Q. If a function f(x) is defined as f(x) = 3x - 5, what is the slope of the graph of this function?
A.
3
B.
-5
C.
0
D.
Undefined
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Solution
In the linear function f(x) = mx + b, m represents the slope. Here, m = 3, so the slope is 3.
Correct Answer:
A
— 3
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Q. If a function f(x) is defined as f(x) = 3x - 5, what is the slope of the graph?
A.
3
B.
-5
C.
0
D.
Undefined
Show solution
Solution
In the linear function f(x) = mx + b, 'm' represents the slope, which is 3 in this case.
Correct Answer:
A
— 3
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Q. If a function f(x) is defined as f(x) = x^3 - 3x + 2, what can be inferred about its behavior at critical points?
A.
It has no critical points.
B.
It has one local maximum and one local minimum.
C.
It is always increasing.
D.
It is always decreasing.
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Solution
To find critical points, we take the derivative and set it to zero. The function has one local maximum and one local minimum based on the nature of cubic functions.
Correct Answer:
B
— It has one local maximum and one local minimum.
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Q. If a function f(x) is defined as f(x) = x^3 - 3x, what is the nature of its critical points?
A.
They can be local maxima, local minima, or points of inflection.
B.
They are always local maxima.
C.
They are always local minima.
D.
They do not exist.
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Solution
Critical points of a function can be local maxima, local minima, or points of inflection, depending on the behavior of the function around those points.
Correct Answer:
A
— They can be local maxima, local minima, or points of inflection.
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Q. If a function is defined as f(x) = 2x + 3, what is the value of f(4)?
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Solution
Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11.
Correct Answer:
B
— 11
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Q. If a function is defined as f(x) = 3x + 2, what is the slope of the line represented by this function?
Show solution
Solution
In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 3.
Correct Answer:
A
— 3
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Q. If a function is defined as f(x) = 3x + 2, what is the value of f(4)?
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Solution
To find f(4), substitute 4 into the function: f(4) = 3(4) + 2 = 12 + 2 = 14.
Correct Answer:
A
— 14
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Q. If a galvanometer shows a deflection when connected to a potentiometer, what does it indicate?
A.
The circuit is open.
B.
The potential difference is zero.
C.
The potential difference is equal to the reference voltage.
D.
The current is flowing through the galvanometer.
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Solution
A deflection in the galvanometer indicates that the potential difference across the galvanometer is equal to the reference voltage.
Correct Answer:
C
— The potential difference is equal to the reference voltage.
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Q. If a gas expands against a constant external pressure, the work done by the gas is given by:
A.
W = P_ext * ΔV
B.
W = ΔU + Q
C.
W = Q - ΔU
D.
W = P_ext / ΔV
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Solution
The work done by the gas during expansion against a constant external pressure is given by W = P_ext * ΔV.
Correct Answer:
A
— W = P_ext * ΔV
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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
Show solution
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
Show solution
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%
Show solution
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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