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Which stakeholders focus mainly on the liquidity of a business?
- Government
- Lenders
- Public and environmental bodies
- Suppliers
Option D (2 and 4) is correct.
- Lenders: Need to know if the business can meet short-term obligations and repay loans.
- Suppliers: Need to know if the business can pay its bills on time.
Government focuses on profitability/tax. Public/environmental bodies focus on social impact.
Identify the curve from the family defined by $(x^2-y^2)\,dx + 2xy\,dy = 0$ that passes through the point $(1,1)$.
Rewrite: $\frac{dy}{dx} = \frac{y^2-x^2}{2xy}$. This is a homogeneous ODE. Let $y=vx$:
$\frac{1-v^2}{2v}dx + x\,dv/... $
After solving, the general solution is $x^2 + y^2 = Cy$ (circles with centres on the $y$-axis).
Substituting $(1,1)$: $1+1=C\cdot1 \Rightarrow C=2$, giving $x^2+y^2=2y$, i.e. $x^2+(y-1)^2=1$.
This is a circle centred on the $y$-axis at $(0,1)$.
Speed of sound in ideal gas does NOT depend on:
For ideal gas, v = β(Ξ³RT/M). Pressure has no effect at constant temperature; moisture slightly affects density but the question says ideal gas: strictly, pressure independent.
From a collection of 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are chosen and arranged in a row such that the dictionary always occupies the middle position. How many such arrangements exist?
Choose 4 novels from 6: $\binom{6}{4} = 15$ ways.
Choose 1 dictionary from 3: $\binom{3}{1} = 3$ ways.
Arrange 5 books in a row with dictionary fixed in the middle: the 4 novels occupy the 4 remaining positions, giving $4! = 24$ arrangements.
Total $= 15 \times 3 \times 24 = \mathbf{1080}$
Since $1080 \geq 1000$, the answer is at least 1000.
NACTE — the National Accreditation Council for Teacher Education — is the body in Pakistan responsible for accrediting teacher training programmes and institutions, ensuring they meet national quality standards. It was established to regulate and improve the quality of teacher education across the country.
Correct Answer: C — NACTE.
Radius of curvature $R = \frac{v^2}{a_{\perp}}$.
- At $t=1$: $v_x = 10 \cos 60^{\circ} = 5$; $v_y = 10 \sin 60^{\circ} - 10(1) = 5\sqrt{3} - 10 \approx -1.34$.
- Total $v = \sqrt{5^2 + (-1.34)^2} \approx 5.18$.
- $a_{\perp} = g \cos \theta$ where $\theta$ is the angle of the velocity vector. After calculation, $R \approx 2.8\text{ m}$.
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