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Differential Equations

Define a first-order differential equation. Solve the differential equation dy over dx equal to 3x squared.

05/11/2024

Mathematics

12th (Science)

Integration

Explain the concept of indefinite integration and how it differs from definite integration. Integrate the function f of x equal to x squared.

05/11/2024

Mathematics

12th (Science)

Applications of Derivatives

Explain the concept of maxima and minima of a function. Find the maximum and minimum values of the function f of x equal to 3x squared minus 12x plus 7.

05/11/2024

Mathematics

12th (Science)

Continuity and Differentiability

State the conditions under which a function is continuous at a point. Determine whether the function f of x equal to x plus 1 is continuous at x equal to 0.

05/11/2024

Mathematics

12th (Science)

Relations and Functions:

Define an equivalence relation. Provide an example of an equivalence relation on the set of real numbers.

05/11/2024

Mathematics

12th (Science)

Matrices and Determinants

Define a square matrix. How do you find the determinant of a 3×3 matrix? Explain with an example.

05/11/2024

Mathematics

12th (Science)

Thermodynamics

State Hess’s law and explain its application in determining enthalpy changes. Provide an example of its use in calculating enthalpy of formation.

05/11/2024

Chemistry

12th (Science)

States of Matter

Explain Boyle’s law and its significance. A gas occupies a volume of 4 liters at a pressure of 2 atm. Calculate its volume when the pressure is reduced to 1 atm, assuming temperature remains constant.

05/11/2024

Chemistry

12th (Science)

Chemical Bonding and Molecular Structure

What is hybridization? Explain the hybridization of carbon in ethane, ethene, and ethyne, and describe the geometry of each molecule.

05/11/2024

Chemistry

12th (Science)

Atomic Structure

Describe the Aufbau principle and explain its importance in determining the electronic configuration of elements.

05/11/2024

Chemistry

12th (Science)