Correct Answer: A. Over-dependence on foreign products

Explanation

Characteristics Low per Capita Income Inequitable Distribution of Wealth and Income Predominance of Agriculture Deficiency of Capital High Rate of Population Growth Unemployment and Underemployment A Dualistic Economy Technical Backwardness dependence on foreign products

Correct Answer: A. Amos

Correct Answer: D. rejecting the laws and statutes of the LORD

Explanation

When f(x) is divided by (x - a), the remainder is f(a). When (x - a) is a factor, then f(a) = 0.

\(f(x) = 6x^{4} + mx^{3} - 13x^{2} + nx + 14\)

(a) When divided by (x + 2), \(f(-2) = 6(-2^{4}) + m(-2^{3}) - 13(-2^{2}) + n(-2) + 14 = 0\)

= \(96 - 8m - 52 - 2n + 14 = 0\)

\(58 = 8m + 2n .... (1)\)

When divided by (x - 1), \(f(1) = 6(1^{4}) + m(1^{3}) - 13(1^{2}) + n(1) + 14 = 0\)

\(6 + m - 13 + n + 14 = 0\)

\(m + n = -7 ... (2)\)

\(m = -7 - n \) (from equation 2)

\(\therefore 58 = 8(-7 - n) + 2n \)

\(-56 - 8n + 2n = 58\)

\(-6n = 58 + 56 = 114 \implies n = -19\)

\(m = -7 - (-19) = -7 + 19 = 12\)

\(\therefore \text{m and n = 12 and -19}\)

\(\therefore f(x) = 6x^{4} + 12x^{3} - 13x^{2} - 19x + 14\)

(b) When divided by (x + 1)

\(f(-1) = 6(-1^{4}) + 12(-1^{3}) - 13(-1^{2}) - 19(-1) + 14\)

= \(6 - 12 - 13 + 19 + 14 = 14\).

Explanation

(a)(i) pH is a measure of the acidity or alkalinity of a solution.

(ii) The pH of the acids solution would increase

(b)(i) Example of acidic oxide is sulphur (IV) oxide (SO\(_2\))

(ii) Example of acid salt is sodium hydrogen tetraoxosulphate(VI)

Correct Answer: C. Tuberculosis

Correct Answer: B. from the Equator

Correct Answer: C. become his enemy

Correct Answer: C. 20mA

Explanation

Here's how to solve the problem:

1. Understand the Setup: When a galvanometer is converted into an ammeter, a shunt resistor (Rs) is connected in parallel with the galvanometer (Rg). The total current (I) of the ammeter splits between the galvanometer and the shunt.

2. Identify Given Values:

* Resistance of galvanometer (Rg) = 5 Ω

* Resistance of shunt wire (Rs) = 0.05 Ω

* Maximum current the ammeter can read (I) = 2 Amp

3. Principle of Parallel Connection: In a parallel connection, the voltage across each component is the same.

* Voltage across galvanometer (Vg) = Ig * Rg

* Voltage across shunt (Vs) = Is * Rs

* Since Vg = Vs, we have: Ig * Rg = Is * Rs

4. Current Relationship: The total current (I) is the sum of the current through the galvanometer (Ig) and the current through the shunt (Is):

* I = Ig + Is

* Therefore, Is = I - Ig

5. Substitute and Solve for Ig:

Substitute the expression for Is into the voltage equality:

Ig * Rg = (I - Ig) * Rs

Now, plug in the given numerical values:

Ig * 5 = (2 - Ig) * 0.05

Expand the right side:

5 * Ig = 2 * 0.05 - Ig * 0.05

5 * Ig = 0.1 - 0.05 * Ig

Move the Ig terms to one side:

5 * Ig + 0.05 * Ig = 0.1

(5 + 0.05) * Ig = 0.1

5.05 * Ig = 0.1

Solve for Ig:

Ig = 0.1 / 5.05 Amperes

6. Convert to Milliamperes (mA):

To convert Amperes to milliamperes, multiply by 1000:

Ig (mA) = (0.1 / 5.05) * 1000

Ig (mA) = 100 / 5.05

Ig (mA) = 10000 / 505

Simplify the fraction by dividing numerator and denominator by 5:

Ig (mA) = 2000 / 101

Now, perform the division:

Ig (mA) ≈ 19.80198... mA

7. Compare with Options:

The calculated value is approximately 19.8 mA. Looking at the options:

A. 2mA

B. 10mA

C. 20mA

D. 25mA

The closest option to 19.8 mA is 20 mA.

The final answer is 20mA.

Correct Answer: C. \((R \cap P) \subset (R \cap U)\)

Explanation

All the statements are false except option C.

\(R \cap P = {3, 5, 7} and R \cap U = {2, 3, 5, 7, 11}\)

\(\therefore (R \cap P) \subset (R \cap U)\)