All questions of 2020 for UPSC CSE Exam

D

1 x 5 x ( 2 x 5) x (3 x 5) x ( 2 x 2 X 5) x (5 x 5) x ( 2 x 3 x 5) x (7 x 5) x ( 2 x 2 x 2 x 5) x (9 x 5) x ( 2 x 5 x 5) x (11 x 5) x ( 2 x 2  x 3 x 5)

7.8 is the answer.

38

1+2+3+4+5=15,1+5=6is a multiple of 3. this shows that any arrangement of these numbers give a multiple of 3.

Given:
- Weight of vessel full of water = 40 kg
- Weight of vessel when one-third filled = 20 kg

To find: Weight of empty vessel

Solution:
Let's assume the weight of water in the vessel when it is one-third filled = x kg

When the vessel is one-third filled:
- Weight of water = x kg
- Weight of vessel = 20 kg
- Total weight = Weight of water + Weight of vessel = x + 20 kg

When the vessel is full of water:
- Weight of water = 40 - weight of empty vessel
- Weight of vessel = weight of empty vessel
- Total weight = Weight of water + Weight of vessel = (40 - weight of empty vessel) + weight of empty vessel = 40 kg

We can write an equation using the above information:
x + 20 = 40
x = 20

Therefore, the weight of water in the vessel when it is one-third filled is 20 kg.

Weight of empty vessel = Weight of vessel full of water - Weight of water in vessel when one-third filled
Weight of empty vessel = 40 - 20 = 20 kg

Hence, the weight of the empty vessel is 20 kg, which is option (A).

The sum of digits in the number (10n + 1) is 2

Given, GHI = 1578 and DEF = 912

We need to find ABC.

Approach:

- As we know that A=1, B=2, C=3, ..., Z=26.
- Also, GHI = 1000*G + 100*H + 10*I and DEF = 100*D + 10*E + F (where G, H, I, D, E, F are digits)
- Therefore, we can write: 1000*G + 100*H + 10*I + 100*D + 10*E + F = 1578 + 912
- Simplifying the above equation, we get: 1000*G + 100*H + 10*I + 100*D + 10*E + F = 2490
- Rearranging the terms, we get: 1000*G + 100*D + 100*H + 10*E + 10*I + F = 2490
- Now, we can easily see that (1000*G + 100*D + 100*H) is a multiple of 100, so we can ignore it.
- Also, (10*E + F) is a multiple of 2, so we can ignore it as well.
- Therefore, we are left with: 100*I + 10*B + C = 2490 - (1000*G + 100*D + 100*H + 10*E + F)
- Substituting the values of G, H, I, D, E, F from their respective letters, we get:
100*I + 10*B + C = 2490 - (100*7 + 100*4 + 100*9 + 10*1 + 10*2 + 9)
= 2490 - 740
= 1750
- Therefore, we have: 100*I + 10*B + C = 1750
- Now, we can see that I cannot be greater than 1, otherwise the value of the left-hand side will be greater than 1750.
- Also, B cannot be greater than 6, otherwise the value of the left-hand side will be greater than 1750.
- Therefore, we can try the values of I and B starting from 1 and 6 respectively, and find the value of C that satisfies the above equation.
- Trying with I=1 and B=6, we get: 100*1 + 10*6 + C = 1750
- Simplifying the above equation, we get: C = 175 - 60 = 115
- But this is not possible as C should be a digit between 0 and 9.
- Therefore, we try with I=1 and B=5, we get: 100*1 + 10*5 + C = 1750
- Simplifying the above equation, we get: C = 175 - 50 = 125
- But this is not possible as C should be a digit between 0 and 9.
- Therefore, we try with I=1 and B=4, we get: 100*1 + 10*4 + C = 1750
- Simplifying the above equation, we get: C = 175

Let numbers be x and y
S1: x * y = 21
x and y can be any number of values as it is nowhere mentioned in the question that the numbers are integers. The numbers can be decimal or fractions as well so S1 alone is not sufficient to answer the question.

S2: x + y = 10
The reasoning for S2 is the same as that for S1.

But when we use the info given in both S1 and S2, we can find the numbers, as there are two equations and two variables.
 

:

The world is facing a major crisis due to the rapid depletion of natural resources. The demand for these resources is increasing at an alarming rate, while their availability is decreasing. This has led to environmental degradation, climate change, and social unrest. The depletion of natural resources is not only affecting the present generation but also the future generations. It is important to take immediate action to conserve natural resources and use them in a sustainable manner. This can be achieved through sustainable development practices, conservation of natural habitats, and reducing our reliance on non-renewable resources. It is our responsibility to ensure that we leave a habitable planet for future generations.

