Q. As of 2023, what is the current account deficit of India as a percentage of GDP? (2023)
A.
1.5%
B.
2.0%
C.
2.5%
D.
3.0%
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Solution
India's current account deficit is approximately 2.0% of GDP as of 2023.
Correct Answer: B — 2.0%
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Q. As of 2023, which country has the highest number of electric vehicles on the road? (2023)
A.
USA
B.
Norway
C.
China
D.
Germany
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Solution
China has the highest number of electric vehicles on the road as of 2023.
Correct Answer: C — China
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Q. As of 2023, which country has the highest number of electric vehicles per capita? (2023)
A.
Norway
B.
Germany
C.
USA
D.
China
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Solution
Norway has the highest number of electric vehicles per capita as of 2023.
Correct Answer: A — Norway
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Q. As of 2023, which Indian bank has the highest number of branches? (2023)
A.
State Bank of India
B.
Punjab National Bank
C.
Bank of Baroda
D.
HDFC Bank
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Solution
State Bank of India has the highest number of branches in India as of 2023.
Correct Answer: A — State Bank of India
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Q. As of 2023, which renewable energy source has the highest capacity in India? (2023)
A.
Solar
B.
Wind
C.
Hydro
D.
Biomass
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Solution
Solar energy has the highest capacity among renewable sources in India as of 2023.
Correct Answer: A — Solar
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Q. As of 2023, which sector is the largest contributor to India's GDP? (2023)
A.
Agriculture
B.
Manufacturing
C.
Services
D.
Construction
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Solution
The services sector is the largest contributor to India's GDP as of 2023.
Correct Answer: C — Services
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Q. At absolute zero, the kinetic energy of gas molecules is:
A.
Maximum
B.
Zero
C.
Minimum
D.
Undefined
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Solution
At absolute zero, the kinetic energy of gas molecules is zero, as they are at their lowest energy state.
Correct Answer: B — Zero
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Q. At absolute zero, what is the expected volume of an ideal gas?
A.
Zero
B.
Infinite
C.
Constant
D.
Undefined
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Solution
At absolute zero, the volume of an ideal gas is expected to be zero according to Charles's Law.
Correct Answer: A — Zero
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Q. At absolute zero, what is the theoretical volume of an ideal gas?
A.
Zero
B.
Infinite
C.
Constant
D.
Undefined
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Solution
At absolute zero, the volume of an ideal gas is theoretically zero according to Charles's Law.
Correct Answer: A — Zero
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Q. At constant pressure, if the temperature of a gas is increased, what happens to its volume?
A.
It decreases
B.
It increases
C.
It remains constant
D.
It becomes zero
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Solution
According to Charles's Law, at constant pressure, the volume of a gas increases with an increase in temperature.
Correct Answer: B — It increases
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Q. At constant pressure, what is the relationship between volume and temperature of a gas?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
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Solution
According to Charles's Law, volume and temperature are directly proportional at constant pressure.
Correct Answer: A — Directly proportional
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Q. At constant temperature and pressure, if ΔH is positive and ΔS is negative, what can be said about ΔG?
A.
ΔG is positive
B.
ΔG is negative
C.
ΔG is zero
D.
ΔG can be either positive or negative
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Solution
If ΔH is positive and ΔS is negative, ΔG will be positive.
Correct Answer: A — ΔG is positive
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Q. At constant temperature and pressure, if ΔH is positive and ΔS is negative, what is the sign of ΔG?
A.
Always negative
B.
Always positive
C.
Depends on temperature
D.
Zero
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Solution
If ΔH is positive and ΔS is negative, ΔG will always be positive.
Correct Answer: B — Always positive
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Q. At constant temperature, the volume of a gas is inversely proportional to its pressure. This is known as which law?
A.
Boyle's Law
B.
Charles's Law
C.
Avogadro's Law
D.
Ideal Gas Law
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Solution
Boyle's Law states that for a given mass of gas at constant temperature, the volume is inversely proportional to the pressure.
Correct Answer: A — Boyle's Law
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Q. At what distance from a mass M does the gravitational potential become zero?
A.
At infinity
B.
At the surface of the mass
C.
At 1 meter
D.
At 2 meters
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Solution
The gravitational potential becomes zero at infinity, as V approaches zero as r approaches infinity.
Correct Answer: A — At infinity
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Q. At what point between two equal masses does the gravitational force become zero?
A.
At the midpoint
B.
At a point closer to one mass
C.
At a point closer to the other mass
D.
