This problem can be solved using Ohm's Law, which relates potential difference (voltage), current, and resistance in an electrical circuit. Ohm's Law states that the potential difference across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.
Correct Option: A) 5 Ω is the correct resistance calculated using Ohm's Law.
This problem requires us to apply a set of given rules for interchanging mathematical operators in an equation and then evaluate the modified equation using the BODMAS/PEMDAS rule.
The original equation is: \(10 + 152 \times 19 - 2 \div 3 = ?\)
Applying the interchanges:
So, the new equation becomes: \(10 - 152 \div 19 + 2 \times 3 = ?\)
First, perform Division and Multiplication from left to right:
Substitute these values back into the equation:
\(10 - 8 + 6 = ?\)
So, the value of the equation is \(8\).
D) The final calculated value is 8, which matches option D.
This problem involves percentage calculations. We are given that A's salary is 20% less than B's salary. We need to find out by what percentage B's salary is more than A's salary. We can assume a value for B's salary to make the calculations easier, or use algebraic variables.
Assume B's salary: Let's assume B's salary is Rs. 100.
Calculate A's salary: A's salary is 20% less than B's salary. So, A's salary is:
\[ \text{A's Salary} = \text{B's Salary} - 20\% \text{ of B's Salary} \]\[ \text{A's Salary} = 100 - (0.20 \times 100) = 100 - 20 = 80 \text{ Rs.} \]Calculate the difference: The difference between B's salary and A's salary is:
\[ \text{Difference} = \text{B's Salary} - \text{A's Salary} = 100 - 80 = 20 \text{ Rs.} \]Calculate the percentage increase of B's salary over A's salary: To find by what percentage B's salary is more than A's, we need to calculate the difference as a percentage of A's salary (the base for comparison).
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{\text{A's Salary}} \right) \times 100\% \]\[ \text{Percentage Increase} = \left( \frac{20}{80} \right) \times 100\% \]\[ \text{Percentage Increase} = \left( \frac{1}{4} \right) \times 100\% \]\[ \text{Percentage Increase} = 25\% \]Thus, B's salary is 25% more than A's salary.
C) 25% is the correct answer, as calculated above.
A) 17% — This option is incorrect. It might arise from an incorrect calculation or misunderstanding of the base for percentage calculation.
B) 20% — This is incorrect. 20% is the percentage by which A's salary is less than B's. The question asks for the percentage by which B's salary is more than A's, which uses A's salary as the base, not B's.
D) 15% — This option is incorrect and does not result from the correct calculation method.
The question asks to identify the satellite launched by ISRO on a specific date, February 14, 2022. This requires knowledge of ISRO's launch history and specific mission details.
Correct Option: A) EOS-04 was indeed launched by ISRO on February 14, 2022. This mission marked ISRO's first launch of 2022.
The question asks to identify who among the given options are NOT stakeholders in forest conservation. A stakeholder is any individual, group, or organization that is affected by or can affect an organization's actions, objectives, and policies. In the context of forest conservation, stakeholders are those who have a direct interest in the forest, its resources, or its management.
Correct Option: D) People living in urban areas are generally not considered direct stakeholders in forest conservation, as their direct dependency and involvement are typically much less immediate compared to local communities, government bodies, or nature enthusiasts.
The problem states a direct relationship: the more a color component is bent during dispersion by a glass prism, the greater the refractive index of the glass for that color component. We need to recall the order of dispersion of white light by a prism (VIBGYOR) and apply this relationship to determine the correct order of refractive indices for violet, green, and yellow light.
Understand Dispersion: When white light passes through a prism, it splits into its constituent colors (spectrum) due to different wavelengths bending at different angles. This phenomenon is called dispersion.
Recall VIBGYOR: The order of colors in the spectrum, from most bent to least bent, is Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR).
Apply the given condition: The problem states that "the more a colour component is bent, the more is the refractive index of the glass for that colour component."
Compare bending for given colors: From the VIBGYOR sequence, violet light is bent the most, followed by green, and then yellow (red is bent the least). Therefore, the order of bending from most to least is Violet > Green > Yellow.
Relate bending to refractive index: Since more bending implies a higher refractive index, we can establish the relationship between the refractive indices for violet (\(\mu_V\)), green (\(\mu_G\)), and yellow (\(\mu_Y\)) light.
Determine the order: Based on the bending order, the refractive index order will be:
\[ \mu_V > \mu_G > \mu_Y \]D) \(\mu_V > \mu_G > \mu_Y\) is correct because violet light is bent the most, followed by green, and then yellow, and the refractive index is directly proportional to the amount of bending.
The question asks to identify one of the cities famous for hosting the Kumbh Mela. The Kumbh Mela is a major Hindu pilgrimage and festival celebrated at four specific locations in India. We need to recall these locations to identify the correct option.
C) Prayagraj is one of the four cities where the Kumbh Mela is celebrated. It is particularly known for the Maha Kumbh Mela, which occurs every 12 years.
The question asks to identify the features of villi that are essential for the absorption of digested food in the small intestine. We need to evaluate each given feature based on its role in maximizing absorption efficiency.
B) (i), (ii), and (iv) are the features that enable the villi to absorb food. Finger-like projections with thin walls (i) increase surface area and reduce diffusion distance. A large surface area (ii) is crucial for maximizing absorption. A rich blood supply (iv) ensures rapid transport of absorbed nutrients, maintaining the concentration gradient for continuous absorption.
To find the remainder when a product of numbers is divided by another number, we can find the remainder of each individual number when divided by the divisor and then multiply these remainders. Finally, we find the remainder of this product of remainders when divided by the original divisor.
We divide 171 by 17:
\[ 171 = 17 \times 10 + 1 \]So, the remainder when 171 is divided by 17 is 1. We can write this as \(171 \equiv 1 \pmod{17}\).
We divide 172 by 17:
\[ 172 = 17 \times 10 + 2 \]So, the remainder when 172 is divided by 17 is 2. We can write this as \(172 \equiv 2 \pmod{17}\).
We divide 173 by 17:
\[ 173 = 17 \times 10 + 3 \]So, the remainder when 173 is divided by 17 is 3. We can write this as \(173 \equiv 3 \pmod{17}\).
Now, we multiply the individual remainders we found:
\[ 1 \times 2 \times 3 = 6 \]The product of the remainders is 6. When 6 is divided by 17, the remainder is 6 itself, because 6 is less than 17.
Therefore, the remainder when \(171 \times 172 \times 173\) is divided by 17 is 6.
A) 6 — As calculated in the step-by-step explanation, the remainder is 6.