Integration Techniques
Integrate: (1/x+4).dx
Differential Equation Solutions
Solve the differential equation dy/dx = (y^2)Sin(x) given that y(0)=1.
Vector Algebra – Dot Product
Prove that for vectors “a” and “b” a.b = |a||b|Cos(x)
Three-Dimensional Geometry – Line Equation
Find the vector and Cartesian equation of the line passing through two points A(1,2,3) and B(4,5,6).
Maxima-Minima Problem Using Calculus
Find the dimensions of a rectangle with maximum area that can be inscribed in a circle of radius 𝑟.
Probability – Binomial Theorem Application
If a die is rolled 5 times, find the probability of getting exactly 3 sixes.
Determinant Value Calculation
Evaluate the determinant for a 3×3 matrix given specific values.
Preparation of potassium dichromate from chromite ore.
Describe the preparation of potassium dichromate from chromite ore.
Explain the difference between order and molecularity of a reaction.
Explain the difference between order and molecularity of a reaction.
Molar Conductivity
Define the term “molar conductivity.” How does it vary with concentration for a strong electrolyte?