To find the surface area of a sphere, we need its radius. The problem provides the diameter, so we first calculate the radius. Then, we use the formula for the surface area of a sphere, which is \(4 \pi r^2\).
The diameter of the sphere is given as \(D = 98 \text{ cm}\).
The radius (\(r\)) is half of the diameter.
\[ r = \frac{D}{2} = \frac{98 \text{ cm}}{2} = 49 \text{ cm} \]The formula for the surface area (\(A\)) of a sphere is \(A = 4 \pi r^2\). We will use the approximation \(\pi = \frac{22}{7}\).
\[ A = 4 \times \frac{22}{7} \times (49 \text{ cm})^2 \]\[ A = 4 \times \frac{22}{7} \times 49 \times 49 \text{ cm}^2 \]First, simplify by dividing 49 by 7:
\[ A = 4 \times 22 \times \frac{49}{7} \times 49 \text{ cm}^2 \]\[ A = 4 \times 22 \times 7 \times 49 \text{ cm}^2 \]\[ A = 88 \times 7 \times 49 \text{ cm}^2 \]\[ A = 616 \times 49 \text{ cm}^2 \]To multiply \(616 \times 49\):
\[ 616 \times 49 = 616 \times (50 - 1) \]\[ = (616 \times 50) - (616 \times 1) \]\[ = 30800 - 616 \]\[ = 30184 \text{ cm}^2 \]C) 30,184 cm² is the correct surface area calculated using the given diameter.
This problem involves setting up and solving a system of linear equations based on the given age relationships. We will define variables for the present ages of Rahul and his daughter and then translate the given conditions into algebraic equations.
Define variables:
Let Rahul's present age be \(R\) years.
Let his daughter's present age be \(D\) years.
Formulate the first equation from the first condition:
"Rahul's age is three times the age of his daughter."
\[R = 3D \quad \text{(Equation 1)}\]
Determine ages after 8 years:
After 8 years, Rahul's age will be \(R+8\) years.
After 8 years, his daughter's age will be \(D+8\) years.
Formulate the second equation from the second condition:
"After 8 years from now, his age will be 5 years more than twice the age of his daughter."
\[R+8 = 2(D+8) + 5 \quad \text{(Equation 2)}\]
Simplify Equation 2:
\[R+8 = 2D + 16 + 5\]
\[R+8 = 2D + 21\]
\[R = 2D + 21 - 8\]
\[R = 2D + 13 \quad \text{(Equation 3)}\]
Solve the system of equations:
Substitute Equation 1 into Equation 3:
\[3D = 2D + 13\]
\[3D - 2D = 13\]
\[D = 13\]
So, the daughter's present age is 13 years.
Find Rahul's present age:
Substitute the value of \(D\) back into Equation 1:
\[R = 3D\]
\[R = 3 \times 13\]
\[R = 39\]
Rahul's present age is 39 years.
Verify the solution (optional but recommended):
Present ages: Rahul = 39, Daughter = 13. (39 = 3 * 13, first condition met)
After 8 years: Rahul = 39 + 8 = 47, Daughter = 13 + 8 = 21.
Check second condition: Is 47 equal to 5 more than twice 21?
\(2 \times 21 + 5 = 42 + 5 = 47\). (Second condition met)
D) 39 years is the present age of Rahul.
In a row of 73 students facing north, Gita is 16th from the left end. If Sunita is 21st to the right of Gita, what is Sunita's position from the right end of the line?
To solve this problem, we need to first find Gita's position from the left end, then calculate Sunita's position from the left end based on her position relative to Gita. Finally, we will use the total number of students to find Sunita's position from the right end.
Gita's position from the left end: It is given that Gita is 16th from the left end.
\[ \text{Gita's position from left} = 16 \]Sunita's position from the left end: Sunita is 21st to the right of Gita. This means we add 21 to Gita's position from the left.
\[ \text{Sunita's position from left} = \text{Gita's position from left} + 21 \\ \text{Sunita's position from left} = 16 + 21 \\ \text{Sunita's position from left} = 37 \]Sunita's position from the right end: We know the total number of students in the row is 73. The formula to find the position from the other end is:
\[ \text{Position from right} = (\text{Total students} - \text{Position from left}) + 1 \\ \text{Sunita's position from right} = (73 - 37) + 1 \\ \text{Sunita's position from right} = 36 + 1 \\ \text{Sunita's position from right} = 37 \]So, Sunita is 37th from the right end of the line.