What is the main idea of the passage?

a. The world is facing a major crisis due to the depletion of natural resources.
b. Environmental degradation is a result of the depletion of natural resources.
c. The depletion of natural resources is affecting the present and future generations.
d. Sustainable development practices are necessary to conserve natural resources.

Answer: a. The world is facing a major crisis due to the depletion of natural resources.

Given: Total amount = Rs. 2,500
Ratio of distribution = 1/2 : 3/4 : 5/6

Let us simplify the ratio:
1/2 : 3/4 : 5/6
= 3/6 : 4/6 : 5/6
= 9 : 8 : 10

Sum of the ratio = 9 + 8 + 10 = 27

Now, we can find the share of each person by dividing the total amount in the ratio 9:8:10
Share of X = (9/27) * 2500 = Rs. 833.33
Share of Y = (8/27) * 2500 = Rs. 740.74
Share of Z = (10/27) * 2500 = Rs. 925.93

Difference between the maximum and minimum share = Rs. (925.93 - 740.74) = Rs. 185.19

Therefore, the closest option is C) Rs. 400, which is not the exact answer, but the closest option.

D) 1971- 1981

Solution:

To compare these numbers, we need to convert them into a common denominator. The least common multiple of 2, 4, 3, and 6 is 12. So, we can write:

a) (1/2) - 1 = (6/12) - (12/12) = -6/12
b) (1/4) - 3 = (3/12) - (12/12) = -9/12
c) (1/3) - 4 = (4/12) - (12/12) = -8/12
d) (1/6) - 2 = (2/12) - (12/12) = -10/12

Now, it is clear that the largest number is -8/12, which is option (c).

Therefore, the correct answer is option (c), (1/3)-4.

Zero

- Option 2 is the right answer, the best implication of the entire passage is risk-taking behaviour that can help us to generate wealth.
- Option 3 is not correct as it talks about trustworthy asset management organizations, however, the author is talking about risk-taking behaviour.
- Option 1 is not correct as it only speaks about the last sentence of the passage.
- Option 4 is not correct as it does not fit the 'best implied' suggestion.
Hence, the correct answer is 'Risk-taking behaviour should be a necessary component of your personality if you want to generate wealth.'

 let the distance between X and Y is d km. 

Given:
- A bottle contains 20 litres of liquid A.
- 4 litres of liquid A is taken out of it and replaced by the same quantity of liquid B.
- 4 litre of the mixture is taken out and replaced by the same quantity of liquid B.

To find: The ratio of the quantity of liquid A to that of liquid B in the final mixture.

Solution:
Let's assume that after n operations of replacement, the amount of liquid A left in the bottle is Aₙ and liquid B is Bₙ.

After the first operation of replacement:
- Quantity of liquid A left in the bottle = A₁ = 20 - 4 + 4×(B/A)
- Quantity of liquid B in the bottle = B₁ = 4

After the second operation of replacement:
- Quantity of liquid A left in the bottle = A₂ = A₁ - 4 + 4×(B/A)
- Quantity of liquid B in the bottle = B₂ = 4×(B/A)

We can write A₂ in terms of A₁ as follows:
A₂ = A₁ - 4 + 4×(B/A)
A₂ = (20 - 4 + 4×(B/A)) - 4 + 4×(B/A)
A₂ = A₁ - 4×(A/A) + 4×(B/A)
A₂ = A₁ + 4×(B/A) - 4

Similarly, we can write Bₙ in terms of A₁ as follows:
B₂ = 4×(B/A)
B₃ = 4×(B/A)×(B/A)
B₄ = 4×(B/A)×(B/A)×(B/A)

After n operations of replacement, we can write:
Aₙ = A₁ + 4×(B/A) - 4×(B/A)³
Bₙ = 4×(B/A)ⁿ

Substituting the values, we get:
Aₙ = 20×(1 - (1/5)³) + 4×(1 - (1/5)²)
Bₙ = 4×(1/5)ⁿ

Therefore, the ratio of the quantity of liquid A to that of liquid B in the final mixture is:
Aₙ:Bₙ = [20×(1 - (1/5)³) + 4×(1 - (1/5)²)]:[4×(1/5)ⁿ]
Aₙ:Bₙ = [16×(125/216) + 4×(16/25)]:[4×(1/5)ⁿ]
Aₙ:Bₙ = [100:27]:[1/5]ⁿ
Aₙ:Bₙ = 16:9 (n=2)

Therefore, the ratio of the quantity of liquid A to that of liquid B in the final mixture is 16:9.

