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The 1973 Constitution of Pakistan provides for a _________ form of government.
The 1973 Constitution established a federal parliamentary system with the Prime Minister as the head of government.
Find the number of surjective (onto) functions $f$ from $\{1,2,3,\ldots,20\}$ to $\{1,2,3,\ldots,20\}$ such that $f(k)$ is a multiple of 3 whenever $k$ is a multiple of 4.
Multiples of 4 in $\{1,\ldots,20\}$: $\{4,8,12,16,20\}$ โ 5 elements. Their images must be multiples of 3 in $\{1,\ldots,20\}$: $\{3,6,9,12,15,18\}$ โ 6 elements.
Assign the 5 multiples-of-4 to 5 of the 6 multiples-of-3 (injectively, since $f$ is onto): $6 \times 5 \times 4 \times 3 \times 2 = 6!/(6-5)! = 720$... but we need surjection on all 20 elements.
The remaining 15 domain elements map to the remaining 15 codomain elements (after fixing the 5 images above): $(15)!$ ways. But 1 multiple-of-3 is unused by the multiples-of-4, so it must be covered by remaining 15 elements.
Total $= 6! \times (15)! = (15)! \times 6!$
In which circumstances are unit costing and job costing used?
| Option | Unit Costing | Job Costing |
|---|---|---|
| A | When a quantity of identical items is made | When each product is different |
| B | When each product is different | In continuous operations |
| C | In continuous operations | In continuous operations |
| D | When a quantity of identical items is made | When each product is different |
Option A is correct.
- Unit costing: Used for large quantities of identical products in a continuous process (e.g., bricks, bottles).
- Job costing: Used when each job/product is unique (e.g., construction, custom printing).
The blue colour of \(\mathrm{Cu}^{2+}\) salt solutions is due to:
Cuยฒโบ (dโน) in water absorbs orange/red light (d-d transition), transmitting blue. d-d transitions are responsible for colors of many transition metal complexes.
Stereotyping in mass communication refers to the application of pre-formed, generalised assumptions about members of a group โ based on race, gender, age, religion, nationality, profession, or social class โ to all members of that group. The textbook explains that media stereotypes are “sometimes inevitable, especially in advertising, entertainment and news industries, which need as wide an audience as possible to quickly understand information.” However, the danger is profound:
- Stereotypes reduce complex individuals to simplified caricatures
- When repeated frequently, they transform assumptions into perceived realities
- They can cause measurable psychological harm โ the textbook's case study on beauty stereotyping in media linked media images to depression, eating disorders, and loss of self-esteem in women and girls
- Stereotypes perpetuate discrimination by associating entire groups with negative or limiting characteristics
The textbook argues that media professionals must be educated about stereotyping to reduce its harmful use.
O has lower EA than S (too small, high eโป repulsion). F has lower EA than Cl (same reason). Cl has the highest EA among these.
Correct order (increasing magnitude of negative EGE):
\(\text{O} < \text{S} < \text{F} < \text{Cl}\)
i.e., Cl releases most energy on gaining an electron.
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