This question tests geographical knowledge, specifically the location of the Gulf of Bothnia and the countries that border it. Identifying the correct countries requires familiarity with the map of Northern Europe.
Correct Option: C) Sweden
To find the rate of profit, we first need to calculate the profit made. Profit is the difference between the selling price and the cost price. Once the profit is known, the profit percentage is calculated by dividing the profit by the cost price and multiplying by 100.
B) 12.5% is the calculated rate of profit.
To find the ratio of the volumes, we need to calculate the volume of the cylinder and the volume of the hollow sphere separately based on the given conditions. We will then express their ratio in the simplest form.
Define variables for the cylinder:
Let the radius of the base of the cylinder be \(R\).
Given that the height of the cylinder is the same as the radius of its base, the height \(H = R\).
The volume of a cylinder is given by the formula \(V_{\text{cylinder}} = \pi R^2 H\).
Substituting \(H = R\), we get:
\[ V_{\text{cylinder}} = \pi R^2 (R) = \pi R^3 \]Define variables for the hollow sphere:
Let the outer radius of the hollow sphere be \(R_{\text{outer}}\).
Given that the outer radius of the hollow sphere is the same as the radius of the base of the cylinder, we have \(R_{\text{outer}} = R\).
The inner radius \(R_{\text{inner}}\) is half of the outer radius, so \[R_{\text{inner}} = \frac{1}{2} R_{\text{outer}} = \frac{1}{2} R\].
The volume of a hollow sphere is the difference between the volume of the outer sphere and the volume of the inner sphere. The formula for the volume of a sphere is \(V = \frac{4}{3} \pi r^3\).
So, the volume of the hollow sphere is:
\[ V_{\text{hollow sphere}} = \frac{4}{3} \pi R_{\text{outer}}^3 - \frac{4}{3} \pi R_{\text{inner}}^3 \]\[ V_{\text{hollow sphere}} = \frac{4}{3} \pi (R^3 - (\frac{1}{2}R)^3) \]\[ V_{\text{hollow sphere}} = \frac{4}{3} \pi (R^3 - \frac{1}{8}R^3) \]\[ V_{\text{hollow sphere}} = \frac{4}{3} \pi (\frac{8R^3 - R^3}{8}) \]\[ V_{\text{hollow sphere}} = \frac{4}{3} \pi (\frac{7R^3}{8}) \]\[ V_{\text{hollow sphere}} = \frac{4 \times 7}{3 \times 8} \pi R^3 \]\[ V_{\text{hollow sphere}} = \frac{28}{24} \pi R^3 \]\[ V_{\text{hollow sphere}} = \frac{7}{6} \pi R^3 \]Calculate the ratio of the volumes:
The ratio of the volume of the cylinder to the volume of the hollow sphere is:
\[ \frac{V_{\text{cylinder}}}{V_{\text{hollow sphere}}} = \frac{\pi R^3}{\frac{7}{6} \pi R^3} \]\[ \frac{V_{\text{cylinder}}}{V_{\text{hollow sphere}}} = \frac{1}{\frac{7}{6}} \]\[ \frac{V_{\text{cylinder}}}{V_{\text{hollow sphere}}} = \frac{6}{7} \]Express the ratio:
The ratio is \(6 : 7\).
Correct Option: C) 6 : 7
This question tests understanding of Newton's First Law of Motion, which describes the relationship between force and the state of motion of an object.
Correct Option: C) force
The problem asks us to calculate the work done when a force acts on an object, causing a displacement in the direction of the force. We need to use the formula for work done and pay attention to the units.
When a constant force acts on an object and the displacement occurs in the direction of the force, the work done (\(W\)) is given by the product of the force and the displacement.
\[ W = F \times d \]The unit Newton-meter (\(\text{Nm}\)) is also known as Joule (\(\text{J}\)). So, 50 Nm is equivalent to 50 J.
D) 50 Nm — The calculated work done is 50 Nm, which is the correct unit for work when force is in Newtons and displacement is in meters. While 50 J is also correct, 50 Nm is explicitly given as an option and is a direct result of the multiplication of force and displacement units.
This problem involves the relationship between speed, distance, and time. The key is that the distance covered remains constant. We can first calculate the total distance using the initial speed and time, and then use this distance with the new time to find the required new speed.
Given the initial speed of the tractor is \(36 \text{ km/hr}\) and the time taken is \(10 \text{ hours}\).
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]\[ \text{Distance} = 36 \text{ km/hr} \times 10 \text{ hours} \]\[ \text{Distance} = 360 \text{ km} \]The same distance (\(360 \text{ km}\)) must be covered in \(8 \text{ hours}\).
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]\[ \text{New Speed} = \frac{360 \text{ km}}{8 \text{ hours}} \]\[ \text{New Speed} = 45 \text{ km/hr} \]Therefore, the tractor's speed should be \(45 \text{ km/hr}\) to cover the same distance in \(8 \text{ hours}\).
Correct Option: C) 45 km/hr
A precipitation reaction is a type of double displacement reaction where two soluble ionic compounds react in an aqueous solution to form an insoluble product, called a precipitate. The precipitate separates from the solution as a solid. We need to identify the reaction among the given options that results in the formation of an insoluble product.
B) Sodium sulphate + Barium chloride \(\rightarrow\) Barium sulphate + Sodium chloride
In this reaction, sodium sulphate (\(\text{Na}_2\text{SO}_4\)) and barium chloride (\(\text{BaCl}_2\)) are both soluble ionic compounds. When they react, they form barium sulphate (\(\text{BaSO}_4\)) and sodium chloride (\(\text{NaCl}\)). Barium sulphate is insoluble in water and precipitates out as a white solid, making this a classic example of a precipitation reaction. The balanced chemical equation is:
\[ \text{Na}_2\text{SO}_4(\text{aq}) + \text{BaCl}_2(\text{aq}) \rightarrow \text{BaSO}_4(\text{s}) \downarrow + 2\text{NaCl}(\text{aq}) \]This is a blood relation question. To solve this, we need to trace the relationship step-by-step from Suresh to Padma.
Correct Option: D) Aunt
If cosec4θ - cosec2θ = 1.24, then cot4θ + cot2θ =?
To determine the number of hydrogen atoms in one molecule of ethanol, we need to recall its chemical formula. The chemical formula explicitly states the number of atoms of each element present in a molecule.
A) Six. Based on the chemical formula \( \text{C}_2\text{H}_5\text{OH} \) or \( \text{C}_2\text{H}_6\text{O} \), there are a total of six hydrogen atoms in one molecule of ethanol.