Given Statements:
All cats are dogs.
All cats are black.

Conclusion-I:
All dogs are black.

Conclusion-II:
Some dogs are not black.

Explanation:
Conclusion-I:
- All cats are dogs and all cats are black.
- But, it is not necessary that all dogs are black.
- Therefore, Conclusion-I does not logically follow from the given statements.

Conclusion-II:
- All cats are black, but it is not necessary that all cats are dogs.
- Therefore, we cannot conclude anything about dogs from the given statements.
- Hence, Conclusion-II does not logically follow from the given statements.

Therefore, neither Conclusion-I nor Conclusion-II logically follows from the given statements. The correct answer is option 'C'.

Solution:

Let's assume that the torn page is "x".

The sum of the numbers on the remaining pages is 195.

We can use the formula to find the sum of consecutive integers from 1 to n:

Sum = n(n+1)/2

We need to find the sum of the numbers on the remaining pages, which is 195. So, we can write:

195 = n(n+1)/2

Solving this equation, we get n = 19.

Therefore, the booklet had 19 pages.

Now, we need to find the torn page. We can use the fact that the sum of consecutive even (or odd) integers is twice the sum of consecutive integers. So, we can find the sum of consecutive even (or odd) integers from 1 to 19, and then subtract the sum of the remaining pages (which is 195) to get the torn page.

Sum of consecutive even integers from 1 to 19:

2+4+6+...+18 = 2(1+2+3+...+9) = 2(9x10/2) = 90

Subtracting the sum of the remaining pages (195) from the sum of consecutive even integers from 1 to 19 (90), we get:

90 - 195 = -105

This means that there is an odd number difference between the sum of consecutive even integers from 1 to 19 and the sum of the remaining pages. This difference is equal to the torn page number.

Now, we need to find an odd number that is less than or equal to 19 (the number of pages in the booklet) and has a difference of 105 with the sum of consecutive even integers from 1 to 19.

We can start by trying odd numbers that are less than or equal to 19 and see which one satisfies the condition. We can write the sum of consecutive odd integers from 1 to n as:

Sum = n^2

Trying n = 1, we get Sum = 1, which is not equal to 105. So, we can try n = 3.

Sum of consecutive odd integers from 1 to 3:

1+3 = 4

Square of 3:

3^2 = 9

Difference between the sum of consecutive odd integers from 1 to 3 and the square of 3:

9 - 4 = 5

This difference is not equal to 105. So, we can try n = 5.

Sum of consecutive odd integers from 1 to 5:

1+3+5 = 9

Square of 5:

5^2 = 25

Difference between the sum of consecutive odd integers from 1 to 5 and the square of 5:

25 - 9 = 16

This difference is not equal to 105. So, we can try n = 7.

Sum of consecutive odd integers from 1 to 7:

1+3+5+7 = 16

Square of 7:

7^2 = 49

Difference between the sum of consecutive odd integers from 1 to 7 and the square of 7:

49 - 16 = 33

This difference is not equal to 105. So, we can try n = 9.

Sum of consecutive odd integers from 1 to 9:

1+3+5+7

Explanation:

The given arrangement is:

abab_b_bcb_dcdcded_d

Let's analyze it.

- The first two letters are "ab". This pattern repeats in the next two letters as well. So, we can infer that the missing letter here should also be 'a'.
- The next three letters are "_b_". There are multiple possibilities for this missing letter. However, we can see that the next letter is 'c'. Hence, the missing letter should be 'b' to form the word "bcb".
- The next two letters are "dc". This pattern repeats in the next two letters as well. So, we can infer that the missing letter here should also be 'd'.
- The next six letters are "dcdcded". We can see that the letters 'c' and 'd' are repeating. Hence, the missing letters should be 'c' and 'e' to form the word "dcdcdedcde".
- The last letter is 'd'.

Therefore, the missing letters that complete the arrangement are "a, c, c, e". Hence, option (c) is the correct answer.

Solution:

When a square and a circle intersect, there can be a minimum of 0 points of intersection and a maximum of 8 points of intersection. Let's explain this in detail.

Minimum number of points of intersection:

1. When a square and a circle do not intersect at all, the number of points of intersection is 0.

2. When a circle is entirely inside the square or the square is entirely inside the circle, there are no points of intersection.

3. When a circle touches the square from the outside or the inside, there is only one point of intersection.

4. When a circle passes through the corners of the square, there are two points of intersection.

Therefore, the minimum number of points of intersection is 0 when there is no intersection at all, and 2 when the circle passes through the corners of the square.

