The question asks for the specific metallurgical process where sulphide ores are converted into their respective oxides by strong heating in the presence of excess air. This is a fundamental concept in the extraction of metals.
Identify the starting material: The question specifies "sulphide ores." These are minerals containing metal sulphides, such as zinc sulphide (ZnS), lead sulphide (PbS), or copper sulphide (CuS).
Identify the desired product: The goal is to convert these sulphide ores "into oxides." For example, ZnS would be converted to ZnO.
Identify the conditions: The process involves "heating strongly" and "in the presence of excess air." The presence of air means oxygen is available for reaction.
Recall metallurgical processes:
Match the description: The description perfectly matches the definition and conditions of roasting, where sulphide ores are heated in excess air to form oxides and sulphur dioxide gas.
B) roasting — Roasting is the metallurgical process of heating a sulphide ore strongly in the presence of excess air to convert it into its metal oxide. This is a crucial step before reduction in the extraction of metals from sulphide ores.
A) blazing — Blazing refers to burning fiercely or shining brightly. It is not a specific metallurgical term for ore conversion.
C) burning — While roasting involves burning in the sense of combustion with oxygen, "burning" is a general term and not the specific technical term used in metallurgy for this process. Roasting is a more precise and scientific term.
D) heating — Heating is a very general term that describes increasing the temperature of a substance. While heating is part of roasting, it does not fully describe the specific chemical transformation (sulphide to oxide) and conditions (excess air) mentioned in the question.
The question asks to identify the glacier known as the highest battlefield in the world. This is a factual question related to geography and military history, specifically pertaining to the high-altitude regions of the Himalayas.
B) Siachen glacier is known as the highest battlefield in the world. It is located in the eastern Karakoram range in the Himalayas, where India and Pakistan have maintained a military presence at altitudes of over 6,000 meters (20,000 ft) since 1984. The extreme conditions, including sub-zero temperatures and difficult terrain, make it one of the most challenging military deployments globally.
The question asks for the specific biological term describing the movement of a sunflower in response to the sun. This involves identifying the type of plant movement that is directional and triggered by a specific external stimulus.
C) phototropism — This term specifically refers to the growth or movement of a plant in response to a light stimulus. The sunflower's heliotropism (tracking the sun) is a form of phototropism.
If θ = 45°, then what will be the value of \(\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}\)?
To find the value of the given trigonometric expression, we need to substitute the value of \(\theta = 45^\circ\) into the expression. We will use the standard trigonometric values for \(\sin 45^\circ\) and \(\cos 45^\circ\).
We know that:
\[ \sin 45^\circ = \frac{1}{\sqrt{2}} \] \[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]The given expression is \[\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}\].
Substitute \(\theta = 45^\circ\):
\[ \frac{\sin 45^\circ + \cos 45^\circ}{\sin 45^\circ - \cos 45^\circ} = \frac{\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}}} \]Numerator:
\[ \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{1+1}{\sqrt{2}} = \frac{2}{\sqrt{2}} \]Denominator:
\[ \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} = 0 \]Now, substitute the simplified numerator and denominator back into the expression:
\[ \frac{\frac{2}{\sqrt{2}}}{0} \]Division by zero is undefined, which is represented by infinity (\(\infty\)).
Correct Option: B) \(\infty\)
The question asks to identify the first Indian woman judge appointed to the Supreme Court of India. This is a factual question related to Indian judiciary and general knowledge.
Correct Option: B) Fatima Beevi was the first woman judge to be appointed to the Supreme Court of India. She was appointed in 1989.
This question is based on linear seating arrangement. Nine persons, A, B, C, D, E, F, G, H, and I, are sitting in a row facing north. We need to determine their positions using the given conditions and identify which option correctly describes the relative positions of three persons. Since everyone faces north, right means moving towards the right side of the row, and left means moving towards the left side.
G is fourth to the right of B and second to the right of C.
Therefore, C must be second to the right of B.
The relative arrangement is:
B → _ → C → _ → G
F is fourth to the right of C.
Since G is second to the right of C, F must be second to the right of G.
Also, F is second to the left of I.
The relative arrangement becomes:
B → _ → C → _ → G → _ → F → _ → I
This structure already occupies nine positions, so the positions are fixed.
I is fifth to the right of A.
Since I occupies Position 9, A must occupy Position 4.
\(9-5=4\)
The arrangement becomes:
B → _ → C → A → G → _ → F → _ → I
Exactly three persons sit between E and A.
Therefore, their positions differ by four.
A occupies Position 4, so E must occupy Position 8.
\(8-4=4\)
The arrangement becomes:
B → _ → C → A → G → _ → F → E → I
The remaining unoccupied positions are 2 and 6.
The remaining persons are D and H.
D cannot be an immediate neighbour of B or I.
If D occupied Position 2, D would be next to B at Position 1, violating the condition.
Therefore, D must occupy Position 6 and H must occupy Position 2.
The final arrangement is:
B → H → C → A → G → D → F → E → I
All seven conditions are satisfied.
In the final arrangement, G occupies Position 5, D occupies Position 6, and F occupies Position 7.
G → D → F
Therefore, D sits directly between G and F.
Hence, option B is correct.
