Major Competitive Exams
Q. In a frequency distribution, if the mode is 10 and the highest frequency is 15, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
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Solution
Since there is one mode (10), the data is unimodal.
Correct Answer: C — It is unimodal
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Q. In a frequency distribution, if the mode is 10 and the highest frequency is 5, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
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Solution
Since there is one mode (10), the data is unimodal.
Correct Answer: C — It is unimodal
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Q. In a frequency distribution, if the mode is 12 and the frequency of 12 is 10, what can be inferred about the data?
A.
Data is uniform
B.
Data is skewed
C.
Data has multiple modes
D.
Data is bimodal
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Solution
A single mode indicates that the data is likely skewed.
Correct Answer: B — Data is skewed
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Q. In a galvanic cell, if the anode reaction is 2Ag⁺ + 2e⁻ → 2Ag, what is the cathode reaction? (2022)
A.
Cu²⁺ + 2e⁻ → Cu
B.
Zn²⁺ + 2e⁻ → Zn
C.
Fe²⁺ + 2e⁻ → Fe
D.
Pb²⁺ + 2e⁻ → Pb
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Solution
The cathode reaction must be a reduction reaction, and Cu²⁺ + 2e⁻ → Cu is a common cathode reaction.
Correct Answer: A — Cu²⁺ + 2e⁻ → Cu
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Q. In a galvanic cell, if the anode reaction is 2H₂ → 4H⁺ + 4e⁻, what is the cathode reaction?
A.
O₂ + 4e⁻ + 4H⁺ → 2H₂O
B.
2H₂O + 4e⁻ → 2H₂ + O₂
C.
4H⁺ + 4e⁻ → 2H₂
D.
2H₂ + O₂ → 2H₂O
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Solution
The cathode reaction is O₂ + 4e⁻ + 4H⁺ → 2H₂O.
Correct Answer: A — O₂ + 4e⁻ + 4H⁺ → 2H₂O
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Q. In a galvanic cell, if the anode reaction is Zn → Zn²⁺ + 2e⁻, what is the cathode reaction if the cathode is Cu²⁺ + 2e⁻ → Cu?
A.
Cu → Cu²⁺ + 2e⁻
B.
Zn²⁺ + 2e⁻ → Zn
C.
Zn + Cu²⁺ → Zn²⁺ + Cu
D.
Cu²⁺ + 2e⁻ → Cu
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Solution
The cathode reaction is Cu²⁺ + 2e⁻ → Cu.
Correct Answer: D — Cu²⁺ + 2e⁻ → Cu
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Q. In a galvanic cell, the anode is where:
A.
Reduction occurs
B.
Oxidation occurs
C.
Electrons are gained
D.
The salt bridge is located
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Solution
In a galvanic cell, oxidation occurs at the anode.
Correct Answer: B — Oxidation occurs
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Q. In a galvanic cell, which electrode undergoes reduction?
A.
Anode
B.
Cathode
C.
Salt bridge
D.
Electrolyte
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Solution
In a galvanic cell, reduction occurs at the cathode.
Correct Answer: B — Cathode
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Q. In a gas mixture, the total pressure is equal to the sum of the partial pressures of the individual gases. This is known as:
A.
Dalton's Law
B.
Boyle's Law
C.
Charles's Law
D.
Ideal Gas Law
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Solution
This principle is known as Dalton's Law of Partial Pressures.
Correct Answer: A — Dalton's Law
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Q. In a gas mixture, what is the partial pressure of a gas?
A.
Total pressure of the mixture
B.
Pressure exerted by the gas alone
C.
Pressure exerted by all gases
D.
Pressure at absolute zero
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Solution
The partial pressure of a gas in a mixture is the pressure that gas would exert if it occupied the entire volume alone.
Correct Answer: B — Pressure exerted by the gas alone
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Q. In a gas mixture, which law can be used to find the total pressure exerted by the gases?
A.
Dalton's Law of Partial Pressures
B.
Boyle's Law
C.
Charles's Law
D.
Ideal Gas Law
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Solution
Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each gas.
Correct Answer: A — Dalton's Law of Partial Pressures
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Q. In a gas, if the volume is halved while keeping the temperature constant, what happens to the pressure?
A.
It remains the same.
B.
It doubles.
C.
It halves.
D.
It quadruples.
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Solution
According to Boyle's Law, if the volume is halved while keeping the temperature constant, the pressure doubles.
Correct Answer: B — It doubles.
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Q. In a gas, the distribution of molecular speeds is described by which law?
A.
Maxwell-Boltzmann distribution
B.
Bernoulli's principle
C.
Boyle's law
D.
Charles's law
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Solution
The distribution of molecular speeds in a gas is described by the Maxwell-Boltzmann distribution.
Correct Answer: A — Maxwell-Boltzmann distribution
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Q. In a gas, the mean free path is defined as the average distance traveled by a molecule between collisions. Which factor does NOT affect the mean free path?
A.
Temperature
B.
Pressure
C.
Molecular diameter
D.
Color of the gas
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Solution
The mean free path is affected by temperature, pressure, and molecular diameter, but not by the color of the gas.
