Q. Which of the following statements about the Fibonacci sequence is true? (2023)
A.
It starts with 0 and 1
B.
It is an arithmetic sequence
C.
It has a constant difference
D.
It is a geometric sequence
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Solution
The Fibonacci sequence starts with 0 and 1, and each subsequent term is the sum of the previous two.
Correct Answer: A — It starts with 0 and 1
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Q. Which of the following statements about the graph of a quadratic function is true?
A.
It is always a parabola that opens upwards.
B.
It can be a straight line.
C.
It can intersect the x-axis at three points.
D.
It is symmetric about its vertex.
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Solution
The graph of a quadratic function is symmetric about its vertex.
Correct Answer: D — It is symmetric about its vertex.
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Q. Which of the following statements about the Heisenberg Uncertainty Principle is true?
A.
It applies only to macroscopic objects
B.
It states that position and momentum can be known exactly
C.
It implies a limit to the precision of simultaneous measurements
D.
It is not applicable to photons
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Solution
The Heisenberg Uncertainty Principle states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously.
Correct Answer: C — It implies a limit to the precision of simultaneous measurements
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Q. Which of the following statements about the law of conservation of energy is true?
A.
Energy can be created
B.
Energy can be destroyed
C.
Energy can be transformed
D.
Energy is only conserved in closed systems
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Solution
The law of conservation of energy states that energy can be transformed from one form to another, but cannot be created or destroyed.
Correct Answer: C — Energy can be transformed
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Q. Which of the following statements about the number 30 is true?
A.
It is a prime number
B.
It has exactly 4 factors
C.
It is a multiple of 5
D.
It is not a composite number
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Solution
30 is a multiple of 5, as it can be expressed as 5 multiplied by 6.
Correct Answer: C — It is a multiple of 5
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Q. Which of the following statements about the photoelectric effect is true?
A.
Light intensity affects the energy of emitted electrons
B.
Only light above a certain frequency can cause emission
C.
Electrons are emitted regardless of light frequency
D.
The number of emitted electrons is independent of light intensity
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Solution
The photoelectric effect shows that only light above a certain frequency can cause the emission of electrons, regardless of intensity.
Correct Answer: B — Only light above a certain frequency can cause emission
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Q. Which of the following statements about the quantum mechanical model of the atom is true?
A.
Electrons have fixed orbits
B.
Electrons are found in defined paths
C.
Electrons are described by wave functions
D.
Electrons have no mass
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Solution
In the quantum mechanical model, electrons are described by wave functions, which give the probability of finding an electron in a certain region.
Correct Answer: C — Electrons are described by wave functions
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Q. Which of the following statements about the Rajya Sabha is correct? (1950)
A.
It is the upper house of the State Legislature.
B.
It is directly elected by the people.
C.
It represents the States and Union territories.
D.
It has a fixed term of 5 years.
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Solution
The Rajya Sabha is the upper house of the Parliament of India and represents the States and Union territories, not the State Legislature.
Correct Answer: C — It represents the States and Union territories.
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Q. Which of the following statements about the rate of reaction is true?
A.
It increases with increasing concentration of reactants.
B.
It decreases with increasing temperature.
C.
It is always constant.
D.
It is independent of the nature of reactants.
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Solution
The rate of reaction generally increases with increasing concentration of reactants.
Correct Answer: A — It increases with increasing concentration of reactants.
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Q. Which of the following statements about the sequence defined by a_n = 3n + 1 is true? (2023)
A.
It is an arithmetic sequence.
B.
It is a geometric sequence.
C.
It is a harmonic sequence.
D.
It is a Fibonacci sequence.
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Solution
The sequence defined by a_n = 3n + 1 has a constant difference between consecutive terms, hence it is an arithmetic sequence.
Correct Answer: A — It is an arithmetic sequence.
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Q. Which of the following statements about the series 1, 1/2, 1/4, 1/8 is true? (2023)
A.
It is an arithmetic series.
