Explanation

\((\log_{2} m)^{2} - \log_{2} m^{3} = 10\)

Let \(\log_{2} m\) = x.

\((\log_{2} m)^{2} - 3\log_{2} m - 10 = 0\)

\(\implies x^{2} - 3x - 10 = 0\)

\(x^{2} + 2x - 5x - 10 = 0 \)

\(x(x + 2) - 5(x + 2) = 0\)

\(\implies x = \text{-2 or 5}\)

When \(\log_{2} m = -2 \implies m = 2^{-2} = \frac{1}{4}\)

When \(\log_{2} m = 5 \implies m = 2^{5} = 32\).

Correct Answer: D. human rights

Explanation

(a)(i) Properties of X-rays are:;

They (a) penetrates substance

(b) travel in straight lines

(c) are able to ionise gases.

(d) affect photographic plate or paper making them to fogge

(e) undergo reflection, or refraction, or polarization or diffraction etc.

(ii) X-rays are electromagnetic waves with wave properties such as;

- reflection

- refraction

- diffraction

- polarisation

- travel in straight line

- cannot be deflected by magnetic or electric field.

(iii) X - rays (a) used to ionise gases causing them to become conducting.

(b) used in industries to locate fractures in machines and metal castings.

(c) used to analyse crystal structure i.e. crystallography.

(iv) X - rays are hazardous because they

- kill mall organisms

- cause leukaemia can damage riving tissues

- cause genetic mutation

- cause damage to cells of large animals.

(b)(i) hf = eV

f = \(\frac{eV}{h}\)

f = 1% of eV = \(\frac{1 \times 1.60 \times 10^{-17} \times 5.00 \times 10^4}{100 \times 6.63 \times 10^{-34}}\) = 1.207 x 10\(^7\) Hz.

(ii) Times rate at which heat is removed = 99% x I x V

= \(\frac{99}{100}\) x 2.00 x 10\(^{-2}\) x 5.00 x 10\(^4\)

= 990W

Correct Answer: C. Links the program with other programs needed for its execution

Correct Answer: C) Electrons

Correct Answer: A. Plutonic rock

Explanation

Plutonic Igneous rocks also known as intrusive igneous rocks are formed when the molten magma cools and solidifies slowly before it gets to the surface of the earth.

Correct Answer: D. telex

Correct Answer: B. technology, weather and population

Explanation

A shift in the supply curve is brought about by a change in supply. Changes in production cost and related factors can cause an entire supply curve to shift right or left. A supply curve will shift to the right when there is an increase in the change in supply, and it will shift to the left when there is a decrease in the change in supply. Some of the factors that may cause a supplier to be unable to supply to the market include; - changes in the costs of production. - changes in technology. - population size. - government taxes/subsidies/regulations. - weather conditions. - wars/disaster

Correct Answer: D) 192 cm³

Explanation

To answer this question, we first need to write down the balanced chemical equation for the combustion of ethyne (C?H?) in oxygen (O?) to produce carbon(IV) oxide (CO?) and water (H?O):

\(2C_2H_2 + 5O_2 ? 4CO_2 + 2H_2O\)

Now, let's analyze the given information:

1. 100 cm\(^3\) of ethyne (C?H?)

2. 240 cm\(^3\) of oxygen (O?)

We need to find the volume of carbon(IV) oxide (CO?) produced.

From the balanced chemical equation, 2 moles of ethyne react with 5 moles of oxygen to produce 4 moles of carbon(IV) oxide. In this case, we have the volumes of ethyne and oxygen, so we need to determine which reactant is the limiting reactant.

First, let's convert the volumes to moles using the molar volume of a gas at standard conditions (22.4 L/mol or 22400 cm\(^3\)/mol):

Moles of ethyne = 100 cm\(^3\) / 22400 cm\(^3\)/mol = 0.00446 moles

Moles of oxygen = 240 cm\(^3\) / 22400 cm\(^3\)/mol = 0.0107 moles

Now, let's determine the limiting reactant:

Moles of ethyne needed = moles of oxygen

Explanation

(a) \(^{18}C_{r} = ^{18}C_{r + 2}\)

\(\frac{18!}{r! (18 - r)!} = \frac{18!}{(r + 2)! (18 - r - 2)!}\)

\(r! (18 - r)! = (r + 2)(r + 1)r! (18 - r - 2)!\)

\((18 - r)! = (r + 2)(r + 1)(18 - r - 2)!\)

\((18 - r)(18 - r - 1)(18 - r - 2)! = (r + 2)(r + 1)(18 - r - 2)!\)

\((18 - r)(17 - r ) = r^{2} + 3r + 2\)

\(306 - 35r + r^{2} = r^{2} + 3r + 2\)

\(306 -2 = r^{2} - r^{2} + 3r + 35r\)

\(304 = 38r \implies r = 8\)

\(\therefore ^{8}C_{5} = \frac{8!}{5! (8 - 5)!}\)

\(\frac{8 \times 7 \times 6}{3 \times 2} = 56\)

(b) p(H) = 10% = 0.1 = a; p(H') = 0.9 = b

6 persons tested. We use the binomial probability distribution.

\((a + b)^{6} = a^{6} + 6a^{5}b + 15a^{4}b^{2} +20a^{3}b^{3} + 15a^{2}b^{4} + 6ab^{5} + b^{6}\)

(i) p(exactly 5 tested positive to the virus) = \(6a^{5}b\)

= \(6 \times (0.1)^{5} \times (0.9) = 0.000054 \approxeq 0.0001\) (to 4 d.p)

(ii) p(none tested positive) = \(b^{6}\)

= \((0.9)^{6} = 0.531441 \approxeq 0.5314\) (to 4 d.p)

(iii) p(at most 2) = p(none) + p(one) + p(two)

= \(b^{6} + 6ab^{5} + 15a^{2}b^{4}\)

= \((0.9)^{6} + 6(0.1)(0.9)^{5} + 15(0.1^{2})(0.9^{4})\)

= \(0.531441 + 0.354294 + 0.098415 = 0.98415\)

\(\approxeq 0.9842\) (to 4 d.p)