) × (10–8) = 14 and (8–6) × (9–5) = 8

So, (6–4) × (11–8) = 6

Question 18. Choose the correct option as the answer.

1. a. 678
2. b. 769
3. c. 824
4. d. 937

Solution:

(5 × 1)(4 × 2)(2 × 2) = 584

and (3×2)(3×3)(2×2) = 694

So, (6 × 1)(7×1)(4×2) = 678

Questions 19. Choose the correct option as the answer.

1. a. 535
2. b. 577
3. c. 755
4. d. 775

Solution:

Columnwise: 3[9×5] = 345

4[6×10] = 460

So, 5[7×11] = 577

Question 20. Choose the correct option as the answer.

1. a. 486
2. b. 72
3. c. 162
4. d. 243

Solution:

102×(6÷3) = 100×2 = 200

112×(4÷2) = 121×2 = 242

So, 92×(6÷3) = 81×2 = 162

Question 21. If, A : B = 2:5 and B : C = 3:4 then, what will be the value of A : C?

1. a. 1:2
2. b. 3:10
3. c. 2:3
4. d. 5:4

Solution:

A: B = 2:5 ________ (1)

B: C = 3: 4 ________ (2)

So, A:B::B:C = 6:20

A : C = 3 : 10

Question 22. A clock runs 5 minutes faster in 1 hour. It has been set right at 12:00 in the afternoon. Now the clock is showing 6:30 in the evening. So, what will be the actual time?

1. a. 5:00 pm
2. b. 5:15 pm
3. c. 5:30 pm
4. d. 6:00 pm

Solution:

The time on the clock will be according to t : (t x 5).

For example, after 1 hour, the time shown will be 1 : 05.

So, if 6 : 30 = t : t x 5

Then, t = 6

And therefore, the actual time is 6 : 00, since in 6 hours clock would have been 6 x 5 = 30 minutes faster.

Direction (Q23 to 25):The following Pie-Chart shows the distribution of fruit trees in a field. Consider the chart and answer the question based on it.

Question 23. Sector angle of banana is.........

1. a. 90°
2. b. 54°
3. c. 72°
4. d. 36°

Solution:

100% = 360°. So, 1% = 3.6°

Now sector angle for banana (15%) = 15×3.6 = 54°

Question 24. If there are 960 trees in total, how many of them are mango trees?

1. a. 192
2. b. 288
3. c. 384
4. d. 336

Solution:

Given that there are 960 total trees.

So, 100% = 960, So 1% = 9.6

Now 35% = 336.

Question 25. What is the proportion of chikoo and mango trees in the field to jamun,orange and banana trees?

1. a. 1
2. b. 1:3
3. c. 11:9
4. d. 3:1

Solution:

Using the given pie chart above,

Proportion of Chikoo and Mango trees in the field to Jamun, Orange and Banana trees

=(20+35)/(20+10+15)=55/45=11/9

Question 26. Which of the following words cannot be formed using the words used in 'HIGHLIGHTS'?

1. a. HIGH
2. b. HABIT
3. c. HITS
4. d. HEAT

Solution:

Option (a) : HIGH

HIGHLIGHTS [Rejected]

Option (b) : HABIT

HIGHLIGHTS

AB does not belongs to HIGHLIGHTS

So, it can’t be formed. [Accepted]

Option (c) : HITS

HIGHLIGHTS [Rejected]

Option (d) : HEAT

HIGHLIGHTS

EA does not belongs to HIGHLIGHTS

So, it can’t be formed. [Accepted]

Question 27. If the following four words are arranged in alphabetical order, which word will come third?

1. a. False
2. b. Fool
3. c. Follow
4. d. Faith

Solution:

Dictionary arrangement of the given words is:

I : faith

II : false

III : follow

IV : fool

Direction Question (28 to 32): Which of the following questions is based on the following Alphabet series:

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Question 28. Which letter is exactly midway between G and Q in the given alphabet?

1. a. K
2. b. L
3. c. M
4. d. N

Solution:

GHIJKLMNOPQ: A total of 11 letters.

Median of ‘n’ odd numbers =(n+1)/2=(11+1)/2=6

Here, the 6th letter is L.

Question 29. Which letter in the alphabet is as far from G as T is from M?

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

Solution:

M = 13, T = 20

T-M = 7

So, ? - G = 7

? = 7+7 = 14 = N

Question 30. Which letter is sixteenth to the right of the letter which is fourth to the left of I?

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

Solution:

Question 31. If the above alphabet is written in the reverse order, which will be the eight letters to the right of O?

1. a. F
2. b. G
3. c. V
4. d. W

Solution:

Question 32. If 'ROME' is written as 'MORE' then 'DARE' is written as :

1. a. RDAE/
2. b. RDEA
3. c. RAED

Solution:

Question 33. How many triangles are there in the figure given below?

1. a. 5
2. b. 12
3. c. 9
4. d. 10

Solution:

Total number of triangles = 4+3+2+1 = 10

Question 34. ‘Mirror’ is related to 'Reflection' in the same way as 'water' is related to........?

1. a. Conduction
2. b. Dispersion
3. c. Immersion
4. d. Refraction

Solution:

A mirror reflects light falling on it into the same media the light came in from. When light travels from air to water or vice-versa (two different transparent media) refraction is observed in the form of bending of light.

Question 35. If the car be a transistor, then what would be Petrol?

1. a. Transmitter Electric
2. b. Electric
3. c. Battery/Cell
4. d. Transmission

Solution:

‘Petrol’ is used in a ‘Car’ as fuel.

Similarly, ‘Battery/Cell’ is used as fuel in ‘transistor’.

Question 36. If the fish were birds, what would be the sea be?

1. a. Forest
2. b. Sky
3. c. Nest
4. d. Island

Solution:

Fish lives in the sea. Birds live in the sky. Therefore, if ‘fish’ were ‘birds’ then, ‘sea’ would be ‘sky’.

Question 37. Shirt is related to Button, in the same way as shoes is related to.......?

1. a. Stitch
2. b. Leg
3. c. Socks
4. d. None of these

Solution:

‘Shirt’ is worn by closing up the ‘button’. Similarly ‘Shoes’ are worn by tying up the ‘laces’.

Direction Question 38 to 40: Three words in bold letters are given in each questions, which have something in common among themselves. Out of the four given alternatives, choose the most appropriate description about these three words.

Question 38. Vote : Ballot : Poll

1. a. Election
2. b. Nomination
3. c. Selection
4. d. Participation

Solution:

A secretly written ’Vote” is called ‘Ballot’. Also, a ‘Poll’ is a way of counting votes during an election.

Question 39. Newspaper : Hoarding : Television

1. a. Press
2. b. Media
4. d. Rumour

Solution:

‘Newspaper’ is press media, ‘Hoarding’ is usually related to promoting and advertising through media and ‘Television’ is visual media. Hence, all are related to ‘Media’.

Question 40. Wheat : Barley : Rice

1. a. Food
2. b. Agriculture
3. c. Grams
4. d. Cereals

Solution:

‘Wheat’, ‘Barley’ and ‘Rice’ all are ‘Cereals’.

Direction Question 41 to 45: In each of the following questions- four words have been given, out of which three are alike in some manner and the fourth one is different. Choose out the odd one and mark it on answer-sheet as directed.

Question 41. Choose out the odd one.

1. a. Venus
2. b. Moon
3. c. Saturn
4. d. Mars

Solution:

Venus, Saturn and Mars are planets, whereas the Moon is a natural satellite.

Question 42. Choose out the odd one.

1. a. Iron
2. b. Silver
3. c. Mercury
4. d. Zinc

Solution:

‘Mercury’ is the only liquid metal among all the listed, hence it is the odd one out.

Question 43. Choose out the odd one.

1. a. Infrared rays
2. b. Ultraviolet rays
4. d. X-rays

Solution:

Since ‘infrared rays’, ‘ultraviolet rays’ and ‘X-rays’ have short wavelength radiation and Radio waves have long-wavelength radiation.

Question 44. Choose out the odd one.

1. a. Man-Earth
2. b. Birds-Sky
3. c. Fish-Water
4. d. Train-Station

Solution:

‘Man’ Sustains at ‘Earth‘

and ‘Birds’ Sustain on ‘Sky’

and ‘Fish’ Sustains in ‘Water’

So, ‘Train Sustains at ‘Track’.

Question 45. Choose out the odd one.

1. a. Mother
2. b. Father
3. c. Brother
4. d. Teacher

Solution:

Mother, father, brother all are blood relations except (d). A teacher is a professional.

Direction Question 46 to 50: In the question given below, four figures are given. Three of the four figures are similar on the basis of any one property and one is different in all the ways. Select this different figure.

Question. 46 Select the different figure.

Solution:

Each figure contains two completely filled triangles and two blank circles except in figure (a).

Question 47. Select the different figure.

Solution:

In options (a), (b) and (c) both shapes intersect with each other except in (d).

Question 48. Select the different figure.

Solution:

Quadrilaterals in (a), (b) and (d) are having right angles at their vertices, however, (c) is a parallelogram with no 90o vertex.

Question 49. Select the different figure.

