Correct Answer: B. \(^{222}_{88}Z\)

Explanation

\(^{226}_{88}X\) \(\to\) \((^{0}_{-1}e)\) + \(^{4}_{2}\alpha\) + \(^{b}_{a}X\)

a + 2 + (-2) = 88 a \(\Rightarrow\) a = 88

b + 4 + 0 = 266 b \(\Rightarrow\) b = 222

Correct Answer: C. 10m

Explanation

H\(^2\) = 8\(^2\) + 6\(^2\) + 6\(^2\)

H\(^2\) = 64 + 36 = 100

H = \(\sqrt{100}\) = 10m

Correct Answer: D. wheat and manufactured goods

Correct Answer: A. not part of the main play

Explanation

\(p = \begin{pmatrix} 5 \\ 3 \end{pmatrix}; q = \begin{pmatrix} -1 \\ 2 \end{pmatrix}; r = \begin{pmatrix} 17 \\ 5 \end{pmatrix}\)

\(r = \alpha p + \beta q\)

\(\begin{pmatrix} 17 \\ 5 \end{pmatrix} = \alpha (\begin{pmatrix} 5 \\ 3 \end{pmatrix}) + \beta (\begin{pmatrix} -1 \\ 2 \end{pmatrix}\)

\(17 = 5\alpha - \beta ... (1); 5 = 3\alpha + 2\beta .... (2)\)

\((1) \times 2 : 34 = 10\alpha - 2\beta ... (3)\)

\((3) + (2) : 39 = 13\alpha \implies \alpha = 3\)

\(5 = 3(3) + 2\beta \implies 2 \beta = 5 - 9 = -4\)

\(\beta = -2\)

\(r = 3p - 2q \implies 2q = 3p - r\)

\(q = \frac{1}{2} (3p - r)\)

Correct Answer: A. -1

Explanation

Gradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)

= \(\frac{-2 -1}{2 + 1}\)

= \(\frac{-3}{3}\)

= -1

Correct Answer: B) 2

Explanation

To determine the number of lone pairs of electrons on the central atom of a molecule, we first need to identify the central atom and its valence electrons. Valence electrons are the electrons in the outermost shell of an atom that are involved in chemical bonding.

For example, let's consider a water molecule (H2O). In this case, the central atom is oxygen, which has 6 valence electrons. When forming bonds with the two hydrogen atoms, each hydrogen atom contributes one electron, and the oxygen atom contributes one electron for each bond. This results in two single bonds (O-H) and uses up 4 of the 6 valence electrons on oxygen.

Since 2 valence electrons are still not used in bonding, they remain as lone pairs on the oxygen atom. Thus, there are 2 lone pairs of electrons on the central atom of the water molecule (H2O), which corresponds to Option B: 2.

Remember that the number of lone pairs may vary for different molecules, and it's essential to understand the molecule's structure and the central atom's valence electrons to determine the number of lone pairs accurately.

Correct Answer: D. magnesium

Correct Answer: D. presence of small, dry surface area of the respiratory organ

Correct Answer: A) Its volume is 24.6 litres