B.
It is a geometric series.
C.
It diverges.
D.
It is a constant series.
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Solution
The series is a geometric series with a common ratio of 1/2.
Correct Answer: B — It is a geometric series.
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Q. Which of the following statements about the series 1, 4, 9, 16, 25 is true? (2023)
A.
It is an arithmetic series.
B.
It is a geometric series.
C.
It consists of perfect squares.
D.
It is a Fibonacci series.
Show solution
Solution
The series consists of perfect squares: 1^2, 2^2, 3^2, 4^2, 5^2.
Correct Answer: C — It consists of perfect squares.
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Q. Which of the following statements about the solubility product (Ksp) is true?
A.
Ksp is temperature dependent
B.
Ksp is constant at all temperatures
C.
Ksp only applies to soluble salts
D.
Ksp is the same for all salts
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Solution
Ksp is temperature dependent; it changes with temperature.
Correct Answer: A — Ksp is temperature dependent
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Q. Which of the following statements about the uncertainty principle is true?
A.
It applies only to macroscopic objects
B.
It states that position and momentum cannot be known simultaneously
C.
It is a classical physics concept
D.
It can be ignored in quantum mechanics
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Solution
The uncertainty principle states that position and momentum cannot be known simultaneously with arbitrary precision in quantum mechanics.
Correct Answer: B — It states that position and momentum cannot be known simultaneously
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Q. Which of the following statements about the union of two sets is true?
A.
The union includes only the elements that are common to both sets.
B.
The union includes all elements from both sets, excluding duplicates.
C.
The union is only applicable to finite sets.
D.
The union can never be larger than the largest set.
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Solution
The union of two sets combines all unique elements from both sets.
Correct Answer: B — The union includes all elements from both sets, excluding duplicates.
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Q. Which of the following statements about the viscosity of liquids is true?
A.
Viscosity increases with temperature
B.
Viscosity decreases with temperature
C.
Viscosity is independent of temperature
D.
Viscosity is the same for all liquids
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Solution
Viscosity generally decreases with an increase in temperature.
Correct Answer: B — Viscosity decreases with temperature
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Q. Which of the following statements about thermal conductivity is true? (2021)
A.
It is higher in gases than in solids
B.
It is a measure of a material's ability to conduct heat
C.
It increases with temperature
D.
It is independent of material type
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Solution
Thermal conductivity is a measure of a material's ability to conduct heat; it varies with material type.
Correct Answer: B — It is a measure of a material's ability to conduct heat
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Q. Which of the following statements about torque is true?
A.
Torque is a scalar quantity.
B.
Torque depends on the angle of application.
C.
Torque is always positive.
D.
Torque does not depend on the point of rotation.
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Solution
Torque depends on the angle of application, as it is calculated using τ = F × d × sin(θ).
Correct Answer: B — Torque depends on the angle of application.
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Q. Which of the following statements about total internal reflection is true?
A.
It can occur at any angle of incidence
B.
It requires a denser medium to be on the incident side
C.
It can occur when light travels from air to water
D.
It is a phenomenon exclusive to optical fibers
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Solution
Total internal reflection requires that the light travels from a denser medium to a rarer medium, making the second statement true.
Correct Answer: B — It requires a denser medium to be on the incident side
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Q. Which of the following statements about triangles is true?
A.
All triangles are equilateral.
B.
The sum of the angles in a triangle is 180 degrees.
C.
A triangle can have two right angles.
D.
The area of a triangle is always greater than its perimeter.
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Solution
The sum of the angles in any triangle is always 180 degrees, which is a fundamental property of triangles.
Correct Answer: B — The sum of the angles in a triangle is 180 degrees.
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Q. Which of the following statements about variable J is supported by the mixed graph? (2023)
A.
J has a linear relationship with variable K.
B.
J is affected by external factors.
C.
J shows a cyclical pattern.
D.
J's trend is unpredictable.
