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Karnataka PUC I — free MCQ practice

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Karnataka PUC I subjects

Biology (816)Physics (647)Chemistry (564)Mathematics (501)Economics (221)Business Studies (150)Accountancy (100)

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Laws of MotionStructure of AtomGravitationWork, Energy and PowerEquilibriumPhotosynthesis in Higher PlantsCell: The Unit of LifeRedox ReactionsChemical ThermodynamicsOrganic Chemistry: Some Basic Principles and TechniquesAnimal KingdomBody Fluids and CirculationBreathing and Exchange of GasesBusiness Services & Emerging ModesCell Cycle and Cell DivisionComplex Numbers and Quadratic EquationsExcretory Products and their EliminationFinancial Statements of Sole ProprietorshipHydrocarbonsKinetic Theory & OscillationsLimits and DerivativesLinear InequalitiesLocomotion and MovementMarket EquilibriumMechanical Properties of Solids and FluidsMorphology and Anatomy of Flowering PlantsMotion in a PlaneNature and Forms of Business OrganisationsNeural Control and Chemical CoordinationPlant Growth and Development

Try a Karnataka PUC I question

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:Read the answer and worked solution →The first law of thermodynamics is mathematically expressed as:Read the answer and worked solution →In an isothermal process for an ideal gas, which thermodynamic quantity remains constant?Read the answer and worked solution →For an ideal gas expanding isothermally from volume $V_1$ to $V_2$ at temperature $T$, the work done by the gas is:Read the answer and worked solution →

Worked practice questions

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:

  1. $\dfrac{1}{2}MR^2$
  2. $\dfrac{2}{3}MR^2$
  3. $\dfrac{2}{5}MR^2$
  4. $MR^2$
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Correct answer: C. $\dfrac{2}{5}MR^2$

Standard result for a solid sphere about a central axis: $I = \dfrac{2}{5}MR^2$. Compare with a hollow (thin-shell) sphere where $I = \dfrac{2}{3}MR^2$ — that's option D and a common trap.

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The first law of thermodynamics is mathematically expressed as:

  1. $dQ = dU + dW$
  2. $dQ = dU - dW$
  3. $dU = dQ \cdot dW$
  4. $dQ \cdot dU = dW$
Show answer and solution

Correct answer: A. $dQ = dU + dW$

The first law states that heat $dQ$ supplied to a system goes into changing its internal energy $dU$ plus doing work $dW$ on the surroundings. So $dQ = dU + dW$. It is just energy conservation applied to thermodynamic systems.

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In an isothermal process for an ideal gas, which thermodynamic quantity remains constant?

  1. Pressure
  2. Volume
  3. Temperature
  4. Internal energy and temperature
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Correct answer: D. Internal energy and temperature

Isothermal means at constant temperature. For an ideal gas, internal energy depends only on temperature ($U$ is a function of $T$ alone) so if $T$ is constant, $U$ is also constant. Hence both temperature and internal energy stay fixed. Pressure and volume change reciprocally to keep $PV = nRT$ constant.

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