Correct Answer: A. x = 4 or 2

Explanation

\(log_2 (6 - x) = 3 - log_2 x\)

⇒ \(log_2 (6 - x) = 3 log_2 2 - log_2 x\) (since \(log_2\) 2 = 1)

⇒ \(log_2 (6 - x) = log_2 2^3 - log_2 x\) \((a log\) c = \(log\) c\(^a)\)

⇒ \(log_2 (6 - x) = log_2 8 - log_2 x\)

⇒\(log_2 (6 - x) = log_2 \frac{8}{x}\) (\(log\) a - \(log\) b = \(log \frac{a}{b})\)

⇒ \(6 - x = \frac{8}{x}\)

⇒ \(x (6 - x) = 8\)

⇒ \(6x - x^2 = 8\)

⇒ \(x^2 - 6x + 8 = 0\)

⇒ \(x^2 - 4x - 2x + 8 = 0\)

⇒ \(x (x - 4) - 2(x - 4) = 0\)

⇒ \((x - 4)(x - 2) = 0\)

⇒ \(x - 4 = 0 or x - 2 = 0\)

∴ x = 4 or 2

Correct Answer: A. kilowatt-hour

Explanation

(a)A state is defined as a politically organised body of people occupying a definite geographical territory, living under a government, entirely or almost entirely free from external control and competent to secure habitual obedience from persons within it.

(b) The Features of a State:

(i) A definite territory: A state must possess a definite territory which can be large or small.

(ii) Population: For a state to exist, there must be a given number of people that occupy it. This number has neither minimum nor maximum.

(iii) Government: A state must have a machinery called government that will steer its affairs.

(iv) Sovereignty and independence: A state must have supreme power to enable it make and enforce laws and it must be free from external control.

(v) A state must be recognised both internally and externally.

(vi)A state is permanent as much as possible.

Explanation

(a)(i) Allotropy is defined as the existence of an element in two or more forms in the same physical state.

(ii) The form of carbon used in gas mask is amorphous carbon/wood charcoal / graphite.

(iii) Other elements which exhibit allotropy are sulphur, phosphorus, oxygen, tin, etc.

(b)(i) Products of heating coal in the absence of air are coal gas, coal tar, ammoniacal liquor, coke.

(ii) Products of burning candle wax in plentiful supply of air are CO\(_2\) and steam/H\(_2\)O.

(c)(i) - It does not support combustion

- It is heavier I denser than air

(ii) CO\(_2\) + Ca(OH)\(_2\) --> CaCO\(_2\) + H\(_2\)O Or 2CO\(_2\) + Ca(OH)\(_2\) —> Ca(HCO\(_3\))\(_2\).

(iii) 2CO\(_{(g)}\) + O\(_{2(g)}\) --> 2CO\(_{2(g)}\). From the equation and according to Gay Lussac's law, 2 volumes of CO react with 1 volume of O\(_2\), 150 cm\(^3\) of CO react with 75cm\(_2\) of O\(_2\). Excess O\(_2\) = (80 - 75)cm\(_3\) = 50cm\(_3\).

(d) Nitrogen can be obtained from ammonia

(i) By passing NH\(_3\) over copper (II) oxide or by oxidation or reaction with chlorine. i.e. 3CuO + 2NH\(_3\) -> 3Cu _ 3H\(_2\)O + N\(_2\) Or 8NH + 3Cl\(_2\) —> 6NH\(_4\)CI + N\(_2\).

(ii) Water gas and producer gas are obtained when steam and air are passed over red hot coke

(iii) Producer gas has a lower heating ability than water gas. Reason: Water gas consists of equal volumes of and Cu both of which are combustible whereas producer gas consists of CO and N\(_2\) only one of which s combustible.

Correct Answer: C. interest should not be allowed on partners drawings

Explanation

In absence of a partnership deed, a partnership Act cannot allow you to charge interest on capital, you cannot charge interest on drawing, you cannot give any salary to any partner, any rent to any partner, and any commission to any partner. also, you have to share profit in an equal ratio.

Correct Answer: D. 1

Correct Answer: C. 0

Explanation

\(\frac{x + P}{(x-1)(x-3)} = \frac{Q}{x-1} + \frac{2}{x-3}\)

\(\frac{x + P}{(x-1)(x-3)} = \frac{Q(x-3) + 2(x-1)}{(x-1)(x-3)}\)

Comparing LHS and RHS of the equation, we have

\(x + P = Qx - 3Q + 2x -2\)

\(P = -3Q - 2\)

\(Q + 2 = 1 \implies Q = 1 - 2 = -1\)

\(P = -3(-1) - 2 = 3 - 2 = 1\)

\(P + Q = 1 + (-1) = 0\)

Correct Answer: C. Satan

Correct Answer: B. #39,000

Correct Answer: A. Eastern