Correct Answer: A. calcium tetraoxsulphate (VI).

Explanation

Water hardness is primarily caused by the presence of dissolved mineral ions, especially divalent cations like calcium (Ca²⁺) and magnesium (Mg²⁺). These ions react with soap to form scum and can lead to scale buildup in pipes and appliances.

Let's break down the options:

• A. calcium tetraoxsulphate (VI): This is Calcium sulfate (CaSO₄). Calcium sulfate is a dissolved salt that contributes to permanent hardness in water.

• B. Magnesium tetraoxosulphate (VI): This is Magnesium sulfate (MgSO₄). Magnesium sulfate is also a dissolved salt that contributes to permanent hardness in water.

• C. Calcium hydrogen trioxocarbonate(IV): This is Calcium bicarbonate (Ca(HCO₃)₂). Calcium bicarbonate is a dissolved salt that contributes to temporary hardness in water.

• D. Magnesium hydrogen trioxcocarbonate (IV): This is Magnesium bicarbonate (Mg(HCO₃)₂). Magnesium bicarbonate is also a dissolved salt that contributes to temporary hardness in water.

All four options represent compounds that cause hardness in water. However, the question asks to identify *a* cause, and all options are valid. In a multiple-choice setting, if only one answer can be selected, there might be an implicit preference for a common example or a specific type of hardness. Calcium salts are very common contributors to hardness. Calcium sulfate is a well-known cause of permanent hardness.

The final answer is A

Correct Answer: D. sterilization of water

Correct Answer: D. autocracy

Explanation

Autocracy a system of government by one person with absolute power.

Correct Answer: B. rebellion

Correct Answer: B. Weathering

Explanation

Weathering is the process whereby rocks are broken down into small particles through factors such as rainfall, erosion etc.

Explanation

The essential features of Communal Land Tenure are: (i) The land is owned by the community.

(ii) Land is allocated ( to members by the head of the family or the community.

(iii) Every member of the community is opportuned to farnt each season to grow annual or biannual crops.

(iv) The system relies on plenty of land for fallow.

The effects of communal land tenure on agriculture include the following:

(i) the land cannot be used as a collateral or security in a procuring agricultural loan for development by members of the community.

(ii) mechanization is difficult to introduce because the farm lands are scattered and small.

(iii) Permanent crops like cocoa and rubber cannot be planted because of possible re-allocation of land in another season.

(iv) discourages permanent land improvement, such as building of structures and alley farming.

(v) leads to fragmentation of land into small and scattered units. (vi) CO operative efforts of farmers are discouraged, thereby, leading to the retardation of the adoption of modern agricultural tehcniques.

(b) The essential features of individual land tenure are: Obtained either as Freehold Ownership or Rent Tenancy Features of Freehold ownership

(i) It gives owner complete freedom on the land

(ii) He may sell it or leave it fallow: It may also farm the land or rent it out.

(iii) It can be used as collateral for agriculture loans.

Features of rent tenancy: (i) partial freedom on land. (ii) cannot be used as security for agricultural loans. (iii) moderate land improvement can be effected on the land. (iv) mechanisation can be introduced if the size of the land is large enough

Effects of free hold ownership on agriculture include: (i) often leads to land improvement (ii) mechanical agriculture can be profitably introduced. (iii) land may be fragmented among children of a freeholder.

Rent Tenancy - Effects on Agriculture include: (i) land can be put to uses other than agricultural production.

Correct Answer: A. climax

Explanation

\(\frac{\sqrt{75} - 3}{\sqrt{3} + 1}\)

Rationalizing, \((\frac{\sqrt{75} - 3}{\sqrt{3} + 1})(\frac{\sqrt{3} - 1}{\sqrt{3} - 1}\)

\(\frac{\sqrt{3 \times 75} - \sqrt{75} - 3\sqrt{3} + 3}{3 - \sqrt{3} + \sqrt{3} - 1}\)

= \(\frac{15 - 5\sqrt{3} - 3\sqrt{3} + 3}{2}\)

= \(\frac{18 - 8\sqrt{3}}{2}\)

= \(9 - 4\sqrt{3}\)

(b)(i) The general form of the circle equation is \(x^{2} + y^{2} + 2gx + 2fy + c = 0\) where (x, y) is a point on the circle.

\(\therefore A(7, 3) = 7^{2} + 3^{2} + 7(2g) + 3(2f) + c = 0\)

\(14g + 6f + c = -58 .... (1)\)

\(B(2, 8) = 2^{2} + 8^{2} + 2(2g) + 2(2f) + c = 0\)

\(4g + 4f + c = -68 ..... (2)\)

\(C(-3, 3) = -3^{2} + 3^{2} - 3(2g) + 3(2f) + c = 0\)

\(6f - 6g + c = -18 ....(3)\)

Solving the equations, we get \(g = -2; f = -3; c = -12\)

\(\text{The equation of the circle is} x^{2} + y^{2} - 4x - 6y - 12 = 0\).

(b)(ii) Radius = \(\sqrt{g^{2} + f^{2} - c}\)

= \(\sqrt{-2^{2} + (-3^{2}) - (-12)}\)

\(\sqrt{25} = 5 units\)

Correct Answer: D. destiny

Explanation

Al-Ima n bil-qadr is one of the six articles of faith, The faith in the Destiny Allah knows what they did and what they will do (Al-Baqarah 255). All events that will befall humans and all information concerning their birth, death, and deeds are written in a book called al-Lawh al-Mahfuz . The pieces of information in this book are called qadar.

Correct Answer: A. arithmetic logic