Solution:

(a), (b) and (d) are related to each other because they are symmetrical about at least one of the vertical or horizontal axis, whereas (c) is not a symmetrical figure.

Question 50. Select the different figure.

Solution:

In (a), (b) and (c) all internal lines are straight or cut at 90° angle but not in (d).

Direction Question 51 to 53: Study the diagram shown below and answer the questions based on it. This Venn diagram shows children's choice of colour.

• Rectangle shows the choice of white colour.

• Circle shows the choice of black colour.

• Capsule shaped shows choice of brown colour.

Question 51. How many children like both brown and white but do not like black?

1. a. 10
2. b. 50
3. c. 20
4. d. None of these

Solution:

Only brown 30 + 20 = 50

Only white = 100

Then, the children like only white and brown = 150

Question 52. What is the ratio of the children who like brown to those who like black?

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

Solution:

Brown : Black

20 + 30 + 50 : 50+20+30+5+10

100:115

The ratio of children who like brown to those who like black = 20:23

Question 53. What is the ratio of children who do not like black to children who only like black and white?

1. a. 3:1
2. b. 3:2
3. c. 12:5
4. d. 5:12

Solution:

Solution :

Children who don’t like black = 100+20+30 = 150

Children who only like black and white = 30+20

Question 54. If, WORLD = YMTJF then, CONCERN = ?

1. a. QLECTL
2. b. EQPEGTP
3. c. EMPAGPP
4. d. AMLACPL

Solution:

WORD = YMTJF

CONCERN = EMPAGPP

Question 55. If, PEN = 613 and STRING = 580934 then, RIPENING = ?

1. a. 09631934
2. b. 09163934
3. c. 09316934
4. d. 09613934

Solution:

By direct coding,

RIPENING → 09613934

Question 56. If ‘UNCLE’ is written as ‘QQYOA’, then what will be written to ‘COLUMN’?

1. a. YROXIQ
2. b. YRHQIQ
3. c. YHRXIQ
4. d. YRHXIQ

Solution:

Question 57. If, HIDE = 1440, then what will be the value of ‘WIDE’?

1. a. 1560
2. b. 3265
3. c. 4140
4. d. 2580

Solution:

Here, the alphabets get their code by multiplying their numerical values assigned as

A → 1, B → 2, C → 3 ... and so on.

H → 8, I → 9, D → 4, E → 5

8 × 9 × 4 × 5 = 1440

Hence, WIDE will be written as:

W → 23, I → 9, D → 4, E → 5

23 × 9 × 4 × 5 = 4140

Question 58. In a class of 52 students, 24 students drink milk. 28 students drink tea and 8 students do not drink anything. Find how many students drink both milk and tea.

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

Solution:

X + Y = 28 ...(a)

Y + Z = 24 ...(b)

X + Y + Z + 8 = 52 ….(c)

X + Y + Z = 44

Z = 44 – 28 = 16

Y + Z = 24

Y = 24 – 16 = 8

So, Y = 8

Question 59. If P means ‘÷’, Q means ‘+’, R means ‘–’ and S means ‘×’, then what will be the value of 10R192P48S48P96Q1?

1. a. 10
2. b. 9
3. c. 8
4. d. 7

Solution:

P → ÷

Q → +

R → –

S → ×

Then, 10R192P48S48P96Q1 becomes

10 – 192 ÷ 48 × 48 ÷ 96 + 1

= 10-4×0.5+1 = 9

Question 60. If ‘+’ means ‘×’, ‘–’ means ‘÷’, ‘×’ means ‘+’ and ‘÷’ means ‘–’ then, compute the value of following expression:

1. a. 21
2. b. 25
3. c. 26
4. d. 23

Solution:

According to question

+ → ×

– → ÷

× → +

÷ → –

So, 45 – 9 + 4 × 5 becomes

= 45 ÷ 9 × 4 + 5 = 5 × 4 + 5

= 20 + 5 = 25

Question 61. Pointing to K, M says that I am the daughter of his grandfather's only son.

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

Solution:

Here,

So, M is the sister of K.

Question 62. Which signs should be interchanged to correct the equation given below?

4 – 13 ÷ 7 + 6 ÷ 7 × 1 = 5

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

Solution:

Original equation: 4 – 13 ÷ 7 + 6 ÷ 7 × 1 = 5

a. 4 – 13 × 7 + 6 × 7 ÷ 1 = 4 - 91 + 42 = -45 ≠ 5

b. 4 × 13 ÷ 7 + 6 ÷ 7 - 1 = 52/7+6/7-1=39/7≠ 5

c. 4 + 13÷ 7- 6 ÷ 7× 1 = 4 + 13/7-6/7 = 4+1 = 5

d. 4 – 13 ÷ 7 × 6 ÷ 7 + 1 = 4 - 78/49+ 1 ≠ 5

Only option (c) follows.

Question 63. A, B, C and D are playing cards. A and B are partners. D faces towards North.If A faces towards West, then who faces towards South?

1. a. B
2. b. C
3. c. D
4. d. None of these

Solution:

All four players face the centre of the table. The seating arrangement is as shown:

Hence, C faces towards the South.

Question 64. After walking 6 km, I turned right and covered a distance 2 km, then turned left and covered a distance of 10 km. In the end, I was moving towards the North. From which direction did I start my journey ?

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

Solution:

The path travelled by me is as shown:

Direction (Q.65 to 69): In the following figure, rectangle, square, circle and triangle represent the regions of wheat, gram, maize and rice cultivation respectively. On the basis of figures, answer the following questions.

Question 65. Which area is cultivated by all the four commodities?

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

Solution:

Question 66. Which area is cultivated by wheat and maize only?

1. a. 8
2. b. 6
3. c. 5
4. d. 4

Solution:

Question 67. Which area is cultivated by Rice only?

1. a. 5
2. b. 1
3. c. 2
4. d. 11

Solution:

Question 68. Which area is cultivated by maize only?

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

Solution:

Question 69. Which area is cultivated by rice and maize and nothing else?

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

Solution:

Question 70. In the numbers from 100 to 600, how many times digit 1 comes at the ten's place?

1. a. 6
2. b. 7
3. c. 60
4. d. 50

Solution:

The digit 1 comes at the ten’s place in numbers from 110 to 119, 210 to 219, 310 to 319, 410 to 419, 510 to 519

∴ Required number of times 1 comes at ten’s place = 10 × 5 = 50

Questions 71. How many combinations of two digits numbers having 8 can be made from the following numbers?

8, 5, 2, 1, 7, 6

1. a. 9
2. b. 10
3. c. 11
4. d. 12

Solution:

When 8 is in one’s place there can be 6 two digit numbers, which are: 88, 58, 28, 18, 78, 68.

Question 72. If every second Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then how many working days are there in that month ?

1. a. 20
2. b. 21
3. c. 22
4. d. 23

Solution:

Since, the month begins on Saturday so, 2nd, 9th, 16th, 23rd, 30th days are Sundays ….

Also, 8th and 22nd are Saturdays that are holidays. Therefore, number of working days, we have are 30 – 5 – 2 = 23.

Question 73. In a row of men, Manoj is 30th from the right and Kiran is 20th from the left. When they interchange their position, Manoj becomes 35th from the right. What is the total number of men in a row?

1. a. 34
2. b. 54
3. c. 45
4. d. 44

Solution:

Hence, total number of men in the row = 35 + 20 – 1 = 54

Direction Question 74 to 77: In each of the questions given below, there are two statements labelled as Assertions (A) and Reason (R). Mark your answer as per the options provided below the question.

Question 74. Assertion (A): We prefer to wear white clothes in winter.

Reason (R): White clothes are good reflectors of heat.

1. a. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. b. Both (A) and (R) are true but (R) is not correct explanation (A)
3. c. (A) is true but (R) is false
4. d. (A) is false but (R) is true

Solution:

We prefer to wear black clothes in winter because they absorb the heat and keep their body warm. However, white clothes are good reflectors of heat and keep us cooler in summer.

Question 75. Assertion (A): Vaccines prevent disease.

1. a. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. b. Both (A) and (R) are true but (R) is not correct explanation (A)
3. c. (A) is true but (R) is false
4. d. (A) is false but (R) is true

Solution:

Vaccines prevent disease by developing immunity inside the body and Vaccine must be given to children to build resistance against diseases.

Question 76. Assertion (A): Copper is used to make electrical wires.

1. a. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. b. Both (A) and (R) are true but (R) is not correct explanation (A)
3. c. (A) is true but (R) is false
4. d. (A) is false but (R) is true

Solution:

A low electrical resistance of copper makes it a good electricity conductor. So, it is used to make electric wires.

Question 77. Assertion (A): Leakage in household gas (LPG) cylinders can be detected.

1. a. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. b. Both (A) and (R) are true but (R) is not correct explanation (A)
3. c. (A) is true but (R) is false
4. d. (A) is false but (R) is true

Solution:

Both (A) and (R) are true and (R) is the correct explanation of (A)

LPG cylinder has Ethyl Mercaptan added which gives the smell.

Direction Question 78 to 80: In each of the following questions, four probable answers have been given as alternatives. Select the most appropriate alternatives as the answer.

