To determine the relationship between the magnetic fields produced by coils A and B, we need to recall the formula for the magnetic field at the center of a circular coil. We will then apply this formula to both coils, considering their respective number of turns, radius, and current, and compare the results.
The magnetic field \(B\) at the center of a circular coil with \(N\) turns, carrying a current \(I\), and having a radius \(R\) is given by:
\[ B = \frac{\mu_0 N I}{2R} \]where \(\mu_0\) is the permeability of free space, a constant.
For coil A:
Substituting these values into the formula:
\[ B_A = \frac{\mu_0 (50) I}{2R} \]For coil B:
Substituting these values into the formula:
\[ B_B = \frac{\mu_0 (100) I}{2R} \]We can express \(B_B\) in terms of \(B_A\):
\[ B_B = \frac{\mu_0 (2 \times 50) I}{2R} = 2 \times \left( \frac{\mu_0 (50) I}{2R} \right) \]\[ B_B = 2 B_A \]This shows that the magnetic field produced by coil B is twice that produced by coil A.
B) by B > that of A
As derived, \(B_B = 2B_A\), which means the magnetic field produced by coil B is greater than that produced by coil A.
The question asks us to identify the relationship between two statements: I. Citizens of city X have multiplied their wealth by investing in government schemes in the past two years, and II. City X has seen a recent rise in the number of luxury cars. We need to determine if one is a cause and the other an effect, or if they are effects of independent causes, or independent causes themselves.
Based on this analysis, Statement I (increased wealth) is a plausible cause for Statement II (rise in luxury cars).
C) I is the cause and II is its possible effect. This option correctly identifies the causal relationship. An increase in wealth (Statement I) directly contributes to people's ability and willingness to purchase luxury items like cars (Statement II).
The question asks to identify the most common simple permanent tissue among the given options. To answer this, we need to recall the classification of plant tissues and the characteristics and functions of each option.
B) Parenchyma ā Parenchyma is the most common and fundamental simple permanent tissue in plants. It forms the bulk of many plant organs, including the cortex and pith of stems and roots, the mesophyll of leaves, and the pulp of fruits. Its cells are living, thin-walled, and involved in various metabolic activities like photosynthesis, storage of food, and secretion.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find a consistent rule (e.g., difference in alphabetical positions) that applies to three of the four options, and the odd one out will be the answer.
C) TB ā ZF ā This pair does not follow the pattern. In this pair, T (20) to Z (26) is a difference of +6, and B (2) to F (6) is a difference of +4. This is different from the -3 pattern observed in the other options.
To solve this problem, we need to first calculate the selling price (SP) required to achieve a 90% gain on the given cost price (CP). Then, using the selling price and the discount percentage, we can work backward to find the marked price (MP).
Thus, the marked price should be ā¹420.
C) ā¹420 is the correct marked price that allows a 90% gain after a 5% discount.
The question asks for the location of the fifth India-U.S. 2+2 Ministerial Dialogue held on November 10, 2023. This is a factual question related to current international relations and requires knowledge of recent diplomatic events.
D) New Delhi ā The fifth India-U.S. 2+2 Ministerial Dialogue, involving the foreign and defense ministers of both countries, was indeed held in New Delhi, India, on November 10, 2023. This dialogue is a crucial platform for discussing strategic, defense, and foreign policy issues between the two nations.
The problem asks us to simplify the given algebraic expression. We can use the algebraic identity \((a-b)(a+b) = a^2 - b^2\) to simplify each term in the expression and then combine them.
C) The value of the expression simplifies to \(0\).
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate the conclusions based on these diagrams. The key is to assume the statements are true, even if they contradict common knowledge.
Correct Option: A) Only conclusion (I) follows.
To find the image distance for a concave mirror, we will use the mirror formula, which relates the focal length, object distance, and image distance. We must also correctly apply the sign conventions for concave mirrors.
Identify the given values and sign conventions:
Apply the mirror formula:
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]Substitute the given values into the formula:
\[ \frac{1}{-20} = \frac{1}{v} + \frac{1}{-60} \]Rearrange the formula to solve for \(v\):
\[ \frac{1}{v} = \frac{1}{-20} - \frac{1}{-60} \] \[ \frac{1}{v} = -\frac{1}{20} + \frac{1}{60} \]Find a common denominator and perform the subtraction:
The common denominator for 20 and 60 is 60.
\[ \frac{1}{v} = -\frac{3}{60} + \frac{1}{60} \] \[ \frac{1}{v} = \frac{-3 + 1}{60} \] \[ \frac{1}{v} = \frac{-2}{60} \] \[ \frac{1}{v} = -\frac{1}{30} \]Calculate \(v\):
\[ v = -30 \text{ cm} \]Interpret the result:
The negative sign for \(v\) indicates that the image is formed on the same side as the object (in front of the mirror). Since the question states a real image is formed, and our calculation yields a negative image distance, this is consistent with the properties of a concave mirror forming a real image.
Correct Option: A) -30 cm
A ball of radius 10 cm is taken and a cylindrical hole of radius 1 cm is drilled through the centre. Which of the options listed below is the closest in value to the ratio of the total surface area of the hollowed out ball to the surface area of the original ball?
\(\frac{219}{200}\)
\(\frac{1}{10}\)
\(\frac{221}{200}\)
\(\frac{11}{5}\)