The problem involves calculating population values at different points in the past given a current population and a constant annual growth rate. We will use the compound interest formula in reverse to find the population in previous years and then calculate the difference.
Correct Option: B) 20,480
This question tests knowledge of the constitutional provisions regarding local self-governance in India, specifically municipalities. The 74th Constitutional Amendment Act of 1992 introduced Part IXA to the Constitution, which deals with municipalities and their functioning, including provisions for their dissolution and subsequent elections.
Correct Option: D) A new election must be held within 6 months.
The question asks to identify an industry closely associated with 'cluster development' and which is the second-largest employer in India after agriculture. We need to evaluate each option based on these two criteria.
Correct Option: B) Textile and apparel — The textile and apparel industry is well-known for its cluster-based development model, with various regions specializing in different aspects of textile production. It is also a highly labor-intensive sector, providing employment to a vast number of people, making it the second-largest employer in India after agriculture.
The question asks to identify the specific DRDO laboratory responsible for conducting a successful laser weapon test in April 2025. This requires knowledge of the specialized functions of various DRDO labs.
The Centre for High Energy Systems and Sciences (CHESS) is a DRDO lab specifically dedicated to research and development in high-energy systems, including directed energy weapons like lasers. Therefore, a laser weapon test would fall under its purview.
Correct Option: C) CHESS (Centre for High Energy Systems and Sciences)
The question asks about the natural occurrence of neptunium and plutonium. These are transuranic elements, meaning they have atomic numbers greater than uranium. We need to identify which of the given options is a known source or environment where these elements can be found, even if in trace amounts.
Correct Option: A) Pitchblende is a uranium-rich mineral. Neptunium and plutonium are formed naturally in trace amounts through neutron capture by uranium isotopes and subsequent beta decay. Therefore, they are found in association with uranium ores like pitchblende.
The problem involves calculating the discount percentage given the marked price, its relation to the cost price, and the profit percentage. We will first find the cost price, then the selling price using the profit percentage, and finally the discount percentage using the marked price and selling price.
Calculate the Cost Price (CP):
The marked price (MP) is ₹744, which is 31% above the cost price (CP). This means:
\[ \text{MP} = \text{CP} + 0.31 \times \text{CP} \]\[ \text{MP} = \text{CP} (1 + 0.31) \]\[ \text{MP} = 1.31 \times \text{CP} \]Given \(\text{MP} = \text{₹}744\), we can find CP:
\[ 744 = 1.31 \times \text{CP} \]\[ \text{CP} = \frac{744}{1.31} \]\[ \text{CP} \approx \text{₹}567.9389 \]Calculate the Selling Price (SP):
The profit percentage is 9%. Profit is always calculated on the cost price. So, the selling price (SP) is:
\[ \text{SP} = \text{CP} + 0.09 \times \text{CP} \]\[ \text{SP} = \text{CP} (1 + 0.09) \]\[ \text{SP} = 1.09 \times \text{CP} \]Using the calculated CP:
\[ \text{SP} = 1.09 \times 567.9389 \]\[ \text{SP} \approx \text{₹}618.0534 \]Calculate the Discount Percentage:
Discount is calculated on the marked price. The discount amount is the difference between the marked price and the selling price.