Question 78. Your friend has lost his/her purse with your important documents in it.

You would..........

1. a. feel angry but do not react as anyone can make mistakes.
2. b. feel angry and ask him/her to replace/duplicate the documents.
3. c. understand the situation and tell him/her that it's OK and not to worry about it.
4. d. blame him/her for being careless and stop talking to him/her.

Solution:

Feeling angry is a natural instinct, however, as anyone can make mistakes, you should not react. Also, you must understand the situation and assure him/her there is nothing to worry about

Question 79. A train always has:

1. a. Engine
2. b. Guard
3. c. Driver
4. d. Passengers

Solution:

A train always has an engine. It drives the train, otherwise the train can’t move.

Question 80. Atmosphere always has:

1. a. Oxygen
2. b. Air
3. c. Dust
4. d. Germs

Solution:

Atmosphere always has air. Without air, it won’t be an atmosphere, but a vacuum.

Direction Question. 81 to 85: In each of the following questions, various terms of an alphabet series/number series/alphanumeral series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives.

Question 81. 3/7, 4/11, (?), 9/31, 13/47

1. a. 6/15
2. b. 6/19
3. c. 6/17
4. d. 5/15

Solution:

Question 82. AJS, GPY, (?), SBK, YHQ

1. a. DMV
2. b. MVE
3. c. OUA
4. d. QZI

Solution:

Question 83. 2A11, 4D13, 12G17, (?)

1. a. 48I19
2. b. 36J21
3. c. 48J21
4. d. 48J23

Solution:

2A11, 4D13, 12G17, ……..

Question 84. 625, 5, 125, 25, 25, (?), 5

1. a. 5
2. b. 25
3. c. 125
4. d. 625

Solution:

Question 85. 4, 8, 28, 80, 244, (?)

1. a. 278
2. b. 428
3. c. 628
4. d. 728

Solution:

Direction Question 86 to 90: Study the given information carefully and answer the questions that follow:

• A, B, C, D, E, F and G are sitting on wall and all of them are facing East.

• C is on the immediate right of D.

• B is at an extreme end and has E as his neighbour.

• G is between E and F

• D is sitting third from the south end.

Given below is the seating arrangement of A, B, C, D, E, F and G.

Question 86. Who is sitting to the right of E?

1. a. A
2. b. G
3. c. D
4. d. F

Solution:

According to the seating arrangement given above, G is sitting to the right of E.

Question 87. Which of the following pairs of people are sitting at the extreme ends ?

1. a. AB
2. b. AE
3. c. CB
4. d. FB

Solution:

According to the seating arrangement given above, AB is the pairs of people sitting at the extreme ends.

Question 88. Name of the person who should change place with C, such that he gets the third place from the north end.

1. a. E
2. b. F
3. c. G
4. d. D

Solution:

According to the seating arrangement given above, G is at 3rd place from North. Hence, C should change places with G in order to come in 3rd place from North.

Question 89. Immediately between which of the following pairs of people is D sitting?

1. a. AC
2. b. AF
3. c. CE
4. d. CF

Solution:

According to the seating arrangement given above, D is sitting between the pair of CF.

1. a. F
2. b. G
3. c. D
4. d. None of these

Solution:

According to the seating arrangement given above, ‘F’ is sitting in the middle of the arrangement.

Direction Question: 91 to 100: Each of the following consists of four 'Problem-figures' marked A, B, C and D, and four 'Answer-figure' marked a, b, c and d. Select the figure from amongst the Answer-figure which will continue the series established by the four problem- figures.

The correct option taken from Answer-figure (a, b, c or d) will be marked as the answer to the related question on the Answer-Sheet.

Question 91. Problem Figures

Solution:

Question 92. Problem Figures

Solution:

The pattern inside the left aligned box goes as follows:

Question 93. Problem Figures

Solution:

One line added in each step.

Question 94. Problem Figures

Solution:

In the given pattern stars at the bottom left corner are decreasing by one at every step.

Question 95.Problem Figures

Solution:

This pattern is formed by two patterns, each with one cross increasing at the next term. First pattern starts with 4 crosses and the second pattern starts with 2 crosses.

Question 96. Problem Figures

Solution:

In this problem, the “Z” rotates 90° in anticlockwise direction and alternately remains the same. Similar is the case with the arrow as shown.

Question 97. Problem Figures

Solution:

The outer figure moves anti-clockwise and changes at every step. On whichever side the outer figure was in the previous step, in the next step it moves inside the pentagon on the same side. It is shown as:

The given logic repeats itself in anticlockwise direction.

Question 98. Problem Figures

Solution:

The pattern goes like this:

For A to B
Top portion: Arrow to flat slanting to the right.

Question 99. Problem Figures

Solution:

Here, in this problem also bottom lines are moving toward and opposite to each other alternatively. Also, the number of circles is increasing by one at every step.

Question 100. Problem Figures

Solution:

Bihar NTSE 2021 Stage 1 SAT Paper

PAPER - SAT

Question 1. For Circular motion, which one holds true

1. a. Constant Velocity
2. b. Zero Acceleration
3. c. Constant Speed
4. d. Speed changes

Solution:

In a circular motion direction of a particle continuously changes, that's why velocity can not be constant but its magnitude is constant i.e. speed. Therefore, speed is constant.

Question 2. A car travels half of the total distance with speed 20 m/sec and next half distance travel with 30 m/sec the average speed of the car is

1. a. Zero
2. b. 25 m/sec
3. c. 24 m/sec
4. d. 5 m/sec

Solution:

Given:

v1 = 20 m/sec

v2 = 30 m/sec

vavg = ?

Average speed = (Total Distance )/(Total time )

vavg = x/(t1+t2)

=x/((x/2)/(v1) + (x/2)/(v2)) {speed=distance/time }

= (2v1v2)/(v1 + v2)

= (2×20×30)/(20+30)

vavg = 24 m/sec

Question 3. A body is travelling with speed 20 m/sec having acceleration 4 m/sec2. The speed of the body after 2 sec will be

1. a. 8 m/sec
2. b. 12 m/sec
3. c. 16 m/sec
4. d. 28 m/sec

Solution:

Given:

u = 20 m/sec

a = 4 m/sec2

t = 2 sec

v = ?

From Ist equation of motion,

v = u + at

v = 20 + 4 × 2

v = 28 m/sec

Question 4. The weight of a body is 9.8 Newton when g = 9.8 m/sec2. The mass of the body is

1. a. Zero
2. b. 9.8 kg
3. c. 10 kg
4. d. 1 kg

Solution:

Given:

Weight, w = 9.8 N

g = 9.8 m/sec2

m = ?

w = mg

9.8 = m × 9.8

m = 1 kg

Question 5. Flying birds have

1. a. only kinetic energy
2. b. only potential energy
3. c. both kinetic energy and potential energy
4. d. only pressure energy

Solution:

The flying bird has kinetic energy because it is moving. It also has potential energy at any point of the time during the flying due to height above the ground at that particular point of time.

Question 6. Two bodies of mass 2 gram and 4 gram having same kinetic energy will have their ratio of linear momentum as

1. a. 2 : 1
2. b. √2 : 1
3. c. 1 : 2
4. d. 1 : 16

Solution:

Given:

mass (m1) = 2 gm

m2 = 4 gm

and kinetic energy =Ek1 = Ek2

or (m1v12)/2 =(m2v22)/2

(v12)/(v22) = (m2)/(m1) = 4/2 = 2

(v1)/(v2) = √2

Now, ratio of linear momentum is

(P1)/(P2) = (m1v1)/(m2v2) = 2/4×√2

=√2/2 = 1/√2

or (P2)/(P1) = √2/1

Question 7. The ratio of gravitational acceleration on the surface of the Earth and the Moon is

1. a. √6 : 1
2. b. 1 : √6
3. c. 1 : 6
4. d. 6 : 1

Solution:

gm = (1/6)ge

ge = Gravitational acceleration on the Earth’s surface.

gm = gravitational acceleration on the Moon.

Therefore, gₑ/(gₘ)=6/1

Question 8. The weight of a wooden block is w. The apparent weight of the body on a floating water will be

1. a. w
2. b. more than w
3. c. less than w
4. d. Zero

Solution:

The apparent weight of the floating block is equal to zero. Because the entire weight of the block is supported by the buoyant force (upward thrust) due to water.

Question 9. In a simple pendulum, the displacement is equal to amplitude. Then, kinetic energy will be

1. a. highest
2. b. Zero
3. c. No change
4. d. None

Solution:

Amplitude is the distance between mean position to extreme position and at the extreme position, velocity is zero. Therefore, kinetic energy is also zero.

Question 10. Heat and work done by the heat were discovered by

1. a. James Watt
2. b. Dr. D. Joule
3. c. Rudolf Diesel
4. d. Newcomen

Solution:

James Prescott Joule.

