Correct Answer: B. \(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\)

Explanation

3M = 3 \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\)

= \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\)

2N = 2 \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\)

= \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\)

(3M - 2N) = \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\) - \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\)

Explanation

\(^9C_x = 4[^7C_{x - 1}]\)

\(\frac{9!}{x!(9 - x)!}=4*\frac{7!}{(x - 1)!(7 - (x - 1)!)}\)

\(={9!}{x!(9 - x)!}=4*\frac{7!}{(x - 1)!(8 - x)!}\)

\(=\frac{9 \times 8 \times 7!}{x(x - 1)!(9 - x)(8 - x)!}=4*\frac{7!}{(x - 1)!(8 - x)!}\)

Cancel out the common terms

\(=\frac{9 \times 8}{x(9 - x)}=\frac{4}{1}\)

\(=x(9-x)=9*8\)

\(=9x-x^2=72\)

\(=x^2-9x+72=0\)

\(=x^2-6x-3x+18=0\)

\(=x(x-6)-3(x-6)=0\)

\(=(x-6)(x-3)=0\)

\(\therefore x\) = 6 or 3

Correct Answer: C. Cairo

Explanation

(b) Factors which encourage cattle rearing in Northern Nigeria: (i) Availability of pasture / fodder. (ii) Absence of tse-tse flies which cause sleeping sickness for cattle.

(iii) Little rainfall does not encourage foot rot disease in cattle. (iv) Availability of traditional cattle rearers / Fulani ethnic group.

(v) Relatively flat plain on which cattle roam about. (vi) Social significance of cattle as a symbol of wealth.

(vii) Favourable tropical continental climate. (viii) Availability of large markets for cattle. (ix) Availability of veterinary services.

(x) Availability of transport network.

(c) Reason for which cattle rearing is less important in Southern Nigeria: (I) Limited pasture.

(ii) Conflict with crop cultivators / farmers. (iii) Poor quality pasture. (iv) Heavy rainfall encourages foot rot disease in cattle.

(v) Presence of tse-tse flies which cause sleeping sickness for cattle. (vi) Southerners are mainly cultivators of plants by tradition

(vii) Presence of dense vegetation which hinders easy movement of cattle. (viii) cattle rearing is alien to the ethnic groups in the south. (ix) Comparative cost advantage about cattle rearing.

Correct Answer: C. restoration

Correct Answer: C) cyclohexane

Explanation

Catalytic hydrogenation is a chemical reaction in which hydrogen is added to a molecule in the presence of a catalyst, usually a transition metal like palladium, platinum, or nickel. In this case, the molecule is benzene, which is a six-membered ring with alternating single and double carbon-carbon bonds.

When benzene undergoes catalytic hydrogenation, hydrogen atoms are added to the carbon atoms in the ring, breaking the double bonds and forming single bonds. This process converts the benzene molecule into a fully saturated, non-aromatic hydrocarbon called cyclohexane. So, the correct answer isOption C: cyclohexane.

It's important to note that this reaction reduces the aromaticity of benzene, which is a highly stable and unreactive compound due to its delocalized pi electrons. Aromatic compounds, like benzene, are characterized by their ability to undergo substitution reactions rather than addition reactions. However, under certain conditions and with the presence of a catalyst, benzene can be hydrogenated to form cyclohexane.

As for the other options, they are incorrect because:

Correct Answer: B. 2

Correct Answer: C. the population exceeds available resources

Correct Answer: A. Connecting wires

Correct Answer: A. Television