Choose a course and topic, attempt each question and open its complete worked solution when you are ready.
A 9 V source is in series with 0.2, 0.3, 0.4, 0.5 and 12 Ω. Find current through 12 Ω.
Series resistance \(=13.4\) Ω, and current is identical through every resistor.
0.672 A.
Describe double circulation in humans and explain its importance.
In one complete circuit blood passes through the heart twice. Pulmonary circulation: right ventricle → pulmonary artery → lungs → pulmonary veins → left atrium. Systemic circulation: left ventricle → aorta → body tissues → venae cavae → right atrium.
It prevents mixing of oxygenated and deoxygenated blood and allows high pressure to the body but lower pressure to delicate lung capillaries, ensuring efficient oxygen delivery.
Separate pulmonary and systemic circuits give complete separation and efficient, pressure-controlled transport.
Why must Plaster of Paris be kept in a moisture-proof container?
Plaster of Paris reacts with moisture and changes into hard gypsum:
If exposed to humid air, it sets inside the container and loses its ability to be mixed and moulded when required.
Moisture converts Plaster of Paris into hard gypsum, making it unusable.
One hundred students are randomly split into sections of 40 and 60. Find the probabilities that you and a named friend enter (a) the same section(b) different sections.
Define the sample space and count each favourable outcome once.
The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.
For the ellipse \(\frac{x^2}{100}+\frac{y^2}{400}=1\), determine its foci, vertices, axis lengths, eccentricity, and latus-rectum length.
Translate every condition into an equation and retain exact values throughout the ellipse calculation.
The last line satisfies the original conditions and supplies every requested part.
Calculate the perpendicular distance from (−1,1) to 12(x+6)=5(y−2).
Translate every condition into an equation and retain exact values throughout the straight-line calculation.
The last line satisfies the original conditions and supplies every requested part.
Multiply corresponding terms of 2,4,8,16,32 and 128,32,8,2,\(\frac{1}{2}\), then add all five products.
Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.
The displayed substitutions cover every requested part and verify the result against the original data.
Count full-length arrangements of EQUATION in which all vowels form one block and all consonants form another block.
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.
On \(\mathbb N\), let \(aRb\) mean \(a=b^2\). Test: (i) \((a,a)\in R\) for all \(a\)(ii) \(aRb\Rightarrow bRa\)(iii) \(aRb,bRc\Rightarrow aRc\).
(i) False: it would require \(a=a^2\), which fails for \(a=2\).
(ii) False: \((4,2)\in R\), but \((2,4)\notin R\).
(iii) False: \((16,4)\in R\) and \((4,2)\in R\), but \((16,2)\notin R\), since \(16 e2^2\).
All three statements are false.
In Kjeldahl analysis, NH₃ from \(0.500\,\mathrm{g}\) compound is absorbed in 50.0 mL 0.500 M H₂SO₄; residual acid needs 60.0 mL 0.500 M NaOH. Determine percentage nitrogen.
Calculate initial acid equivalents and subtract the equivalents neutralised by NaOH. Each mole of absorbed NH₃ consumes one mole of H⁺; convert its nitrogen to mass percent.
Nitrogen=56.0%.