It never becomes zero
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Solution
The gravitational forces exerted by both masses cancel each other out at the midpoint.
Correct Answer: A — At the midpoint
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Q. At what point does the function f(x) = x^3 - 3x^2 + 4 have a local minimum? (2020)
A.
(1, 2)
B.
(2, 1)
C.
(0, 4)
D.
(3, 0)
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Solution
To find local minima, we find f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Checking the second derivative, f''(2) = 6 > 0, so (2, 1) is a local minimum.
Correct Answer: A — (1, 2)
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Q. At what point in a gravitational field is the gravitational potential constant?
A.
At the center of the mass
B.
At infinity
C.
Along an equipotential surface
D.
At the surface of the mass
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Solution
The gravitational potential is constant along an equipotential surface.
Correct Answer: C — Along an equipotential surface
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Q. At what point in space is the gravitational potential energy of an object zero?
A.
At the center of the Earth
B.
At infinity
C.
At the surface of the Earth
D.
At the Moon
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Solution
The gravitational potential energy is considered zero at infinity.
Correct Answer: B — At infinity
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Q. At what point in space is the gravitational potential zero?
A.
At the center of the Earth.
B.
At infinity.
C.
At the surface of the Earth.
D.
At the center of the Moon.
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Solution
The gravitational potential is considered zero at infinity.
Correct Answer: B — At infinity.
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Q. At what temperature (in Kelvin) does the volume of a gas become zero according to Charles's Law?
A.
0 K
B.
273 K
C.
100 K
D.
32 K
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Solution
According to Charles's Law, the volume of a gas approaches zero at absolute zero, which is 0 K.
Correct Answer: A — 0 K
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Q. At what temperature does a reaction become spontaneous if ΔH = 50 kJ and ΔS = 0.1 kJ/K?
A.
500 K
B.
250 K
C.
1000 K
D.
200 K
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Solution
Set ΔG = 0: 0 = ΔH - TΔS; T = ΔH/ΔS = 50 kJ / 0.1 kJ/K = 500 K.
Correct Answer: A — 500 K
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Q. At what temperature does the Gibbs Free Energy change from negative to positive?
A.
At absolute zero
B.
At the melting point
C.
At the boiling point
D.
At the transition temperature
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Solution
The Gibbs Free Energy changes from negative to positive at the transition temperature, where the system shifts from one phase to another.
Correct Answer: D — At the transition temperature
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Q. At what temperature does the volume of a gas become zero according to Charles's Law?
A.
0 K
B.
-273.15 °C
C.
273.15 K
D.
None of the above
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Solution
According to Charles's Law, the volume of a gas approaches zero at absolute zero, which is -273.15 °C.
Correct Answer: B — -273.15 °C
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Q. At what temperature does the volume of a gas theoretically become zero?
A.
0°C
B.
0 K
C.
273 K
D.
100 K
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Solution
According to Charles's Law, the volume of a gas approaches zero at absolute zero, which is 0 K.
Correct Answer: B — 0 K
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Q. At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol? (R = 8.314 J/(mol K))
A.
500 K
B.
600 K
C.
700 K
D.
800 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), we solve for T: T = (v_rms^2 * M) / (3R) = (1000^2 * 0.044) / (3 * 8.314) = 700 K.
Correct Answer: C — 700 K
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Q. At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol?
A.
300 K
B.
400 K
C.
500 K
D.
600 K
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Solution
Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 500 K.
Correct Answer: C — 500 K
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Q. At what temperature will the RMS speed of a gas be 300 m/s if its molar mass is 28 g/mol?
A.
300 K
B.
600 K
C.
900 K
D.
1200 K
Show solution
Solution
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T. Setting v_rms = 300 m/s and M = 28 g/mol, we find T = (M * v_rms^2)/(3R) = 600 K.
Correct Answer: B — 600 K
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Q. At what temperature will the RMS speed of a gas be 500 m/s if its molar mass is 0.02 kg/mol? (2000)
A.
250 K
B.
500 K
C.
1000 K
D.
2000 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), rearranging gives T = (v_rms^2 * M) / (3R). Substituting values gives T = 500 K.
Correct Answer: B — 500 K
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Q. At what temperature will the RMS speed of a gas be 600 m/s if its molar mass is 0.02 kg/mol?
A.
300 K
B.
600 K
C.
900 K
D.
1200 K
Show solution
Solution
Using v_rms = sqrt(3RT/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T = (600^2 * 0.02) / (3 * 8.314) = 900 K.
Correct Answer: C — 900 K
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