Maximum number of points of intersection:

1. When a circle passes through the corners of the square, there are two points of intersection.

2. When a circle intersects the sides of the square twice, there are a total of 8 points of intersection.

Therefore, the maximum number of points of intersection is 8 when the circle intersects the sides of the square twice.

Conclusion:

Hence, statement 1 is incorrect as the minimum number of points of intersection is 0, not 2. Statement 2 is correct as the maximum number of points of intersection is 8. Therefore, the correct answer is option B.

Given:
- Average score of a batsman after his 50th innings = 46.4
- After 60th innings, his average score increases by 2.6

To find:
- Average score in the last ten innings

Approach:
- Let the total runs scored by the batsman in his first 50 innings be X
- Then, his total runs scored in his first 60 innings = X + 10a (where 'a' is the increased average score)
- Using the given information, we can form an equation as:
(X + 10a)/60 = 46.4
(X + 10a)/50 = 46.4 + 2.6
- Solve the above two equations to get the value of X and a
- Finally, using the value of a, we can find the average score in the last ten innings

Calculation:

(X + 10a)/60 = 46.4
(X + 10a) = 2784 --------- (1)

(X + 10a)/50 = 46.4 + 2.6
(X + 10a) = 2530 --------- (2)

Solving equations (1) and (2), we get:

X = 240
a = 12

Therefore, the total runs scored by the batsman in his last ten innings = (60 x 59) - (50 x 49) = 110
And, the average score in the last ten innings = 110/10 = 11

Adding the increased average score of 2.6, we get:
Average score in the last ten innings = 11 + 2.6 = 13.6

Rounding off to the nearest integer, we get:
Average score in the last ten innings = 14

Hence, the correct option is (C) 62.

B

Given, selling price of the car = Rs. 3,00,000
Loss incurred = 20%

We need to find the cost price of the car.

Let the cost price be x.

Loss percentage = (Loss / Cost Price) x 100
20 = (Loss / x) x 100
2000 = Loss / x
Loss = 2000x

Selling price = Cost price - Loss
300000 = x - 2000x
300000 = - 1000x
x = - 300000 / -1000
x = Rs. 3,75,000

Therefore, the person spent Rs. 3,75,000 to buy the car.

Answer: Option D) Rs. 3,75,000

Given data:
A man walks down the backside of his house straight 25 meters.
Then he turns to the right and walks 50 meters.
Then he turns towards left and again walks 25 meters.
His house faces East.

To find:
The direction of the man from the starting point.

Solution:
Let us assume that the man starts his journey from point A, which is the starting point.

- The man walks down the backside of his house straight 25 meters. This means he moves towards the south direction from point A and reaches point B.
- Then he turns to the right and walks 50 meters. This means he moves towards the west direction from point B and reaches point C.
- Then he turns towards left and again walks 25 meters. This means he moves towards the south direction from point C and reaches point D.

Now, let us draw a diagram to understand the direction of the man from the starting point.

From the above diagram, we can see that the man is now at point D, which is towards the southwest direction from point A.

Therefore, the correct answer is option (d) North-west.

Note: It is important to understand that the direction of the man is based on the assumption that the house faces the East direction. If the direction of the house changes, then the direction of the man will also change accordingly.

Explanation:

• S1: C is younger than D, but older than A and B.


• S2: D is the oldest.


• S3: A is older than B.

Answer: Option D, S1 and S3 together are sufficient to answer the Question.

Explanation:

• From S2, we know that D is the oldest.


• From S1, we know that C is younger than D, but older than A and B.


• From S3, we know that A is older than B.


• So, we can arrange the people in order of their ages as follows: D > C > A > B


• Therefore, B is the youngest among A, B, C, and D.

Explanation:

Relying on a homogeneous food source is not desirable:
- The passage highlights the dangers of relying solely on one type of crop as a staple food.
- The Irish became almost wholly dependent on the Lumper potato, which had genetic frailty.
- When the deadly fungus Phytophthora infestans struck in 1845, it destroyed nearly all the Lumpers, leading to a devastating famine.

Importance of crop diversity:
- Relying on a single crop makes a population vulnerable to crop failure due to factors like disease, pests, or environmental conditions.
- Having a variety of crops ensures food security and reduces the risk of famine in case one crop fails.

Lessons learned from history:
- The Irish Potato Famine serves as a poignant reminder of the importance of crop diversity and sustainable farming practices.
- It emphasizes the need for careful consideration when introducing foreign crops to ensure they are resilient to local conditions.

Conclusion:
- The critical message of the passage is that diversifying food sources is crucial to avoid catastrophic consequences like the Irish Potato Famine. It underscores the importance of sustainable agricultural practices and the need to learn from past mistakes to ensure food security for future generations.