Question 11. The focal length of a convex lens is 20 cm. The image formed is double the length of the object. The distance of the object from the lens is

1. a. –30 cm
2. b. –20 cm
3. c. –60 cm
4. d. 30 cm

Solution:

Given:

f = +20 cm (Convex lens)

I = 2h

O = h

∴ m = I/O=v/u

(-2h)/h=v/u

v = –2u

Now, from the lens formula

1/f=1/v-1/u

1/20=1/(-2u)-1/u

1/20=(-1-2)/(-2u)

1/20=(-1-2)/2u

1/20=(-3)/2u

u = –30 cm

Question 12. An Electric motor takes 37.5 amp to start. Then, its efficiency is

1. a. 1 Horsepower
2. b. 500 Watt
3. c. 54 Watt
4. d. 7500 Watt

Solution:

Efficiency = Power (P) = VI

Since V is not given, it can’t be solved.

Question 13. The intensity of the bulb will decrease when a resistance is connected

1. a. In series
2. b. In parallel
3. c. Series or parallel
4. d. Intensity cannot be decreased

Solution:

Intensity of the bulb will decrease when resistance is high and resistance is high when they are connected in series combination.

Question 14. Assertion: 2-Bromobutane on reaction with sodium ethoxide in ethanol gives 2-butene as a major product.

Reason: 1-Butene is more stable than 2-butene.

Read the assertion and reason carefully to mark the correct option.

1. a. Both assertion and reason are true and the reason is the correct explanation of the assertion.
2. b. Both assertion and reason are true and the reason is not the correct explanation of the assertion.
3. c. Assertion is true but the reason is false.
4. d. Assertion is false but the reason is true.

Solution:

2-Bromobutane on reaction with sodium ethoxide in ethanol gives 2-butene as a major product.

This is according to Saytzeff's rule, i.e. the predominant product is the most substituted alkene. Thus, 2-butene is more stable than 1-butene.

Question 15. KO2 (Potassium superoxide) is used in oxygen cylinders in space and submarines because it

1. a. absorbs CO2 and increases O2 content
2. b. eliminates moisture
3. c. absorbs CO2
4. d. produces Ozone

Solution:

Potassium superoxide is used in oxygen cylinders in space and submarines because it absorbs CO2 and increases O2 concentration according to the following reaction:

4KO2 + 2CO2 → 2K2CO3 + 3O2

Question 16. A solution of sodium sulphate in water is electrolysed using inert electrodes. The products at the anode and cathode are respectively -

1. a. H2, O2
2. b. O2, H2
3. c. O2, Na
4. d. O2, SO2

Solution:

A solution of sodium sulphate in water is electrolysed using inert electrodes. The products at the cathode and anode are H2 and O2 respectively.

Hydrogen ions having lower discharge (or higher reduction) potential than sodium ions will be liberated at the cathode.

2H+ + 2e → H2

Hydroxide ions will form oxygen at anode.

4OH → 2H2O + O2 + 4e

Question 17. A substance on treatment with dilute H2SO4 liberates a colourless gas which produces (i) turbidity with baryta solution and (ii) turns acidified dichromate solution green. The reaction indicates the presence of -

1. a. CO32–
2. b. S2–
3. c. SO32–
4. d. NO3

Solution:

The reaction indicates the presence of SO32–.

Dilute H2SO4 decomposes with the evolution of sulphur dioxide.

SO32– + 2H+ → SO2 + H2O

SO2 + Ba(OH)2 (Baryta water) → BaSO3 + H2O

K2Cr2O7 + H2SO4 + 3SO2 → K2SO4 + Cr2(SO4)3 (Green) + H2O

Question 18. A gas formed by the action of alcoholic KOH on ethyl iodide decolourises alkaline KMnO4 solution, the gas is -

1. a. CH4
2. b. C2H6
3. c. C2H4
4. d. C2H2

Solution:

In the presence of alcoholic KOH, ethyl iodide undergoes dehydrohalogenation to form ethylene C2H4.

Alkaline KMnO4 is called Baeyer's reagent and is reduced to MnO2 by ethylene which is colourless.

CH2=CH2 + alkaline KMnO4 → CH2(OH)–CH2–OH

Question 19. Given pH of a solution A is 3 and it is mixed with another solution B having pH 2. The resultant pH of solution will be -

1. a. 3.2
2. b. 1.9
3. c. 3.4
4. d. 3.5

Solution:

Assuming that equal volumes of both the solutions are mixed.

Molarity is defined as the moles of a solute per liter of a solution.

Let the volume of each solution be V.

Let the number of H+ ions be n1 and n2 respectively.

For the first solution,

n1 = 10–3 V

For the second solution,

n2 = 10–2 V

Resultant

Total volume = 1V + 1V

Total number of H+ ions = n1 + n2

[H+] = (n1+n2)/2V

[H+] = (10-3V + 10-2V)/ 2V

[H+] = 0.0055

pH = –log[H+]
pH = 2.25

Question 20. A light greenish salt is soluble in water. On passing H2S gas into the solution, a black precipitate is obtained which dissolves readily in HCl. The metal ion present is -

1. a. Fe2+
2. b. Co2+
3. c. Ni2+
4. d. Mn2+

Solution:

FeS is soluble in HCl. Also, Fe2+ salts are green in colour.

Fe2+ + H2S → FeS (Black ppt) + 2H+

FeS(s) + 2HCl(aq) → FeCl2(aq) + H2S(g)

Question 21. Bonds present in CuSO4.5H2O are -

1. a. Electrovalent and Covalent
2. b. Electrovalent and Co-ordinate
3. c. Electrovalent, Covalent and Co-ordinate
4. d. Covalent and Co-ordinate

Solution:

A covalent bond is formed between sulfur and oxygen and the bond between copper and sulfate is ionic.

Hydrated copper sulfate is a complex which is bonded to water molecules acting as ligands forming a coordinate bond.

Question 22. An organic compound (X) on treatment with acidified K2Cr2O7 gives a compound (Y) which reacts with I2 and sodium carbonate to form triiodomethane. The compound (X) is-

Solution:

The compound Y should be a ketone as it is responding to an iodoform test. Since it is formed by treating X with potassium dichromate (acidic), X should be a secondary alcohol.

Question 23. How many litres of CO2 at STP will be formed when 100 ml of 0.1 M H2SO4 reacts with excess of Na2CO3?

1. a. 22.4
2. b. 2.24
3. c. 0.224
4. d. 5.6

Solution:

Na2CO3 + H2SO4 → Na2SO4 + H2O + CO2

1 mole of sulfuric acid will produce 1 mole (22.4 L at STP) of carbon dioxide.

100 ml (0.1 L) of 0.1 M H2SO4 corresponds to 0.01 moles.

Thus, 0.01 mole of sulfuric acid will produce 0.224 L of carbon dioxide at STP.

Question 24. Which compound has the weakest bond?

1. a. Diamond
2. b. Neon (solid)
3. c. KCl
4. d. Water (ice)

Solution:

Diamond contains strong covalent bonds. In potassium chloride (KCl), an ionic bond is present whereas in ice molecules, a hydrogen bond is present. Neon solids are usually held together by Van Der Waals forces.

Decreasing order of strength of bond is as follows:-

Ionic > Covalent > Hydrogen > Dipole−Dipole > Van der Waals

Question 25. Which one of the following is used as an antiknock compound?

Solution:

An anti-knock agent is the substance which is used to reduce the engine knocking. It helps in auto-ignition by raising the temperature and pressure. TEL is Tetraethyl Lead which is used as an anti-knock compound.

Question 26. A bottle of ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends. The white ammonium-chloride ring first formed will be -

1. a. At the centre of the tube
2. b. Near the hydrogen chloride bottle
3. c. Near the ammonia bottle
4. d. Throughout the length of the tube

Solution:

HCl diffuses slower than NH3 because the mass of HCl is more than the mass of NH3. Therefore, ammonia will travel more distance than HCl at the same time interval and the two gases will first meet nearer to the HCl end.

Question 27. The Xylem is responsible for -

1. a. Transport of food in plants
2. b. Transport of water in plants
3. c. Transport of amino acids
4. d. Transport of oxygen

Solution:

The higher plants have highly specialized vascular tissues – xylem and phloem. Xylem is responsible for transporting water from the roots to other parts of the plants. The phloem transports food from the leaves to other parts of the plants.

Question 28. Which of the following is not a polymer

1. a. Cellulose
2. b. Glycogen
3. c. Protein
4. d. Glucose

Solution:

A polymer is a substance or material consisting of very large molecules composed of many repeating subunits called monomers. Examples are cellulose, protein and glycogen. On the other hand, glucose is a monomer which forms the polymer glycogen.

Question 29. The disease that affects our lungs is -

1. a. AIDS
2. b. Rabies
3. c. Polio
4. d. Tuberculosis

Solution:

Out of all the diseases given, only tuberculosis affects our lungs. It is a contagious infection caused by the bacteria that spread through air while coughing or sneezing. Rabies affects the brain. Polio affects the spinal cord. In AIDS, the immune system is affected.

Question 30. Which of the following is not a plant hormone?

1. a. Auxin
2. b. Florigen
3. c. Cytokinin
4. d. Oxytocin

Solution:

Auxin, cytokinin and florigen are all plant hormones whereas oxytocin is a hormone found in mammals including human beings. It is mainly responsible for the ejection of milk for newborn babies during lactation period.