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Solution
The mixed graph reveals that variable J exhibits a cyclical pattern, indicating periodic fluctuations over time.
Correct Answer: C — J shows a cyclical pattern.
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Q. Which of the following statements about viscosity is true?
A.
Viscosity is a scalar quantity
B.
Viscosity is a vector quantity
C.
Viscosity is temperature independent
D.
Viscosity increases with shear rate
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Solution
Viscosity is a scalar quantity that measures a fluid's resistance to flow.
Correct Answer: A — Viscosity is a scalar quantity
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Q. Which of the following statements about weak acids is true?
A.
They completely dissociate in solution
B.
They have a high pKa value
C.
They have a low pH
D.
They are strong electrolytes
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Solution
Weak acids do not completely dissociate in solution and typically have a higher pKa value compared to strong acids.
Correct Answer: B — They have a high pKa value
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Q. Which of the following statements about X-rays is true?
A.
They have a longer wavelength than visible light
B.
They are charged particles
C.
They can be focused with a lens
D.
They are a form of electromagnetic radiation
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Solution
X-rays are a form of electromagnetic radiation, similar to visible light but with much higher energy and shorter wavelength.
Correct Answer: D — They are a form of electromagnetic radiation
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Q. Which of the following statements best describes the concept of 'Sustainable Development'?
A.
Development that meets the needs of the present without compromising the ability of future generations to meet their own needs.
B.
Development that focuses solely on economic growth without considering environmental impacts.
C.
Development that prioritizes industrialization over agricultural practices.
D.
Development that is limited to urban areas and neglects rural development.
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Solution
Sustainable Development emphasizes balancing economic growth with environmental protection and social equity.
Correct Answer: A — Development that meets the needs of the present without compromising the ability of future generations to meet their own needs.
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Q. Which of the following statements best describes the impact of the British education system on Indian society?
A.
It completely eradicated traditional education systems.
B.
It led to the rise of a new educated middle class.
C.
It had no significant impact on Indian society.
D.
It promoted only technical education.
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Solution
The British education system led to the emergence of a new educated middle class that played a crucial role in the socio-political landscape of India.
Correct Answer: B — It led to the rise of a new educated middle class.
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Q. Which of the following statements best describes the impact of the Gupta Empire on Indian culture?
A.
It marked the decline of trade and commerce.
B.
It was a period of significant advancements in science, art, and literature.
C.
It led to the complete dominance of Buddhism over Hinduism.
D.
It resulted in the establishment of foreign rule in India.
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Solution
The Gupta Empire (c. 320-550 CE) is often referred to as the Golden Age of India due to its remarkable achievements in various fields such as mathematics, astronomy, and literature, which flourished during this period.
Correct Answer: B — It was a period of significant advancements in science, art, and literature.
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Q. Which of the following statements best describes the role of a facilitator in team formation?
A.
To make decisions for the team
B.
To ensure all voices are heard
C.
To set the team's goals
D.
To evaluate team performance
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Solution
A facilitator's primary role is to guide discussions and ensure that all team members contribute.
Correct Answer: B — To ensure all voices are heard
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Q. Which of the following statements best describes the role of a team leader in a newly formed team? (2023)
A.
To dictate tasks without input
B.
To facilitate discussions and encourage participation
C.
To focus solely on individual performance
D.
To avoid conflict at all costs
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Solution
A team leader should facilitate discussions and encourage participation to foster a collaborative environment and ensure all voices are heard.
Correct Answer: B — To facilitate discussions and encourage participation
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Q. Which of the following statements best describes the role of NGOs in the context of social reform in India during the 20th century? (2000)
A.
They primarily focused on economic development.
B.
They played a crucial role in advocating for women's rights and education.
C.
They were mainly involved in political lobbying.
D.
They had no significant impact on social reform.
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Solution
NGOs in India during the 20th century were instrumental in advocating for women's rights and education, significantly contributing to social reform.
Correct Answer: B — They played a crucial role in advocating for women's rights and education.
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