Given, 1 litre of water weighs 1 kg.

We need to find the volume of water that weighs 0.1 gm.

1 kg of water = 1000 gm of water
1 litre of water = 1000 ml of water

1 ml of water = 1 gm of water

Therefore, 0.1 gm of water = 0.1 ml of water

But we need to find the volume of water in cubic millimeters.

1 ml = 1000 cubic millimeter (mm³)

Therefore, 0.1 ml = 0.1 x 1000 = 100 cubic millimeter (mm³)

Hence, 100 cubic millimeters of water will weigh 0.1 gm.

Therefore, option C is the correct answer.

Volume of a cube= (side) .. (1)

Let the side of cube P be = s
Mass of cube P = m

Can play a significant role in addressing climate change through the development of GM crops, but there are concerns about their potential negative impacts.

Assumptions about Sustainable Delivery of Water in Cities

Valid Assumptions:

1. Rich cities only can ensure sustainable delivery of water.
The passage mentions that delivering water in cities requires heavy investment in collecting it from a natural source, treating it to make it potable, and laying a distribution network of pipes for delivery to the users. It also requires investments in sewerage infrastructure and sewage treatment plants so that the sewers can carry the wastewater to these plants to ensure that no untreated sewage is discharged back into natural water bodies. The passage further states that if cities were rich enough to meet the entire cost, water could be delivered for free. Therefore, it can be assumed that cities need to have financial resources to ensure sustainable delivery of water.

2. Sustainable delivery of water in cities means much more than supplying water to households.
The passage highlights that water delivery requires investment in collecting, treating, and distributing water as well as in sewerage infrastructure and treatment plants. The focus is not just on supplying households with water but also on ensuring that wastewater is treated and not discharged back into natural water bodies. Therefore, it can be assumed that sustainable delivery of water in cities involves a comprehensive approach that goes beyond just supplying water to households.

Invalid Assumptions:

None of the assumptions made in the passage are invalid.

Overall, the passage emphasizes the need for financing mechanisms to ensure sustainable delivery of water in cities, which requires significant investments in infrastructure and treatment facilities. It emphasizes the need for a comprehensive approach that goes beyond just supplying water to households and highlights the role of financial resources in ensuring sustainable delivery of water.

Monitoring India's Public Distribution System:
- The Union Government should closely monitor India's Public Distribution System to ensure that essential food items reach malnourished children and families in need.

Encouraging Girls to Delay Marriage and First Pregnancy:
- Girls should be encouraged to delay marriage and first pregnancy to reduce the risk of malnutrition in both mothers and children. This will also allow girls to focus on their education and career before starting a family.

Promoting Breastfeeding:
- Mothers should be encouraged to breastfeed their children immediately after birth as breast milk provides essential nutrients for the baby's growth and development. This can help prevent malnutrition in infants.

Ensuring Supply of Safe Drinking Water and Sanitation Facilities:
- It is crucial to provide safe drinking water and proper sanitation facilities to all individuals, especially in regions where malnutrition is prevalent. Access to clean water and sanitation can help prevent waterborne diseases and improve overall health.
By implementing these rational and practical implications, authorities can work towards reducing malnutrition in India and improving the overall health and well-being of children and families.

Right to privacy.

The correct assumptions based on the passage are:
1. State should have some institutions to ensure its appropriate role in a digital society.
2. State should ensure that private parties are not able to block the citizens' right to free expression.
3. A right to free expression is meaningless without actual availability of security that guarantees that private force cannot be used to thwart this right.

Note: The passage does not directly mention the compatibility of digital economy with the idea of not violating citizens' right to privacy.

C) 3 only

Explanation: The passage states that people will invest in education when they have the economic freedom to enjoy its benefits, and that the return on education increases with the level of economic freedom. This supports assumption 3, that economic freedom has a positive impact on building up human capital.
Assumption 1 is not valid because the passage does not say that lower tax rates will always lead to greater investments in higher education. It only states that when people are allowed to retain more of their income due to lower tax rates, it makes sense to invest in education.
Assumption 2 is not valid because the passage does not discuss whether investing in a child's education ensures their economic freedom. It only states that the same incentives apply to parents who decide on whether to invest in their children's education.

"TRIANGLE"?

First, we count the number of letters in the word "TRIANGLE": 8.

Since we want to construct 5-letter words, we need to choose 5 letters out of the 8.

This can be done in 8 choose 5 ways:

8C5 = 8! / (5! * 3!) = 56

Therefore, there are 56 different 5-letter words that can be constructed using all the letters of the word "TRIANGLE".