Question 31. Select the odd one from the following:

1. a. Stigma: Style: Ovary
2. b. Anther: Filament: Pollen
4. d. Pollen: Pollen tube : Pellicle

Solution:

Stigma, style and ovary are all female reproductive parts of the flower. Anther, filament and pollen are all male reproductive parts of the flower. Cotyledon, radicle and plumule are all parts of a seed.

Thus, the odd one out is Pollen: pollen tube : pellicle. Here, pollen and pollen tubes are both parts of the flower whereas pellicle is a proteinaceous layer in protozoans.

Question 32. The mode of nutrition in Fungi is -

1. a. Autotrophic nutrition
2. b. Holozoic nutrition
3. c. Saprotrophic nutrition
4. d. Parasitic nutrition

Solution:

The mode of nutrition in fungi is saprotrophic i.e. obtaining nutrients from dead organic matter.

Autotrophic nutrition is the mode of nutrition in which organisms synthesize their own food. Organisms that cannot prepare their own food are said to have heterotrophic nutrition.

In parasitic nutrition, an organism (parasite) lives in or on another organism (host) and takes its nutrition from it and thus, harms it.

Question 33. Which of the following composition represents energy rich food?

1. a. Vitamins and minerals
2. b. Carbohydrates and fats
3. c. Water and roughage
4. d. Proteins and mineral salts

Solution:

Carbohydrates and fats are energy rich foods. They have high calories. Vitamins and minerals boost the immune system. Water and roughage (fibers) aids in digestion and excretion. Proteins are also energy rich food but mineral salts are not.

Question 34. The products obtained during anaerobic respiration in plants are -

1. a. Lactic acid + Energy
2. b. Pyruvic acid + Energy
3. c. Ethanol + Carbon dioxide + Energy
4. d. Carbon dioxide + Energy

Solution:

Anaerobic respiration takes place in the absence or lack of oxygen. Different organisms produce different products during anaerobic respiration. Plants produce ethanol, carbon dioxide and energy during anaerobic respiration.

Question 35. What will happen if all the deers are killed in the given food chain?

1. a. The population of Lion increases
2. b. The population of grass decreases
3. c. The population of Lion decreases and grass increases
4. d. The population of Lion remains unchanged

Solution:

If all the deer are killed in the given food chain, there won’t be any food available for the lions. Hence, the lions will starve to death and their population will decrease. On the other hand, there won’t be any consumers of grass hence, its population would increase.

Question 36. The pores in a leaf through which respiratory exchange of gases takes place are -

1. a. Xylem
2. b. Stigma
3. c. Lenticels
4. d. Stomata

Solution:

Stomata are the pores present on the leaf surface through which respiratory exchange of gases take place. Xylem transports water and minerals in plants. Lenticels are pores found on epidermis. Stigma is a part of the female reproductive part of a flower.

Question 37. When we destroy forest, we destroy -

1. a. Population of wild life
2. b. The trees
3. c. The environment
4. d. Food and shelter of wild animals

Solution:

The answer for this question can be all of these. When we destroy a forest, the trees are destroyed. Due to this, the wild animals lose their food and shelter. And in turn the population of wild life goes down. And all of this leads to destroying the environment.

Question 38. Which of the following is not a natural resource?

1. a. Soil
2. b. Water
3. c. Electricity
4. d. Air

Solution:

Electricity is not a natural resource. It is a manmade resource i.e., a form of energy that is not found in nature but can be produced artificially, by man. Whereas air, soil and water are all natural resources.

Question 39. Purebred Pea Plant A is crossed with purebred pea plant B. It is found that the plants which look like A do not appear in Fl generation but re-emerge in F2 generation, which of the plants A and B are tall and dwarf?

1. a. A are tall and B are also tall
2. b. A are tall and B are dwarf
3. c. A are dwarf and B are tall
4. d. A are dwarf and B are also dwarf

Solution:

Plant ‘A’ and ‘B’ are purebred, which means they are homozygous. So, when they are crossed, all the plants in the F1 generation would be crossbred or heterozygous. Only the characteristic of a dominant trait is expressed in heterozygous condition. This means plant ‘B’ had dominant traits. Out of the characters ‘tall’ and ‘dwarf’, tall is dominant. So, plant ‘B’ was tall. Which also concludes that plant ‘A’ was a dwarf. The following would be the cross:

Question 40. Pick the right combination of terms which has no fossil fuel -

1. a. Wind, Wood, Sun
2. b. Kerosene, Wind, Tide
3. c. Petroleum, Wood, Sun
4. d. Wind, Ocean, Coal

Solution:

Fossil fuels are hydrocarbons formed from the remains of dead plants and animals and are non-renewable resources. Examples are coal, petroleum and kerosene. Thus, option A does not have any fossil fuel. Wind and sun are all renewable resources of energy. While wood is not a fossil fuel.

Question 41. Three numbers prime to each other are such that the product of the first two is 437 and the product of the last two is 551. The sum of the numbers is........

1. a. 59
2. b. 63
3. c. 69
4. d. 71

Solution:

Let 3 prime numbers be a, b and c.

Now, 437 = a × b (given)

⇒ 437 = 19 × 23 = a × b ...(i)

And 551 = b × c (given)

⇒ 551 = 19 × 29 = b × c ...(ii)

From equation (i) and (ii), we get

a = 23, b = 19 and c = 29

So, a + b + c = 19 + 23 + 29 = 71

Question 42. If the sum of the remainders obtained by dividing each of x3 + 8x2 – 3kx + 7 and 2x3 + kx2 – 5x + 6 by x – 1 is 9 then K=.......

1. a. 0
2. b. 2
3. c. 3
4. d. 5

Solution:

(x3 + 8x2 – 3kx + 7) = M(x – 1) + R1 ...(1)

(2x2 + kx2 – 5x + 6) = N(x – 1) + R2 ...(2)

By using remainder theorem,
Let p(x) = x3 –8x2 – 3kx + 7

p(1) = 16 – 8k = R1 ...(3)

Also, q(x) = 2x3 + kx2 – 5x + 6

q(1)= 3 + k = R2 ...(4)

From (3) and (4),

(16 – 3k) + (3 + k) = 9 (given)

19–2 k = 9

or k =5

Question 43. A polynomial of degree 2 is divided respectively by x – 1, x – 2 and x – 3. The reminders obtained are 1, 2 and 3 respectively. The polynomial is.......

1. a. x2 – x + 1
2. b. x2 – x + 1
3. c. (1/2)x2 -(1/2)x + 2
4. d. None of these

Solution:

Let polynomial be p(x) = px2 + qx + r

Given, p(1) = 1 ⇒ p + q + r = 1 ...(1)

p(2) = 2 ⇒ 4p + 2q + r = 2 ...(2)

p(3) = 3 ⇒ 9p + 3q + r = 3 ...(3)

By solving equations (1), (2) and (3), we get

3p+q = 1

4p+q = 1

Which gives us 3 = 4, which is not possible. Hence, a quadratic polynomial can’t be formed.

Question 44. If the equations x2 + bx + a = 0 and x2 + ax + b = 0, (a ≠ b) have equal roots, then a + b =......

1. a. –1
2. b. 0
3. c. 1
4. d. None of these

Solution:

Given, x2 + bx + a = 0 and x2 + ax + b = 0 (a ≠ b) have equal roots.

Condition for equal roots is

D = 0 and D’ = 0

⇒ b2 – 4a = 0 ...(1)

and a2 – 4b = 0 ...(2)

Now from (1) and (2),

b2 – 4a= a2 – 4b

⇒ a2 – b2 = – 4(a – b)

⇒ a + b = – 4 or a = b

But, a ≠ b (given).

So, a + b = – 4

Question 45. In a right-angled triangle, the difference of the hypotenuse and the base is 2 cm. The hypotenuse exceeds twice the height by 1 cm. The base of the triangle is ..... cm.

1. a. 8
2. b. 15
3. c. 17
4. d. 21

Solution:

Let base be B and hypotenuse be B + 2 (given)

Now, (B + 2) – 2H = 1 (given)

⇒ B + 2 = 1 + 2H

⇒ B + 1 = 2H

⇒ H = (B+1)/2

Now, (B + 2)2 = B2 + ((B+1)/2 ) 2 (by Pythagoras theorem)

⇒ B2 + 4 + 4B = B2 + 1/4(B2 + 1 + 2B)

⇒ 4 + 4B = ( ¼) B2 + 1/4 + 1/2B

⇒ 0 = 1/4 B2 – (7/2)B – 15/4

⇒ 0 = B2 – 14B – 15

⇒ B2 – 15B + B – 15 = 0

⇒ B (B – 15) + 1 (B – 15) = 0

⇒ B = 15 cm

Question 46. By adding 1 to the sum of all natural numbers between 1 and 300, which are divisible by 7 and 8 a number p is obtained, then + √p =.......

1. a. 25
2. b. 29
3. c. 33
4. d. 37

Solution:

Numbers which are divisible by both 7 and 8 should be multiples of 8x7 = 56.