\[ \text{Discount Amount} = \text{MP} - \text{SP} \]\[ \text{Discount Amount} = 744 - 618.0534 \]\[ \text{Discount Amount} = \text{₹}125.9466 \]Now, calculate the discount percentage:
\[ \text{Discount Percentage} = \frac{\text{Discount Amount}}{\text{MP}} \times 100 \]\[ \text{Discount Percentage} = \frac{125.9466}{744} \times 100 \]\[ \text{Discount Percentage} \approx 0.169283 \times 100 \]\[ \text{Discount Percentage} \approx 16.9283\% \]Round off to two decimal places:
The discount percentage is approximately 16.93%. Let's recheck the calculations with more precision or by using fractions to avoid early rounding errors if needed. Alternatively, we can use the formula directly:
\[ \text{CP} = \frac{744}{1.31} \]\[ \text{SP} = 1.09 \times \frac{744}{1.31} = \frac{1.09 \times 744}{1.31} \]\[ \text{Discount Percentage} = \left(1 - \frac{\text{SP}}{\text{MP}}\right) \times 100 \]\[ \text{Discount Percentage} = \left(1 - \frac{1.09 \times 744 / 1.31}{744}\right) \times 100 \]\[ \text{Discount Percentage} = \left(1 - \frac{1.09}{1.31}\right) \times 100 \]\[ \text{Discount Percentage} = \left(\frac{1.31 - 1.09}{1.31}\right) \times 100 \]\[ \text{Discount Percentage} = \left(\frac{0.22}{1.31}\right) \times 100 \]\[ \text{Discount Percentage} \approx 0.1679389 \times 100 \]\[ \text{Discount Percentage} \approx 16.79\% \]Rounding off to two decimal places, the discount percentage is 16.79%.
Correct Option: D) 16.79%
This is a direction and distance reasoning problem. We need to visualize the positions of the towns based on the given statements and then determine the relative position of Town C with respect to Town F. We can use a simple coordinate system or draw a diagram to represent the towns.
Let's combine these statements:
From the first three points, we know that C and F are on the same east-west line, or F is south of C. Since E is north of C, and F is south of E, F can be north of C, south of C, or exactly on the same east-west line as C. However, the statement "Town D is to the north-east of Town G" helps clarify the relative positions.
If D is north-east of G, then G must be south-west of D. We also know that G is west of F, and F is south of E, and E is north of C, and C is east of D.
Let's place D at \((0,0)\).
C is to the east of D, so C is at \((x_C, 0)\) where \(x_C > 0\).
E is to the north of C, so E is at \((x_C, y_E)\) where \(y_E > 0\).
F is to the south of E, so F is at \((x_F, y_F)\) where \(x_F\) is the same as \(x_C\) (or close to it) and \(y_F < y_E\).
G is to the west of F, so G is at \((x_G, y_F)\) where \(x_G < x_F\).
Now consider "Town D is to the north-east of Town G". This means G must be to the south-west of D. For G to be south-west of D (which is at \((0,0)\)), G's coordinates \((x_G, y_F)\) must have \(x_G < 0\) and \(y_F < 0\).
If \(y_F < 0\), and F is south of E, and E is north of C, then C must also be at a positive y-coordinate, or at least \(y_C > y_F\). Since E is north of C, \(y_E > y_C\). Since F is south of E, \(y_F < y_E\). If D is at \((0,0)\), C is east of D, so C is at \((x_C, 0)\) for some \(x_C > 0\). Then E is north of C, so E is at \((x_C, y_E)\) where \(y_E > 0\). F is south of E, so F is at \((x_C, y_F)\) where \(y_F < y_E\). G is west of F, so G is at \((x_G, y_F)\) where \(x_G < x_C\).
For D to be north-east of G, G must be south-west of D. This implies G's y-coordinate \(y_F\) must be negative. If \(y_F < 0\), and C is at \((x_C, 0)\), then F is south of C. So, F is to the south of C.
The question asks for the position of Town C with respect to Town F. If F is to the south of C, then C must be to the north of F.
C) North
The question asks to identify the Article of the Indian Constitution that prohibits human trafficking. This requires knowledge of the Fundamental Rights enshrined in Part III of the Constitution, specifically those related to the right against exploitation.
D) Article 23 — Article 23 of the Constitution of India explicitly prohibits "traffic in human beings and begar and other similar forms of forced labour." This article is a fundamental right against exploitation, ensuring the dignity and freedom of individuals from being bought, sold, or forced into labor.
The question asks about the location of the Utkal Plains. To answer this, one needs to recall the geographical divisions of India's coastal plains and identify where the Utkal Plains fit within these divisions.
A) Eastern Coastal Plain – The Utkal Plains are situated in Odisha, which is a state on the eastern coast of India. Therefore, they are a significant part of the Eastern Coastal Plain.