Forum

Integrals

Evaluate the area of the region bounded by the lines y = x, y = 0, and x = 2.

Application of Derivatives

A 10-meter ladder is leaning against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at a speed of 1 meter per second. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 meters from the wall?

Continuity and Differentiability

Prove that the function f(x) = |x| is continuous for all real values of x but not differentiable at x = 0.

Determinants

If A is a 3×3 matrix such that det(A) = 5, find the value of det(3A).

Matrices

If A and B are two square matrices of order 3 such that AB = BA = I, where I is the identity matrix, show that B is the inverse of A.

Hydrocarbons

11. Explain Markovnikov’s rule with an example. Why is this rule important in the addition reactions of alkenes?

Equilibrium

• What is the equilibrium constant? How does it vary with temperature for an exothermic reaction?

Thermodynamics

Define enthalpy and internal energy. How are they related in a chemical reaction?

Chemical Bonding

Explain the concept of hydrogen bonding. How does hydrogen bonding affect the physical properties of compounds?

Structure of Atom

Describe the Bohr model of the atom. How does it explain the stability of an atom?