So, the numbers are: 56, 112, .... , 280 (required series)

Sum of those numbers = 56 + 112 + ... + 280

= 56 (1 + 2 + 3 + 4 + 5)

= 56 × 15

p = sum + 1 = 840 + 1 = 841

Now, +√p = +√841 = 29

Question 47. If in an A.P., the pth term is 1/q and the qth term is 1/p, then the pqth term

1. a. –1
2. b. 0
3. c. 1
4. d. None of these

Solution:

Given, Tp= 1/q= a + (p – 1) d ...(1)

and, Tq = 1/p= a + (q – 1) d ...(2)

Subtracting (2) from (1), we get

(p – q) d = (p-q)/pq

⇒ d=1/pq

Putting value of d in equation (1), we get

⇒ a=1/pq

Now, Tpq = a + (pq – 1) d = 1/pq+ (pq – 1) 1/pq

Tpq = 1

Question 48. If x =2(sin2 θ) , y = 2(cos2 θ) for all real values of θ, then

1. a. x + y = 1
2. b. x + y = 2
3. c. x + y ≤ 2 √2
4. d. x + y ≥ 2√2

Solution:

We also know that, x2+y2 ≥ 0

(x+y)2 - 4xy ≥ 0

x+y ≥ 2√xy or x+y ≤ -2√xy

⇒ x+y ≥ 2√(2(sin2 θ).2(cos2 θ) ) [By observing the options, the other one is rejected]

⇒ x+y ≥ 2√2 (Since cos2θ + sin2θ = 1)

Question 49. If, for all real values of θ; a = sin2θ + cos4θ then

1. a. a ≥ 3/4
2. b. a ≤ 3/4
3. c. a = 1
4. d. a = 1/2

Solution:

a = sin2θ + cos4θ = sin2θ + (1 - sin2θ)2

a = sin2θ + 1 + sin4θ - 2sin2θ = sin4θ - sin2θ + 1 + (1/2 )2-(1/2 )2

a = (sin2θ - 1/2)2 + 3/4

(sin2θ - 1/2)2min = 0

⇒ a ≥ ¾

Question 50. If sinα + cosα = a and x = sin6α + cos6α then

1. a. x ≤ 1
2. b. x < 1
3. c. x = 1
4. d. x > 1

Solution:

Given sin α + cos α = a ...(1)

x = sin6x + cos6x ...(2)

Squaring equation (1), we get

sin2α + cos2α + 2 sin α cos α = a2

⇒ sin α cos α = (a2-1)/2 ...(3)

Now, sin6α + cos6α = (sin2α+cos2α)3 – 3 sin2α cos2α(sin2α + cos2α)

sin6α + cos6α = 1 - 3sin2α cos2α

x = 1 – 3 ((a2-1)/2)2 [From equation (3)]

((a2-1)/2) 2 ≥ 0

a ≥ 1

So, x ≤ 1

Question 51. The angle of elevation of the top of a 'H' m. high tower from two points A and B on the horizontal plane are 60° and 30° respectively. If the distance of A from the foot of the tower is 'a' m. then the distance of B from the foot of the tower will be .......m.

1. a. H2/a
2. b. (2H) 2/a
3. c. √H/a
4. d. None of these

Solution:

tan 60° = H/a (Since tan θ = P/B)

√3 = H/a

H = √3a ...(i)

Similarly,

In BDC

tan 30° = H/BD

1/√3=H/BD

BD = √3 H ...(ii)

From (i) and (ii),

BD = H2/a

Question 52. The co-ordinates of the vertices of a triangle are (3, 0), (0, 4) and (3, 4) respectively. The radius of the circle inscribed inside the triangle is......units.

1. a. 1/√2
2. b. √2
3. c. 1/2
4. d. 1

Solution:

AB = 5 units (By Pythagoras)

AC = 4 units

BC = 3 units

∵ BP = BR = 4–r

Since, lengths of tangents to a circle from a point are equal.

Similarly, AQ = AR = 3–r

Now, (3–r)+(4–r) = 5 (∵ BR+AR = AB)

7-2r = 5

2r = 2

r=1 unit

Question 53. In a ∆ABC, C = 90°. On the sides, CA and CB two points P and Q are taken such that they divide CA and CB in the ratio 2 : 1 respectively. Then, (Aa2+BP2) : AB2 =......

1. a. 7/9
2. b. 4/9
3. c. 13/9
4. d. 11/9

Solution:

If there is ‘a’ in place of ‘Q’ , the question is to find (AQ2+BP2) : AB2 ,it can be solved as given below

Given that = CP:PA = CQ : QB = 2:1

we have to find,

(AQ2+BP2) : AB2

Now,

Let, PC = 2K and AP= K

Similarly, QC = 2P and BQ = P

In ∆AQC, AQ2 = (3K)2+(2P)2 = 9K2+4P2 ...(i)

Similarly, in ∆BCP

BP2 = (3P)2+(2K)2

BP2= 9P2 + 4K2 ...(ii)

From (i) and (ii),

(AQ2+BP2)/(AB2 )

=(9K2+4P2+9P2+4K2)/((3K) 2+(3P) 2))

=(13(P2+K2))/(9(P2+K2))=13/9

Question 54. In ∆ABC, ∠C = 90°, D is a point on CA from which a perpendicular drawn to AB meets it at E. If ∠EDA = ∠ABC, BC = a cm, AD = x cm, AE = y cm, BE = Z cm, then DE =......cm.

1. a. ay/(z+x)
2. b. az/(x+y)
3. c. ax/(y+z)
4. d. None of these

Solution:

DE = ?

in ∆AED and ∆ABC,

∠E = ∠C= 90°

Also, ∠ADE = ∠CAB (Common angle)

So, By AA Rule

∆DEA ∼ ∆BCA

ΔAED ∼ ΔACB by AA

⇒DE/BC = DA/BA = EA/CA

⇒DE/a = x/(y+z) = y/AC

⇒DE/BC = ax/(y+z)

Question 55. Two circles of radii 9 cm and 25 cm touch each other externally. The length of a direct common tangent is.....cm.

1. a. 15
2. b. 30
3. c. 706
4. d. 544

Solution:

Given, AM = 9 cm

MC = 25 cm

BC = 25–9 = 16 cm

By Pythagoras

AB2+BC2 = AC2

AB2= (34)2 – (16)2 = 900

AB = DE = (direction common tangent) = √900

AB = 30 cm

Question 56. ABCD is a rectangle. Taking AD as diameter a semi-circle is drawn which cuts the diagonal DB at E. If AB = 12 cm and AD = 9 cm then BE =.......cm.

1. a. 9
2. b. 9.6
3. c. 10.2
4. d. 10.6

Solution:

Given, AB = 12 cm, AD = 9 cm

By Pythagoras theorem in △ABD

= (12)2+(9)2 = 144+81

⇒(BD)2 = 225

⇒BD = 15 cm

Now, By Tangent Secant theorem (Let BE = Kcm)

⇒ BE×BD = (BA)2

⇒K×15 = (12)2

⇒K = 144/15 = 9.6 cm

Question 57. A semi-circular piece of paper of radius r cm is folded to form a cone. The volume of the cone thus formed is......cm3.

1. a. (πr3)/√3
2. b. (πr3)/(8√3)
3. c. (πr3)/(2√3)
4. d. (πr3)/(4√3)

Solution:

⇒2πR=πr

⇒R=r/2 ...(i)

Also, l2+R2 = h2

h = √(l2-(r/2 ) 2 )

h = √(r2-(r/2 ) 2 )

h =( √3 r)/2 ...(ii)

Now, volume = 1/3 πR2h = 1/3 π(r/2)2 ((√3 r)/2) [Form (i) and (ii)]

v = (πr3)/(8√3)

Question 58. A variable x takes the values x1, x2....xn. Given Σ(xi – 2) = 110 and Σ(xi – 5) = 20, i = l, 2.....n, then n =.......

1. a. 30
2. b. 80
3. c. 85
4. d. 90

Solution:

Given that,

Σ(xi – 2) = 110, i= ,1,2, ...... n ...(i)

and Σ(xi – 5) = 20, i = 1,2, ..... n ...(ii)

we have to find ‘n’

Now, Subtract (ii) from (i), we get

Σ(xi – 2) - Σ(xi – 5) = (Σxi – Σ2) - (Σxi – Σ5) = (Σxi – 2n) – (Σxi – 5n) = 110 - 20

⇒3n = 90

⇒n = 30

Question 59. C is the mid-point of the line segment AB of length L cm. Two points P and Q are taken randomly on the line segments CA and CB. Then, the probability for PQ < 1/2 is

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

Solution:

PQ < L/2 must be given to find the solution for the question.
P and Q can be any point, if it is less than 1/2.
PQ< 1/2 has many possibilities.
PQ=1/2 means P and Q are on the midpoint.
so, none of these can be correct answer.