Correct Option: B) D between F and G
In the final seating arrangement B, H, C, A, G, D, F, E, I, the positions of G, D, and F are 5, 6, and 7 respectively. Therefore, D is seated directly between G and F. Hence, option B is correct.
To find the volume of a sphere, we use the standard formula for the volume of a sphere, which involves its radius. We will substitute the given radius into the formula and perform the necessary calculations.
The volume \(V\) of a sphere with radius \(r\) is given by:
\[ V = \frac{4}{3} \pi r^3 \]The radius of the sphere is given as \(r = 21 \text{ cm}\).
We will use the approximation for \(\pi = \frac{22}{7}\).
\[ V = \frac{4}{3} \times \frac{22}{7} \times (21 \text{ cm})^3 \]First, divide 9261 by 7:
\[ 9261 \div 7 = 1323 \]\[ V = \frac{4}{3} \times 22 \times 1323 \text{ cm}^3 \]Next, divide 1323 by 3:
\[ 1323 \div 3 = 441 \]\[ V = 4 \times 22 \times 441 \text{ cm}^3 \]D) 38808 cm³ is the correct volume calculated using the formula for the volume of a sphere with the given radius.
This problem involves work and time. We will use the concept that if a person can complete a task in \(N\) days, their one day's work is \(1/N\) of the task. We will set up equations based on the given information and solve for the time B alone takes to complete the task.
Let the time taken by A, B, and C alone to complete the task be \(t_A\), \(t_B\), and \(t_C\) days respectively.
The one day's work for A, B, and C will be \(\frac{1}{t_A}\), \(\frac{1}{t_B}\), and \(\frac{1}{t_C}\) respectively.
From the first statement, "A can complete a task in the same time in which B and C together can complete it":
\[ t_A = t_{B+C} \]This implies that A's one day work is equal to the combined one day work of B and C:
\[ \frac{1}{t_A} = \frac{1}{t_B} + \frac{1}{t_C} \quad \text{(Equation 1)} \]From the second statement, "A and B together can complete it in 10 days":
\[ \frac{1}{t_A} + \frac{1}{t_B} = \frac{1}{10} \quad \text{(Equation 2)} \]From the third statement, "C alone can complete it in 60 days":
\[ t_C = 60 \implies \frac{1}{t_C} = \frac{1}{60} \]Substitute the value of \(\frac{1}{t_C}\) into Equation 1:
\[ \frac{1}{t_A} = \frac{1}{t_B} + \frac{1}{60} \quad \text{(Equation 3)} \]Now, substitute Equation 3 into Equation 2:
\[ \left( \frac{1}{t_B} + \frac{1}{60} \right) + \frac{1}{t_B} = \frac{1}{10} \]Combine the terms involving \(\frac{1}{t_B}\):
\[ \frac{2}{t_B} + \frac{1}{60} = \frac{1}{10} \]Isolate \(\frac{2}{t_B}\):
\[ \frac{2}{t_B} = \frac{1}{10} - \frac{1}{60} \]Find a common denominator for the right side:
\[ \frac{2}{t_B} = \frac{6}{60} - \frac{1}{60} \]\[ \frac{2}{t_B} = \frac{5}{60} \]\[ \frac{2}{t_B} = \frac{1}{12} \]Solve for \(t_B\):
\[ t_B = 2 \times 12 \]\[ t_B = 24 \]So, B alone can complete the task in 24 days.
D) 24 days
To find the length of the rectangle, we first use the given ratio of length to breadth to express them in terms of a common variable. Then, we use the formula for the area of a rectangle to set up an equation and solve for that variable. Finally, we substitute the value of the variable back into the expression for the length.
Let the length of the rectangle be \(L\) and the breadth be \(B\).
The ratio of the length to the breadth is given as 7 : 4. So, we can write:
\[ \frac{L}{B} = \frac{7}{4} \]We can express \(L\) and \(B\) in terms of a common variable, say \(x\):
\[ L = 7x \]\[ B = 4x \]The area of the rectangle is given as 12348 cm². The formula for the area of a rectangle is \( \text{Area} = \text{Length} \times \text{Breadth} \).
Substitute the expressions for \(L\) and \(B\) into the area formula:
\[ (7x) \times (4x) = 12348 \]\[ 28x^2 = 12348 \]Now, solve for \(x^2\):
\[ x^2 = \frac{12348}{28} \]\[ x^2 = 441 \]Take the square root of both sides to find \(x\):
\[ x = \sqrt{441} \]\[ x = 21 \]Finally, substitute the value of \(x\) back into the expression for the length \(L\):
\[ L = 7x \]\[ L = 7 \times 21 \]\[ L = 147 \text{ cm} \]B) 147 cm is the correct length of the rectangle.
The question asks about the institution that NITI Aayog replaced. This is a direct factual question related to the structure and evolution of policy-making bodies in the Government of India.
Correct Option: D) Planning Commission of India
NITI Aayog was established on January 1, 2015, by a resolution of the Union Cabinet, replacing the erstwhile Planning Commission. Its primary role is to act as a think tank of the Government of India, providing both directional and policy inputs. It aims to foster cooperative federalism by involving State Governments in the economic policy-making process.