Q. If a gas expands and does 150 J of work while absorbing 100 J of heat, what is the change in internal energy?
A.
-50 J
B.
50 J
C.
250 J
D.
100 J
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Solution
Using the first law of thermodynamics, ΔU = Q - W = 100 J - 150 J = -50 J.
Correct Answer:
A
— -50 J
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Q. If a gas expands and does 50 J of work while absorbing 30 J of heat, what is the change in internal energy?
A.
-20 J
B.
20 J
C.
80 J
D.
30 J
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Solution
Using the First Law of Thermodynamics, ΔU = Q - W. Here, ΔU = 30 J - 50 J = -20 J.
Correct Answer:
B
— 20 J
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Q. If a gas occupies 10 L at 1 atm, what will be its volume at 2 atm if the temperature remains constant?
A.
5 L
B.
10 L
C.
20 L
D.
15 L
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Solution
Using Boyle's Law (P1V1 = P2V2), if P1 = 1 atm, V1 = 10 L, and P2 = 2 atm, then V2 = (P1V1)/P2 = (1 atm * 10 L) / 2 atm = 5 L.
Correct Answer:
A
— 5 L
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Q. If a gas occupies a volume of 10 L at 1 atm, what will be its volume at 2 atm if the temperature remains constant?
A.
5 L
B.
10 L
C.
20 L
D.
15 L
Show solution
Solution
Using Boyle's Law (P1V1 = P2V2), if the pressure doubles from 1 atm to 2 atm, the volume will halve from 10 L to 5 L.
Correct Answer:
A
— 5 L
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Q. If a global conference has 10 sessions and each session lasts 2 hours, what is the total duration of the conference in hours?
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Solution
Total duration = 10 sessions * 2 hours/session = 20 hours.
Correct Answer:
C
— 20
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Q. If a global organization has 12 member countries and each country contributes equally to a fund of $240 million, how much does each country contribute? (2023)
A.
$15 million
B.
$20 million
C.
$25 million
D.
$30 million
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Solution
Contribution per country = Total fund / Number of countries = $240 million / 12 = $20 million.
Correct Answer:
B
— $20 million
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Q. If a government decides to allocate more resources to education rather than healthcare, which of the following best describes this decision?
A.
A trade-off.
B.
An investment.
C.
A misallocation.
D.
A balanced approach.
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Solution
The decision to allocate more resources to one sector over another represents a trade-off, making option 0 the correct choice.
Correct Answer:
A
— A trade-off.
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Q. If a government decides to allocate more resources to public health rather than education, this decision can be seen as prioritizing: (2023)
A.
Short-term benefits over long-term investments.
B.
Equity over efficiency.
C.
Economic growth over social welfare.
D.
Immediate needs over future needs.
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Solution
Allocating more resources to public health reflects a focus on immediate needs, making option 3 the correct choice.
Correct Answer:
D
— Immediate needs over future needs.
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Q. If a government plans to increase its budget by 15% next year, and the current budget is $300 billion, what will be the new budget?
A.
$345 billion
B.
$330 billion
C.
$315 billion
D.
$300 billion
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Solution
New budget = 300 billion * (1 + 0.15) = 300 billion * 1.15 = $345 billion.
Correct Answer:
A
— $345 billion
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Q. If a government scheme allocates a budget of ₹50,000 for education and it is to be distributed equally among 5 schools, how much will each school receive?
A.
₹5,000
B.
₹10,000
C.
₹15,000
D.
₹20,000
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Solution
Each school will receive ₹50,000 / 5 = ₹10,000.
Correct Answer:
B
— ₹10,000
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Q. If a government scheme distributes ₹4,00,000 among 16 beneficiaries equally, how much does each beneficiary receive?
A.
₹20,000
B.
₹25,000
C.
₹30,000
D.
₹35,000
Show solution
Solution
Each beneficiary receives ₹4,00,000 / 16 = ₹25,000.
Correct Answer:
B
— ₹25,000
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Q. If a government scheme has a budget of ₹1.2 billion and 25% is allocated for education, how much is allocated for education?
A.
₹200 million
B.
₹300 million
C.
₹400 million
D.
₹500 million
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Solution
25% of ₹1.2 billion = 0.25 * 1200 = ₹300 million.
Correct Answer:
C
— ₹400 million
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Q. If a government scheme increases the employment rate by 5% in a region with 20,000 workers, how many additional workers are employed? (2000)
A.
500
B.
1000
C.
1500
D.
2000
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Solution
5% of 20,000 = 0.05 * 20000 = 1000 additional workers.
Correct Answer:
B
— 1000
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Q. If a government scheme is expected to reduce poverty by 10% in a population of 1 million, how many people will be lifted out of poverty?
A.
50,000
B.
100,000
C.
150,000
D.
200,000
Show solution
Solution
10% of 1,000,000 = 0.10 * 1000000 = 100,000 people.
Correct Answer:
B
— 100,000
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Q. If a government scheme provides ₹2,50,000 to 10 villages, and each village receives an equal amount, how much does each village receive?
A.
₹20,000
B.
₹25,000
C.
₹30,000
D.
₹35,000
Show solution
Solution
Each village receives ₹2,50,000 / 10 = ₹25,000.
Correct Answer:
B
— ₹25,000
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Q. If a habitat loses 10% of its area each year due to deforestation, how much area will remain after 3 years if it started with 200 hectares?
A.
162 hectares
B.
170 hectares
C.
180 hectares
D.
190 hectares
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Solution
After 1 year: 200 - (10% of 200) = 180; After 2 years: 180 - (10% of 180) = 162; After 3 years: 162 - (10% of 162) = 145.8, rounded to 146 hectares.