Question 60. If a, b, c, d denote the sides of a quadrilateral ABCD then,

a/(b+c+d) + b/(c+d+a) + c/(a+b+d) + d/(a+b+c) is

1. a. <1
2. b. ≥1
3. c. >1
4. d. None of these

Solution:

[Since, AM ≥ GM] ... eq.(1)

Also, we have

⇒ XY ≥ 16/3

Then, XY – 4 ≥ 16/3-4

⇒ XY – 4 ≥ 4/3

Question 61. After the defeat of Napoleon where did the Victor Powers assemble in 1815 ?

1. a. Vienna
2. b. London
3. c. Paris
4. d. Rome

Solution:

After the defeat of Napoleon, Britain, Russia, Prussia and Austria assembled in Vienna and decided to draw up a settlement for Europe. This settlement came to be known as the Treaty of Vienna. It was signed in 1815. Hosted by Austrian Chancellor Metternich, it aimed to undo the effects of the Napoleonic Wars in Europe.

Question 62. Which dynasty succeeded the Bourbon dynasty after the 1830 revolution?

1. a. Habsburg
2. b. Orleans
3. c. Tsardom
4. d. None of these

Solution:

The Bourbon dynasty was succeeded by the Orleans after the July Revolution of 1830 in France. Louis-Philippe, a member of the Orleans line became the king of the people in France.

Question 63. Charles Albert was the King of which country?

1. a. Naples
2. b. Parma
3. c. Modena
4. d. Sardinia

Solution:

Charles Albert was the king of Piedmont-Sardinia from 1831-1849. It was during this period that Italian unification took place. This period of Italian unification is also known as the Risorgimento.

Question 64. What was Zollverein?

1. a. Intellectual’s Union
2. b. Clergy’s Union
3. c. Revolutionaries Union

Solution:

In 1834, a customs union called the Zollverein was established under Prussian leadership in German speaking states. This removed tariff barriers and cut down the number of currencies. This move is also seen as a crucial step towards German reunification.

Question 65. When was Karl Marx born?

1. a. 1810
2. b. 1818
3. c. 1825
4. d. 1830

Solution:

Karl Heinrich Marx was born on 5th May, 1818 in the Rhine province of Prussia. He was a historian, sociologist, economist and a revolutionary. Some of his most celebrated works include the Communist Manifesto and Das Kapital among others.

Question 66 Who was the author of ‘War and Peace”?

1. a. Tolstoy
2. b. Karl Marx
3. c. Lenin
4. d. St. Simon

Solution:

War and Peace is a historical novel composed by Leo Tolstoy. It is considered a classic of Russian literature and one of the greatest novels in the world.

Question 67. Who built the Angkor Wat Temple?

1. a. Jayavarman
2. b. Suryavarman II
3. c. Mahendravarman
4. d. Rudravarman

Solution:

The Angkor Wat Temple complex in Cambodia was built by Suryavarman II in the 12th century. One of the greatest cultural wonders of the world, it is the largest religious structure in the world.

Question 68. In 1878 which Viceroy passed the “Vernacular Press Act”?

1. a. Lord Ripon
2. b. Lord Lytton
3. c. Lord Curzon
4. d. Lord Chelmsford

Solution:

Lytton passed the Vernacular Press Act in 1878. The act curtailed the freedom of the vernacular press in India. Native newspapers were discouraged from being critical of British policies. The act did not target English publications.

Question 69. Who established the Ramakrishna Mission?

1. a. Ramkrishna Paramhans
2. b. Ishwar Chandra Vidyasagar
3. c. Swami Vivekananda
4. d. Devendra Nath Thakur

Solution:

The Ramakrishna Mission was established by Swami Vivekananda in 1897. It aimed to spread the teachings of Vedanta and to improve the lives of common Indians. As of now, the organisation carries out extensive philanthropic and educational activities in India.

Question 70. After which incident Rabindra Nath Tagore surrendered the title “Knight”?

1. a. Rowlatt Act
2. b. Khilafat Movement
3. c. Jallianwala Bagh massacre
4. d. Coming of Simon Commission

Solution:

Rabindra Nath Tagore surrendered the title of ‘Knight’ in August 1919. This was in response to the brutalities meted out to a group of peaceful protestors at Jallianwala Bagh in Punjab by the British administration. The infamous incident came to be known as the Jallianwala Bagh massacre.

Question 71. Who invented the “Safety Lamp”?

1. a. Humphrey Dury
2. b. Richard Arkwright
3. c. James Hargreaves
4. d. Edmund Cartwright

Solution:

The Safety Lamp was invented by Humphrey Dury in 1815 in England. The lamp was designed in a way that it would be safe to use in underground mines. Underground mines often have concentrated levels of methane, so the type of lamps which can be used often have to be scrutinised. Dury’s safety lamp was the first prototype of such a lamp.

Question 72. Who published the newspaper “Som Prakash”?

1. a. Ishwar Chandra Vidyasagar
3. c. Ram Mohan Roy

Solution:

Som Prakash was published by Ishwar Chandra Vidyasagar in 1859. Dwarakanath Vidyabhushana served as the editor of this weekly. It is remembered for its contribution to the Indigo Movement.

Question 73. Bharatpur Bird sanctuary is situated in -

1. a. Gujarat
2. b. Rajasthan
3. c. Assam
4. d. Bihar

Solution:

Bharatpur Bird Sanctuary is located in Rajasthan. It is a famous avifauna sanctuary, home to over 230 species of birds. Thousands of rare and highly endangered birds such as the Siberian Crane come here during the winter season.

Question 74. The highest Literacy rate in India is in______?

1. a. West Bengal
2. b. Maharashtra
3. c. Kerala
4. d. Punjab

Solution:

In 2011, Kerala had the highest literacy rate in India. According to 2011 census data, Kerala has a literacy rate of 94 %. 96.11% of the male and 92.07 % of the female population in Kerala are literate.

Question 75. Where is ropeway in Bihar?

1. a. Bihar Sharif
2. b. Rajgir
3. c. Gaya
4. d. Munger

Solution:

Rajgir has the only ropeway in Bihar. It is a single-person ropeway that runs at the top of Ratnagiri Hill. It leads to the Vishwa Shanti Stupa (Peace Pagoda), Makhdoom Kund and monasteries built by Japanese devotees of the Buddha on top of the Ratnagiri Hills.

Question 76. Select the correct statements -

1. Koshi river is sorrow of Bihar.

2. Parrot is the national bird of India.

3. Maruti Industry is situated in Delhi.

4. Varanasi is situated on the bank of river ganges.

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

Solution:

Koshi river is called the sorrow of Bihar. Due to siltation, it changes its course and breaches the embankments on its path. The breach of embankments causes flo­ods.

The Indian peacock is the National Bird of India.

Maruti Industry is situated in Gurgaon and Manesar in Haryana.

Varanasi, also called Benares in Uttar Pradesh, is located on the left bank of the Ganges.

Question 77. Which one is correct?

1. a. Jammu and Kashmir – Zojila
2. b. Himachal Pradesh – Thagla
3. c. Uttarakhand – Nathula
4. d. Sikkim – Shipkila

Solution:

The following list provides names of the mountain passes and respective locations.

Location/States Mountain passes Jammu and Kashmir Zojila (connects Srinagar with Kargil and Leh) Himachal Pradesh Shipkila (located through Sutlej Gorge) Uttarakhand Thagla Sikkim Nathula (located in the India- China border)

Question 78. Which name is correct for Patna Airport ?

1. a. Jai Prakash Narayan International Airport
2. b. Patna Airport
3. c. Rajendra Prasad International Airport
4. d. Bihar Airport

Solution:

1. Answer: (a) Jai Prakash Narayan International Airport

The Patna Airport is known by the name of Jai Prakash Narayan International Airport. It is a customs airport located in the state capital of Bihar. It is named after independence activist Jayaprakash Narayan.

Question 79. The main problems of industrial backwardness of Bihar is -

1. a. Lack of raw material
2. b. Lack of capital/money
3. c. Lack of electricity
4. d. All of the above

Solution:

The problem of industrial backwardness in Bihar is due to inadequate infrastructure facilities – the lack of working capital, non-availability of raw material, inadequacy of a road network and communication services, poor and uncertain power position and weak research support. Besides, unsatisfactory credit availability, abnormally high interest rates, delay in granting term loans and rigid attitude of banks and other financial institutions in the state are also some other inhibiting factors.

Question 80. Which statement is not correct ?

1. Medha Patkar is related with Narmada Bachao Andolan.

2. New alluvial soil is termed as Bangar.

3. Mangrove Forest found in the costal area of India.

4. Plantation agriculture is one of the type of commercial farming.

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

Solution:

The second statement is not correct. The new alluvial soil formed due to the alluvial deposit along the course of the river is known as Khadar. Bangar refers to the terraced and elevated old alluvial deposits along the river course. All the remaining statements are correct.

Question 81. Which of the following cities are located on the Western Coast of India?

1. a. Puri, Chennai, Visakhapatnam
3. c. Kozhikode (Calicut), Goa, Mumbai
4. d. Amravati, Puna, Puducherry (Pondicherry)

Solution:

The cities of Kozhikode (Calicut), Goa, Mumbai are located on the western coast of India. Kozhikode is a coastal city in the state of Kerala. Goa is located on the western coast near the Arabian sea. Mumbai too is a coastal city located in the western margin of the state of Maharashtra.

