This is a logical reasoning problem involving arrangement. We need to deduce the floor on which each person lives based on the given clues and then answer the question about the number of people living below M.
Understand the setup: There are six floors, numbered 1 (lowermost) to 6 (topmost).
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Clue 1: S lives on floor numbered 5.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | S |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Clue 2: O lives on a floor above S. Since S is on floor 5, O must be on floor 6.
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | S |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Clue 3: Only T lives below N. This is a crucial clue. It means N lives on a floor, and immediately below N, only T lives. This implies that T is on floor 1, and N is on floor 2. If N were on a higher floor, there would be more than one person below N (unless N was on floor 2 and T on floor 1, which fits the condition perfectly).
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | S |
| 4 | |
| 3 | |
| 2 | N |
| 1 | T |
Clue 4: U lives on an even numbered floor. The remaining empty floors are 3 and 4. The only even-numbered floor available is 4. So, U lives on floor 4.
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | S |
| 4 | U |
| 3 | |
| 2 | N |
| 1 | T |
Final placement: The only person left is M, and the only empty floor is 3. So, M lives on floor 3.
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | S |
| 4 | U |
| 3 | M |
| 2 | N |
| 1 | T |
Answer the question: How many people live below M? M lives on floor 3. The people living below M are N (on floor 2) and T (on floor 1). Therefore, two people live below M.
C) Two. As determined in the step-by-step solution, N and T live below M.
The question asks to identify the leader of the 1857 rebellion specifically in the Sambalpur region. This requires knowledge of prominent figures associated with the 1857 revolt and their respective areas of operation.
D) Veer Surendra Sai was indeed the leader of the 1857 rebellion in Sambalpur. He was a great freedom fighter from Odisha who continued his struggle against the British even after the main rebellion of 1857 had been suppressed, fighting for a long period until his capture.
The question asks for the theme used to promote voting on National Voters' Day in January 2025. This is a factual question related to current events and specific government initiatives. To answer this, one needs to recall or know the official theme announced for National Voters' Day for the specified year.
C) Nothing Like Voting, I Vote for Sure is the correct theme announced by the Election Commission of India for National Voters' Day in January 2025. This theme aims to inspire citizens to take pride in their right to vote and participate in the electoral process.
The problem involves calculating the total time taken for a boat to travel upstream and downstream. We are given the time and distance for an initial upstream journey, and the ratio of the boat's speed in still water to the stream's speed. We need to find the individual speeds of the boat and stream, then calculate the upstream and downstream speeds, and finally determine the total time for the new journey.
Convert time to hours:
The initial time taken is 75 minutes. Convert this to hours:
\[ 75 \text{ minutes} = \frac{75}{60} \text{ hours} = \frac{5}{4} \text{ hours} = 1.25 \text{ hours} \]Define speeds and set up ratio:
Let the speed of the boat in still water be \(V_b\) and the speed of the stream be \(V_s\).
Given ratio: \[\frac{V_b}{V_s} = \frac{3}{2}\]. So, \(V_b = 3k\) and \(V_s = 2k\) for some constant \(k\).
Calculate upstream speed:
Upstream speed \(V_u = V_b - V_s = 3k - 2k = k\).
Use initial upstream journey to find \(k\):
Distance upstream = 62.3 km, Time = 1.25 hours.
Upstream speed \(V_u = \frac{\text{Distance}}{\text{Time}}\)
\[ k = \frac{62.3 \text{ km}}{1.25 \text{ hours}} = 49.84 \text{ km/hr} \]Determine individual speeds:
Speed of boat in still water \(V_b = 3k = 3 \times 49.84 = 149.52 \text{ km/hr}\)
Speed of stream \(V_s = 2k = 2 \times 49.84 = 99.68 \text{ km/hr}\)
Calculate downstream speed:
Downstream speed \(V_d = V_b + V_s = 3k + 2k = 5k\)
Alternatively, \(V_d = 149.52 + 99.68 = 249.2 \text{ km/hr}\)
Using \(k\): \(V_d = 5 \times 49.84 = 249.2 \text{ km/hr}\)
Calculate time for the new upstream journey:
New upstream distance = 67.6 km
Time upstream \[T_u = \frac{\text{Distance}}{\text{Speed}} = \frac{67.6 \text{ km}}{49.84 \text{ km/hr}} = 1.35634 \text{ hours}\]
Calculate time for the new downstream journey:
New downstream distance = 35.8 km
Time downstream \[T_d = \frac{\text{Distance}}{\text{Speed}} = \frac{35.8 \text{ km}}{249.2 \text{ km/hr}} = 0.14366 \text{ hours}\]
Calculate total time:
Total time \(T_{\text{total}} = T_u + T_d = 1.35634 + 0.14366 = 1.50000 \text{ hours}\)
Correct Option: B) 1.5
To calculate the simple interest, we will use the formula for simple interest, which is Principal \(\times\) Rate \(\times\) Time divided by 100. We are given the principal amount, the rate of interest, and the time period.
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]Substitute P = 2,00,000, R = 8, and T = 4 into the formula:
\[ \text{SI} = \frac{2,00,000 \times 8 \times 4}{100} \]First, multiply the numbers in the numerator:
\[ 2,00,000 \times 8 \times 4 = 16,00,000 \times 4 = 64,00,000 \]Now, divide by 100:
\[ \text{SI} = \frac{64,00,000}{100} = 64,000 \]So, the simple interest Tushar will pay is ₹64,000.