Correct Answer:
A
— 162 hectares
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Q. If a helicopter ascends at a rate of 300 meters per minute, how high will it be after 10 minutes? (2021)
A.
2000 m
B.
2500 m
C.
3000 m
D.
3500 m
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Solution
Height = Rate × Time = 300 m/min × 10 min = 3000 m
Correct Answer:
C
— 3000 m
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Q. If a heterozygous tall plant (Tt) is crossed with a homozygous short plant (tt), what is the probability of obtaining a tall plant?
A.
0%
B.
25%
C.
50%
D.
75%
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Solution
The cross Tt x tt results in 50% Tt (tall) and 50% tt (short), so the probability of obtaining a tall plant is 50%.
Correct Answer:
C
— 50%
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Q. If a heterozygous tall plant (Tt) is crossed with a homozygous short plant (tt), what is the probability of obtaining a short plant?
A.
0%
B.
25%
C.
50%
D.
75%
Show solution
Solution
The cross Tt x tt results in 50% Tt (tall) and 50% tt (short), so the probability of obtaining a short plant is 50%.
Correct Answer:
C
— 50%
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Q. If a hexagon is regular, what is the relationship between its sides and angles?
A.
All sides are equal, and all angles are equal.
B.
Sides can be of different lengths, but angles are equal.
C.
Sides are equal, but angles can vary.
D.
No specific relationship exists.
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Solution
In a regular hexagon, all sides are equal in length and all interior angles are equal.
Correct Answer:
A
— All sides are equal, and all angles are equal.
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Q. If a hollow cylinder and a solid cylinder of the same mass and radius roll down the same incline, which one reaches the bottom first?
A.
Hollow cylinder
B.
Solid cylinder
C.
Both reach at the same time
D.
Depends on the angle of incline
Show solution
Solution
The solid cylinder reaches the bottom first because it has a smaller moment of inertia compared to the hollow cylinder.
Correct Answer:
B
— Solid cylinder
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Q. If a hollow cylinder rolls down an incline, how does its acceleration compare to that of a solid cylinder?
A.
Hollow cylinder accelerates faster
B.
Solid cylinder accelerates faster
C.
Both accelerate equally
D.
Depends on the angle of incline
Show solution
Solution
The solid cylinder has a lower moment of inertia compared to the hollow cylinder, thus it accelerates faster down the incline.
Correct Answer:
B
— Solid cylinder accelerates faster
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Q. If a hollow sphere and a solid sphere of the same mass and radius roll down the same incline, which one reaches the bottom first?
A.
Hollow sphere
B.
Solid sphere
C.
Both reach at the same time
D.
Depends on the angle of incline
Show solution
Solution
The solid sphere has a smaller moment of inertia compared to the hollow sphere, thus it accelerates faster and reaches the bottom first.
Correct Answer:
B
— Solid sphere
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Q. If a hollow sphere rolls down an incline, how does its acceleration compare to that of a solid sphere?
A.
Greater
B.
Less
C.
Equal
D.
Depends on mass
Show solution
Solution
The hollow sphere has a greater moment of inertia, resulting in less acceleration compared to the solid sphere.
Correct Answer:
B
— Less
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Q. If a household uses 250 liters of water per day, how much water will it use in a month (30 days)?
A.
6000 liters
B.
7500 liters
C.
8000 liters
D.
9000 liters
Show solution
Solution
250 liters/day * 30 days = 7500 liters
Correct Answer:
B
— 7500 liters
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Q. If a hybrid set contains elements from both set X and set Y, which of the following is a valid conclusion?
A.
All elements of set X are in the hybrid set.
B.
All elements of set Y are in the hybrid set.
C.
Some elements of set X may not be in the hybrid set.
D.
The hybrid set cannot contain elements from both sets.
Show solution
Solution
It is possible for some elements of set X to not be included in the hybrid set, as hybrid sets can vary in composition.
Correct Answer:
C
— Some elements of set X may not be in the hybrid set.
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Q. If a hybrid set contains elements from three different categories, which of the following is a valid inference?
A.
All elements belong to the same category.
B.
At least one element must belong to each category.
C.
No elements can belong to more than one category.
D.
The categories must be mutually exclusive.
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Solution
In a hybrid set with elements from different categories, at least one element must belong to each category.
Correct Answer:
B
— At least one element must belong to each category.
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Q. If a hybrid set contains elements from three different sets, what can be inferred about its composition?
A.
It must contain at least one element from each set.
B.
It can only contain elements from the largest set.
C.
It will have no duplicates.
D.
It can include elements that are not in any of the three sets.
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Solution
A hybrid set formed from multiple sets typically includes at least one element from each contributing set.
Correct Answer:
A
— It must contain at least one element from each set.
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Q. If a hybrid set contains elements from three different sets, what can be inferred about its size compared to the individual sets? (2023)
A.
It will always be smaller than the smallest set.
B.
It can be larger than the sum of the sizes of the individual sets.
C.
It will be equal to the largest set.
D.
It can be smaller than the sum of the sizes of the individual sets.
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Solution
The size of a hybrid set can vary and may be smaller than the sum of the sizes of the individual sets due to overlapping elements.
Correct Answer:
D
— It can be smaller than the sum of the sizes of the individual sets.
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Q. If a hybrid set contains elements from three different sets, which of the following is a possible characteristic of this hybrid set?
A.
It can only contain elements from two of the sets.
B.
It must contain all elements from each of the three sets.
C.
It may contain elements that are common to all three sets.
D.
It cannot have any elements that are unique to one set.
Show solution
Solution
A hybrid set can include elements that are common to all three sets, as well as unique elements.
Correct Answer:
C
— It may contain elements that are common to all three sets.
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