Question 82. Select the correct statements -

1. Mount k2 is the highest peak of India

2. Sunderban is in West Bengal

3. Nuclear disaster is very dangerous for the world

4. Cactus plants found in evergreen forest

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

Solution:

Only the last statement is not correct. Cactuses are desert plants. They grow in arid or dry places. They are succulent plants, which hold large amounts of water in their tissues to keep them alive during dry periods. On the other hand, the evergreen forests flourish in the areas having more than 200 cm of rainfall.

Question 83. The Golden Quadrilateral Super highway connected with the following -

1. a. Jammu, Bikaner, Jodhpur, Rojkote
2. b. Porbandar, Bikaner, Amritsar, Srinagar
3. c. Delhi, Mumbai, Chennai, Kolkata
4. d. Sikkim, Siliguri, Jorhat, Agartala

Solution:

Golden Quadrilateral is a network of highways connecting India’s four major metropolitan cities, namely Delhi, Mumbai, Chennai and Kolkata, thereby forming a quadrilateral. This project was launched in 2001 as part of National Highways Development Project (NHDP).

Question 84. Select the correct statements -

1. Muscovite is known as Bengal Ruby.

2. Gold is metallic mineral.

3. Kahalgaon Super Thermal Power is in Uttar Pradesh.

4. Anthracite is one type of iron.

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

Solution:

The statement 3 and 4 are not correct. Kahalgaon Super Thermal Power is in Bhagalpur, Bihar. This coal based power plant supplies electricity to states like West Bengal, Bihar,Jharkhand, Orissa and Sikkim. Anthracite is a type of coal. It is the highest quality hard coal.

Question 85. Which one of the following term is not included in the preamble to the Indian Constitution ?

1. a. Republic
2. b. Justice
3. c. Monarchy
4. d. Equality

Solution:

The Preamble is a summary of the Constitution of India. It states that India would be a sovereign, socialist, secular and democratic republic. The makers of the Constitution envisioned India to be independent of foreign influences, to ensure equitable distribution of wealth, to be free from religious discriminations, and to ensure that people democratically elect their leaders and remain a republic, where the head of state is selected and not hereditary, unlike monarchy.

Question 86. Which of the following does not lead to the spread of democracy?

1. a. Struggle by people
2. b. Invasion by Foreign Government
3. c. End of Colonialism

Solution:

Invasion by foreign government would kill the spirit of sovereignty or the idea of self rule. Democracy is rule of the people, for the people, by the people. It essentially involves freedom and independence for its constituents.

Question 87. Which one of the following statement about the Indian President is true?

1. a. He appoints Chief Minister in States
2. b. He exercises real power
3. c. He is elected directly by the people
4. d. He is the formal head in the Country

Solution:

The President of India is recognised as the head of the state or the formal head of the country and represents the nation. However, the President of India does not rule the country directly. The President of India makes decisions under the advice of the cabinet headed by the Prime Minister, who exercises real power.

Question 88. Which of the following institutions can amend the Constitution of India?

1. a. The Parliament
2. b. The Cabinet
3. c. The Prime Minister
4. d. The President

Solution:

Article 368 (1) of the Constitution of India empowers the Parliament of India to make changes or alter the Constitution and is known as Constitutional amendments. Amendments involve addition, removal or repeal of a provision.

Question 89. Which of the following are the features of Federal Government ?

I. Unwritten Constitution

II. Division of Powers

III. Single Citizenship

IV. Independent Judiciary

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

Solution:

Federalism is a system in which there exists more than one tier of government. There is division of power between the central government and other regional and local governments. A federal government is characterised by features like a written constitution, division of powers, independent judiciary, etc. The provision for dual citizenship is also a feature of federalism. Unlike India, the U.S.A. has provision for dual citizenship.

Question 90. Dealing with social divisions which one of the following statement is not true about democracy?

1. a. Democracy is the best way to accommodate social diversity.
2. b. Democracy always leads to disintegration of society.
3. c. In a democracy, it is possible for communities to voice their grievances in a peaceful manner.
4. d. Due to political competition in a democracy, social division get reflected in politics.

Solution:

Democracy allows space for addressing conflicts and resolving them through the participation of people. It facilitates opportunities for communities to voice their grievances peacefully. There is space for accommodations and negotiations, therefore democracy in the long run will lead to social unity and not social disintegration as seen in Belgium.

Question 91. What do the civil servants do?

1. a. They take policy decisions.
2. b. They implement minister’s decision.
3. c. They settle the disputes.
4. d. None of these.

Solution:

Civil servants form the bureaucratic organ of the Government. They play a major role in implementing the policies and schemes framed by the Government of India. They also help draft policies through recommendations.

Question 92. Which one of the following does not help in the formation of Public Opinion?

1. a. Newspaper
3. c. Playground
4. d. Educational Institutional

Solution:

Public opinion plays a crucial role in expressing the voices of the people. It expresses the opinions, dissent and criticisms of the government. Democracy ensures people enjoy the freedom to do so by empowering them with appropriate rights. Mediums like newspapers, radio, television, internet and educational institutions like universities help forming public opinion on matters of civil, social, political and economical happenings in the country.

Question 93. At present which form of money is increasingly used apart from paper money?

1. a. Commodity money
2. b. Metallic money
3. c. Plastic money
4. d. All of the above

Solution:

Plastic money is a generic term used to describe all types of bank cards. These include debit cards, credit cards, smart cards, automated teller machine cards and charge cards. In recent years, the use of plastic money apart from paper money has increased exponentially.

Question 94. Choose the correct combination

Standardized Marks Product

(i) ISI (a) Jewellery

(ii) FPO (b) Electrical

(iii) Hallmark (c) Food

(iv) Agmark (d) Agricultural

1. a. i-a, ii-b, iii-c, iv-d
2. b. i-c, ii-d, iii-a, iv-b
3. c. i-b, ii-c, iii-a, iv-d
4. d. i-d, ii-c, iii-b, iv-a

Solution:

Standardized marks can be found in products which meet set standards with respect to quality of the said product, manufacturing methods, packaging, labelling and performance.

The ISI mark is used on electrical items, FPO on food items, Hallmark on jewellery and Agmark on agricultural products.

Question 95. There are 1000 households in the village of Almora, of which the loan taken by 200 households are from the State Bank of India, another 200 households from their friends and relatives, 50 households from Indian Bank, 100 households from Regional Rural Bank, 150 households from businessmen 100 households from village headmen and 200 households from cooperative societies. Which of the following statements is/are correct?

I. Formal sources of credit are lower than the others.

II. Institutional sources of credit are higher than others.

III. Non-institutional sources of credit are higher than others.

IV. Informal sources of credit are higher than others.

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

Solution:

Formal sources of credit are the ones that are taken from banks and cooperatives. Whereas, informal sources of credit include moneylenders, merchants, workers, relatives and friends etc. Here 550 households borrow from Institutional/formal sources and 450 households borrow from Non-institutional/informal sources.

Question 96. Which of the following statements about Sustainable Development is/are correct?

I. The word ‘Sustainable Development’ came into existence in the year 1980.

II. Sustainable Development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs.

III. Brundtland Commission is related to Sustainable Development.

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

Solution:

Sustainable development was first coined by the International union for conservation of nature (IUCN) 1980. Later on, it was defined by the Brundtland Commission report, also known as “Our common future” released in 1987 as given in statement II.

Question 97. Which of the following statements is/are correct about the NITI Aayog?

I. NITI Aayog was established on 1 January 2015

II. The Prime Minister of India is the ex officio Chairperson of the NITI Aayog.

III. NITI Aayog replaced the Planning Commission of India in 2014.

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

Solution:

The NITI Aayog stands for National Institution for Transforming India which acts as the policy think tank of the Government of India. NITI Aayog is chaired by the prime minister and consists of other chief ministers, it intends to foster regional cooperation by emphasising on the federal aspect of policy making in India by involving the state governments. The NITI Aayog was established by the Government of India on 1st January, 2015 and hence replaced the Planning Commission of India in 2015.

Question 98. Mixed Economy means an economy where there is

1. a. Existence of capitalism
2. b. Privatization, liberalization and globalization
3. c. Existence of both public and private sectors
4. d. Growing crops along with rearing animals

Solution:

A mixed economy is one where capitalism and socialism co-exists. This type of an economic system allows for private ownership and control of means of production, but under government regulation. Certain industries which are considered essential or produce public goods are often socialised (under government) in a mixed economy. India is a mixed economy.

Question 99. Which of the following is not a function of the commercial bank in an economy?

1. a. Accepting Deposits
2. b. Providing Loans
3. c. Locker Facilities
4. d. Acting as a Banker’s Bank

Solution:

Commercial banks perform functions like accepting deposits, providing loans and facilitating locker services. The Reserve Bank of India is the central bank of the nation which performs the function of being a banker to other banks. It is also known as a lender of last resort.

Question 100. If GDP for a country X is Rs. 130 million in 2020 and its population is 20,000, GDP per capita is -

1. a. 6500
2. b. 130
3. c. 0.0065
4. d. 650

Solution: