Effective leaders must be flexible and adaptive to guide their teams through challenges and changes.

The Pigeonhole Principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

The area of a regular polygon can indeed be calculated using the formula A = (1/4) * n * s^2 * cot(π/n), where n is the number of sides and s is the side length.

The Arrhenius equation relates temperature to the rate constant and includes the activation energy.

In the Bohr model, energy levels are quantized, meaning electrons can only exist in specific energy states.

In the Bohr model, only certain orbits (or energy levels) are allowed for electrons, which correspond to specific energy states.

The boiling point is the temperature at which the vapor pressure of a liquid equals the atmospheric pressure.

The common ion effect states that the solubility of a salt decreases in the presence of a common ion.

The law of conservation of energy states that energy can neither be created nor destroyed, but can be transformed from one form to another.

Momentum is conserved in all types of collisions, provided no external forces act on the system.

The mixed graph reveals that while some variables follow a linear trend, others exhibit non-linear patterns.

The statement that the decimal system is the only system used in mathematics is incorrect; other systems like binary and hexadecimal are also used.

A triangle has no diagonals, as it has only three vertices. The formula for the number of diagonals in a polygon is n(n-3)/2, where n is the number of sides.

The number of diagonals in a polygon is calculated using the formula n(n-3)/2, where n is the number of sides.

Electrons fill orbitals in order of increasing energy, and the 4s orbital is filled before the 3d orbital.

The equilibrium constant K is dependent on temperature; it changes if the temperature of the system changes.

The Fibonacci sequence starts with 0 and 1, and each subsequent term is the sum of the previous two.

The graph of a quadratic function is symmetric about its vertex.

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.

The inverse of a function is symmetric to the original function about the line y = x, provided the original function is one-to-one.

The law of conservation of energy states that energy can be transformed from one form to another, but cannot be created or destroyed.

30 is a multiple of 5, as it can be expressed as 5 multiplied by 6.

The photoelectric effect shows that only light above a certain frequency can cause the emission of electrons, regardless of intensity.

In the quantum mechanical model, electrons are described by wave functions, which give the probability of finding an electron in a certain region.

The Rajya Sabha is the upper house of the Parliament of India and represents the States and Union territories, not the State Legislature.

The rate of reaction generally increases with increasing concentration of reactants.

The sequence defined by a_n = 3n + 1 has a constant difference between consecutive terms, hence it is an arithmetic sequence.

The series is a geometric series with a common ratio of 1/2.

The series consists of perfect squares: 1^2, 2^2, 3^2, 4^2, 5^2.

Ksp is temperature dependent; it changes with temperature.