Correct Option: D) 37 th
The question asks about the number of new branches Muthoot Finance received RBI approval to open in February 2025. This is a factual question related to current affairs and business news.
Correct Option: A) 115 new branches. This number was officially reported in February 2025 as the RBI's approval for Muthoot Finance's expansion.
The question asks for the primary objective of the Chandra's Surface Thermophysical Experiment (ChaSTE) payload aboard Chandrayaan-3. To answer this, one needs to recall the specific scientific goals associated with this particular instrument.
A) To measure the vertical temperature profile of the lunar regolith
ChaSTE is equipped with a temperature probe capable of penetrating the lunar surface to a certain depth. Its primary function is to measure the temperature variation with depth in the lunar regolith, providing crucial data on the thermal conductivity and heat flow of the Moon's surface layer.
The question asks about the initial number of cities included in the Smart Cities Mission. This is a factual question related to a major government initiative in India. Recalling the details of the mission's launch will provide the correct answer.
B) 100 is the correct answer. The Smart Cities Mission was launched with the goal of developing 100 smart cities across India.
This problem involves work and time. We will use the concept of work rate, where the rate is the reciprocal of the time taken to complete a task. First, we'll find Ashish's individual work rate, then the time he takes to paint one hall, and finally, the time he takes to paint four halls.
Calculate the combined work rate of Varun and Ashish:
Varun and Ashish together can paint a hall in 3 days. So, their combined work rate is:
Calculate Varun's individual work rate:
Varun alone can paint a hall in 7 days. So, Varun's work rate is:
Calculate Ashish's individual work rate:
The combined work rate is the sum of individual work rates. So, Ashish's work rate can be found by subtracting Varun's work rate from the combined work rate:
Calculate the time Ashish takes to paint one hall:
Time taken is the reciprocal of the work rate. So, Ashish alone can paint one hall in:
Calculate the time Ashish takes to paint four halls:
To paint 4 such halls, Ashish will take 4 times the time he takes to paint one hall:
Correct Option: D) 21
To find the speed of the stream, we first need to calculate the speed of the boat against the stream (upstream speed) and with the stream (downstream speed). Once we have these two speeds, we can use the standard formula to find the speed of the stream.
Given, distance covered against the stream = 721 km
Time taken against the stream = 42 hours
Upstream speed \( (U) = \frac{\text{Distance}}{\text{Time}} \)
\[ U = \frac{721 \text{ km}}{42 \text{ hours}} = 17.166... \text{ km/hr} \approx 17.17 \text{ km/hr} \]Given, distance covered with the stream = 721 km (since it's the same journey)
Time taken with the stream = 15 hours
Downstream speed \( (D) = \frac{\text{Distance}}{\text{Time}} \)
\[ D = \frac{721 \text{ km}}{15 \text{ hours}} = 48.066... \text{ km/hr} \approx 48.07 \text{ km/hr} \]The formula for the speed of the stream \( (S) \) is:
\[ S = \frac{1}{2} (D - U) \]Substitute the values of \( D \) and \( U \):
\[ S = \frac{1}{2} (48.066... - 17.166...) \] \[ S = \frac{1}{2} (30.90) \] \[ S = 15.45 \text{ km/hr} \]Correct Option: D) 15.45 km/hr
The question asks about the winner of the Women's Premier League (WPL) 2025 title. To answer this, one needs to know the results of the WPL 2025 season. Since the year 2025 is in the future, the question is likely a trick question or based on a misunderstanding. The WPL has been held in 2023 and 2024. Therefore, we should consider the winners of the most recent completed season, which is WPL 2024.
Correct Option: B) Mumbai Indians
While the Women's Premier League (WPL) 2025 has not yet taken place, Mumbai Indians won the inaugural WPL title in 2023. If the question contains a typo and refers to the 2023 season, then Mumbai Indians is the correct answer. If it's a hypothetical question about future dominance, Mumbai Indians, being the first champion, is a strong choice. Royal Challengers Bangalore won the WPL 2024 title.
The question asks to identify the Parthian ruler mentioned in the Takht-i-Bahi inscription. This requires knowledge of ancient Indian history, specifically the Indo-Parthian kingdom and associated epigraphic evidence.
Correct Option: A) Gondophernes