Correct Option: B) 64,000
The question asks to identify the river that originates in the western slopes of the Aravalli Range near Ajmer and is known as Sagarmati at its source. This requires knowledge of the geography and origin points of major rivers in the region, particularly those associated with the Aravalli Range.
Correct Option: B) The Luni River originates in the western slopes of the Aravalli Range, near Ajmer, specifically from the Pushkar valley. At its source, it is known as Sagarmati. After it meets the Saraswati stream (which originates from Pushkar Lake) near Govindgarh, it is then known as the Luni River.
The question asks about the mandatory action required by State legislators under Article 188 of the Constitution of India before they can take their seats for the first time in the state assembly. This requires knowledge of the specific provisions of the Indian Constitution related to state legislatures.
A) Take oath or affirmation — Article 188 of the Constitution of India explicitly states that every member of the Legislative Assembly or the Legislative Council of a State must make and subscribe an oath or affirmation before taking their seat. This is a fundamental requirement to uphold the Constitution and the duties of their office.
A hollow spherical shell is made of a metal of density 11 g/cm³. Its internal and external radii are 3 cm and 6 cm, respectively. What is the weight (in kg) of the shell?
(Use π = \( \frac{22}{7} \), Density = \(\frac{\text{Mass}}{\text{Volume}}\))
To find the weight of the hollow spherical shell, we first need to calculate the volume of the material used to make the shell. This can be done by subtracting the volume of the inner sphere from the volume of the outer sphere. Once the volume of the material is known, we can use the given density to find the mass, and then convert the mass to kilograms to find the weight.
Identify given values:
Calculate the volume of the outer sphere:
The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^3\).
\[ V_{\text{outer}} = \frac{4}{3} \times \frac{22}{7} \times (6 \text{ cm})^3 \] \[ V_{\text{outer}} = \frac{4}{3} \times \frac{22}{7} \times 216 \] \[ V_{\text{outer}} = \frac{4 \times 22 \times 216}{21} = \frac{19008}{21} \text{ cm}^3 \] \[ V_{\text{outer}} \approx 905.1428 \text{ cm}^3 \]Calculate the volume of the inner sphere:
\[ V_{\text{inner}} = \frac{4}{3} \times \frac{22}{7} \times (3 \text{ cm})^3 \] \[ V_{\text{inner}} = \frac{4}{3} \times \frac{22}{7} \times 27 \] \[ V_{\text{inner}} = \frac{4 \times 22 \times 27}{21} = \frac{2376}{21} \text{ cm}^3 \] \[ V_{\text{inner}} \approx 113.1428 \text{ cm}^3 \]Calculate the volume of the metal (material) in the shell:
This is the difference between the outer and inner sphere volumes.
\[ V_{\text{material}} = V_{\text{outer}} - V_{\text{inner}} \] \[ V_{\text{material}} = \frac{19008}{21} - \frac{2376}{21} \] \[ V_{\text{material}} = \frac{19008 - 2376}{21} = \frac{16632}{21} \text{ cm}^3 \] \[ V_{\text{material}} = 792 \text{ cm}^3 \]Alternatively, we can factor out \(\frac{4}{3}\pi\):
\[ V_{\text{material}} = \frac{4}{3}\pi (r_2^3 - r_1^3) \] \[ V_{\text{material}} = \frac{4}{3} \times \frac{22}{7} \times (6^3 - 3^3) \] \[ V_{\text{material}} = \frac{4}{3} \times \frac{22}{7} \times (216 - 27) \] \[ V_{\text{material}} = \frac{4}{3} \times \frac{22}{7} \times 189 \] \[ V_{\text{material}} = 4 \times 22 \times \frac{189}{21} \] \[ V_{\text{material}} = 4 \times 22 \times 9 = 88 \times 9 = 792 \text{ cm}^3 \]Calculate the mass of the shell:
Given Density = \(\frac{\text{Mass}}{\text{Volume}}\), so Mass = Density \(\times\) Volume.
\[ \text{Mass} = 11 \text{ g/cm}^3 \times 792 \text{ cm}^3 \] \[ \text{Mass} = 8712 \text{ g} \]Convert the mass to kilograms:
Since 1 kg = 1000 g,
\[ \text{Mass (in kg)} = \frac{8712}{1000} \text{ kg} \] \[ \text{Mass (in kg)} = 8.712 \text{ kg} \]The weight of the shell is numerically equal to its mass in kilograms (assuming standard gravity, which is implied when asking for weight in kg).
A) 8.712 kg is the calculated weight of the shell.
The problem presents a series of letter groups, each consisting of three letters. We need to identify the pattern in the progression of these letters based on their positions in the English alphabet and then apply this pattern to find the missing group.
Let's analyze the pattern for each position (first, second, and third letter) separately.
Combining these, the next group in the series is YGS.
A) YGS is the correct option because it follows the established patterns for each letter position: +6 for the first letter, +7 for the second letter (with wrap-around), and +6 for the third letter (with wrap-around).
The question asks to identify the Indian state where the Kachchh and Kathiawar coasts are located. This requires knowledge of the geographical distribution of India's coastal regions.
Correct Option: C) Gujarat is the state where both the Kachchh and Kathiawar coasts are situated. Gujarat has a long and varied coastline, and these two regions form significant parts of it.