Live practice

Adding/removing electrons affects the π* antibonding orbitals. Higher bond order means greater stability; unpaired π* electrons cause paramagnetism.

All have 10 electrons in the same shells. Increasing nuclear charge contracts the electron cloud.

The length divided by the number of atoms gives one diameter; the radius is half of it.

Convert MnO₂ to moles, use the 4:1 stoichiometric ratio, and convert the required HCl amount to mass.

Apply the definition or the stated differentiation rules term by term.

Substitution into the original expression verifies the stated domain and final value.

A multiple of 10 must end in 0; arrange the remaining five nonzero digits.

\[\begin{aligned}9 &= 3^2\Rightarrow f(9)\\&= 3\end{aligned}\]; \[\begin{aligned}10 &= 2\cdot5\Rightarrow f(10)\\&= 5\end{aligned}\]; \(f(11)=11\); \[\begin{aligned}12 &= 2^2\cdot3\Rightarrow f(12)\\&= 3\end{aligned}\]; \(f(13)=13\). Distinct images form the range.

First, \(A\cup B=\{2,3,4,5,6,7,8\}\), so \((A\cup B)'=\{1,9\}\). Also \(A'=\{1,3,5,7,9\}\) and \(B'=\{1,4,6,8,9\}\), giving \(A'\cap B'=\{1,9\}\).

Next, \(A\cap B=\{2\}\), so \((A\cap B)'=\{1,3,4,5,6,7,8,9\}\). Further, \(A'\cup B'=\{1,3,4,5,6,7,8,9\}\).

Both corresponding sides are equal.

Separately \(R=24\): \(I=9.17\) A. Series \(R=48\): \(I=4.58\) A. Parallel \(R=12\): \(I=18.3\) A.

Define the sample space and count each favourable outcome once.

The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.