Correct Answer: D — Color of the gas
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Q. In a generator, if the speed of rotation is doubled, what happens to the induced EMF?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It becomes zero
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Solution
The induced EMF in a generator is directly proportional to the speed of rotation. Therefore, if the speed is doubled, the induced EMF also doubles.
Correct Answer: A — It doubles
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Q. In a generator, mechanical energy is converted into electrical energy through the principle of:
A.
Electrostatics
B.
Electromagnetic induction
C.
Thermodynamics
D.
Optics
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Solution
In a generator, mechanical energy is converted into electrical energy through the principle of electromagnetic induction, as the motion of conductors in a magnetic field induces an EMF.
Correct Answer: B — Electromagnetic induction
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Q. In a generator, mechanical energy is converted into electrical energy through which process?
A.
Electromagnetic induction
B.
Thermal conduction
C.
Photoelectric effect
D.
Electrolysis
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Solution
In a generator, mechanical energy is converted into electrical energy through the process of electromagnetic induction.
Correct Answer: A — Electromagnetic induction
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Q. In a generator, mechanical energy is converted into electrical energy through which principle?
A.
Electromagnetic induction
B.
Thermal conduction
C.
Photoelectric effect
D.
Capacitance
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Solution
In a generator, mechanical energy is converted into electrical energy through the principle of electromagnetic induction.
Correct Answer: A — Electromagnetic induction
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Q. In a generator, what is the role of the rotating coil in a magnetic field?
A.
To create a magnetic field
B.
To induce current
C.
To store energy
D.
To measure voltage
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Solution
In a generator, the rotating coil in a magnetic field induces current through electromagnetic induction, converting mechanical energy into electrical energy.
Correct Answer: B — To induce current
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Q. In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th term?
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Solution
The nth term of a geometric series is given by a_n = ar^(n-1). Thus, a_4 = 4 * 3^(4-1) = 4 * 27 = 108.
Correct Answer: A — 108
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Q. In a gravitational field, the potential energy of an object is maximum at which point?
A.
At the surface of the Earth
B.
At infinity
C.
At the center of the Earth
D.
At the highest point in the field
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Solution
The gravitational potential energy is considered maximum at infinity, where it is defined to be zero.
Correct Answer: B — At infinity
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Q. In a group of 100 people, 60 like cricket, 30 like football, and 10 like both. What is the probability that a person likes football given that they like cricket?
A.
1/6
B.
1/3
C.
1/2
D.
1/4
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Solution
P(Football|Cricket) = P(Football and Cricket) / P(Cricket) = 10/60 = 1/6.
Correct Answer: A — 1/6
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Q. In a group of 100 people, 60 like football, 30 like basketball, and 10 like both. What is the probability that a person likes football given that they like basketball?
A.
0.5
B.
0.3
C.
0.6
D.
0.7
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Solution
Using conditional probability, P(Football | Basketball) = P(Football and Basketball) / P(Basketball) = 10/30 = 1/3.
Correct Answer: C — 0.6
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Q. In a group of 50 people, 20 are smokers and 30 are non-smokers. If a person is selected at random, what is the probability that the person is a non-smoker given that they are not a smoker?
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Solution
If the person is not a smoker, they must be a non-smoker. Therefore, the probability is 1.
Correct Answer: A — 1
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Q. In a group of 50 people, 20 are smokers. What is the probability of selecting a non-smoker? (2022)
A.
2/5
B.
3/5
C.
1/2
D.
1/4
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Solution
Number of non-smokers = 50 - 20 = 30. Probability = 30/50 = 3/5.
Correct Answer: B — 3/5
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Q. In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
A.
0.4
B.
0.6
C.
0.5
D.
0.7
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Solution
Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is 30 + 20 - 10 = 40. The probability is 40/50 = 0.8.
Correct Answer: B — 0.6
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Q. In a harmonic oscillator, the total mechanical energy is constant. What is the form of this energy?
A.
Kinetic energy only
B.
Potential energy only
C.
Sum of kinetic and potential energy
D.
None of the above
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Solution
In a harmonic oscillator, the total mechanical energy is the sum of kinetic and potential energy, which remains constant over time.
Correct Answer: C — Sum of kinetic and potential energy
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Q. In a heat engine, if the input heat is 800 J and the work output is 300 J, what is the efficiency?
A.
37.5%
B.
50%
C.
62.5%
D.
75%
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Solution
Efficiency = (Work output / Heat input) × 100 = (300 J / 800 J) × 100 = 37.5%.
Correct Answer: C — 62.5%
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Q. In a heat engine, if the work done is 200 J and the heat absorbed is 500 J, what is the efficiency?
A.
40%
B.
50%
C.
60%
D.
80%
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Solution
Efficiency = (Work done / Heat absorbed) * 100 = (200 J / 500 J) * 100 = 40%.
Correct Answer: B — 50%
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Q. In a heat engine, if the work output is 200 J and the heat input is 600 J, what is the efficiency?
A.
33.33%
B.
50%
C.
66.67%
D.
75%
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Solution
Efficiency = (Work output / Heat input) × 100 = (200 J / 600 J) × 100 = 33.33%.
Correct Answer: C — 66.67%
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