The question asks about the authority responsible for classifying urban areas (large, small, or transitional) within a state. This falls under the constitutional provisions related to local self-governance, specifically the 74th Constitutional Amendment Act.
Correct Option: D) Governor of the State
The question asks about the annual emission reduction required to limit global warming to 1.5°C, according to the UNEP Emissions Gap Report 2024. This is a specific figure released in the report.
C) 7.5% is the correct answer. The UNEP Emissions Gap Report 2024 states that an annual reduction of 7.5% in emissions is required until 2035 to limit global warming to 1.5°C.
The question asks how to customize bullets in MS Word. This involves navigating to the specific menu option that allows for modifying the appearance or type of bullet points used in a list.
Correct Option: C) Home → Bullets → Define New Bullet
This path correctly leads to the functionality for customizing bullets in MS Word. The 'Home' tab contains the 'Paragraph' group, which includes the 'Bullets' option. From there, 'Define New Bullet' is the specific command to access customization options.
The question asks to identify the international entity that has partnered with India for joint research initiatives on marine plastic litter and waste-to-hydrogen technologies. This requires knowledge of recent international collaborations involving India in environmental and technological domains.
D) European Union (EU) — India and the European Union (EU) have a strategic partnership that includes cooperation on climate change, clean energy, and environmental protection. They have specifically announced joint research initiatives and calls for proposals to address marine plastic litter and develop waste-to-hydrogen technologies, aligning perfectly with the question's description.
This problem involves properties of regular polygons, specifically the sum of interior and exterior angles. We will use the formulas for these sums and the given relationship between them to find the number of sides of the polygon. Once the number of sides is known, we can calculate the measure of each interior angle.
Recall formulas for sum of angles:
For a polygon with \(n\) sides:
Set up the relationship given in the problem:
The problem states that the sum of the interior angles is 50% more than the sum of its exterior angles. This can be written as:
\[ \text{Sum of interior angles} = \text{Sum of exterior angles} + 0.50 \times \text{Sum of exterior angles} \]\[ \text{Sum of interior angles} = 1.5 \times \text{Sum of exterior angles} \]Substitute the formulas into the equation:
Substitute the known formulas for the sums into the equation from step 2:
\[ (n-2) \times 180^\circ = 1.5 \times 360^\circ \]Solve for \(n\):
First, calculate the right side:
\[ 1.5 \times 360^\circ = 540^\circ \]\[ (n-2) \times 180^\circ = 540^\circ \]Now, divide both sides by \(180^\circ\):\[ n-2 = \frac{540}{180} \]\[ n-2 = 3 \]Add 2 to both sides to find \(n\):\[ n = 3 + 2 \]\[ n = 5 \]So, the polygon is a regular pentagon.Calculate each interior angle:
For a regular polygon, all interior angles are equal. The measure of each interior angle \(x\) is the sum of interior angles divided by the number of sides \(n\):
\[ x = \frac{\text{Sum of interior angles}}{n} \]We know the sum of interior angles is \(540^\circ\) (from step 3) and \(n=5\):\[ x = \frac{540^\circ}{5} \]\[ x = 108^\circ \]Therefore, the value of \(x\) is \(108\).
Correct Option: D) 108
This problem involves calculating the net displacement and direction from a starting point (Y) to an ending point (Z) after a series of movements. We need to track the horizontal (East-West) and vertical (North-South) components of Dhiraj's journey separately.
At Point Z, Dhiraj's final position relative to Point Y is \(0\) km East/West and \(-5\) km North/South. This means Point Z is 5 km South of Point Y.
To reach Point Y from Point Z, Dhiraj needs to drive 5 km towards the North.
A) 5 km towards the north. This is the correct calculation for the distance and direction needed to return to the starting point Y from the final point Z.
To find the weighted average price, we need to multiply each product's price by its respective percentage of sales (weight), sum these values, and then divide by the sum of the weights (which is 100% or 1 in decimal form).
Weighted contribution of A \( = P_A \times W_A \)
\[ = \text{₹}156 \times 0.55 \]\[ = \text{₹}85.80 \]Weighted contribution of B \( = P_B \times W_B \)
\[ = \text{₹}220 \times 0.45 \]\[ = \text{₹}99.00 \]The weighted average price is the sum of the weighted contributions divided by the sum of the weights. Since the weights are percentages that sum to 100% (or 1), we just sum the weighted contributions.
Weighted Average Price \( = (\text{Weighted contribution of A}) + (\text{Weighted contribution of B}) \)
\[ = \text{₹}85.80 + \text{₹}99.00 \]\[ = \text{₹}184.80 \]Correct Option: B) ₹184.80 is the calculated weighted average price.
The question asks to identify the captain of the Mumbai Indians team that won the Women's Premier League (WPL) 2025 title. This is a factual question related to sports current affairs, specifically cricket.
Correct Option: A) Harmanpreet Kaur was the captain of the Mumbai Indians team that won the inaugural Women's Premier League (WPL) title in 2023. She is the established captain of the team.
This is a logical reasoning problem involving the arrangement of boxes. We need to deduce the exact order of the seven boxes (D, E, F, G, S, T, U) based on the given clues and then determine the number of boxes between E and G.
Total boxes: There are 7 boxes. Let's number the positions from bottom to top as 1 to 7.
Clue 1: "Only two boxes are kept below T."
This means T is at position 3 from the bottom (or 5 from the top).
Position 7 Position 6 Position 5 Position 4 T (Position 3) Box Box
Clue 2: "Only one box is kept above U."
This means U is at position 6 from the bottom (or 2 from the top).
Position 7 U (Position 6) Position 5 Position 4 T (Position 3) Box Box
Clue 3: "Only one box is kept between U and D."
Since U is at position 6, D must be at position 4 (because there's one box between them, and D cannot be above U as there's only one box above U, which is position 7).
Position 7 U (Position 6) Box (Position 5) D (Position 4) T (Position 3) Box Box
Clue 4: "G is kept immediately above S."
This means G and S are together in consecutive positions (G above S). The available consecutive slots are (Position 1, Position 2) or (Position 5, Position 6) or (Position 7, Position 8 - not possible). Since U is at position 6, (Position 5, Position 6) is not available. The only remaining consecutive slots are Position 1 and Position 2. So, G is at Position 2 and S is at Position 1.
Position 7 U (Position 6) Box (Position 5) D (Position 4) T (Position 3) G (Position 2) S (Position 1)
Clue 5: "F is kept at some place below E."
The remaining boxes are E and F. The only remaining empty slot is Position 5. Therefore, E must be at Position 5. If E is at Position 5, then F must be below E. The only remaining box is F, and it must be placed somewhere below E. This condition is already satisfied by the remaining box F, which has no specific position yet, but E is placed at position 5. This implies F must be one of the boxes already placed below E (S, G, T, D, U). However, this interpretation is incorrect. The clue means that F is one of the boxes, and E is another, and F is below E. The only remaining box to be placed is F, and the only remaining position is Position 7. This contradicts the condition that F is below E. Let's re-evaluate.
Let's list the boxes and positions:
The remaining boxes are E and F. The remaining positions are Position 7 and Position 5.
If F is kept at some place below E, then E must be at Position 7 and F must be at Position 5.
So the final arrangement is:
Position 7: E Position 6: U Position 5: F Position 4: D Position 3: T Position 2: G Position 1: S
Final Question: "How many boxes are kept between E and G?"
E is at Position 7.
G is at Position 2.
Boxes between E and G are U (Position 6), F (Position 5), D (Position 4), T (Position 3).
There are 4 boxes between E and G.
D) Four