To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform Division and Multiplication from left to right, and then Addition and Subtraction from left to right.
Thus, the value of the expression is \(1145\).
D) 1145 — The calculation following the BODMAS rule correctly yields 1145.
The question asks to identify the RBI-constituted committee that studied issues and concerns in the Micro Finance Institutions (MFI) sector. This requires knowledge of various committees set up by the Reserve Bank of India and their respective mandates.
Correct Option: C) Y H Malegam committee
The Reserve Bank of India (RBI) constituted a Sub-Committee of its Central Board, under the chairmanship of Shri Y. H. Malegam, in October 2010. The committee's mandate was to study issues and concerns in the Micro Finance Institutions (MFI) sector, particularly in the context of the Andhra Pradesh crisis, and to recommend appropriate regulatory and supervisory measures.
To solve this problem, we need to compare the original positions of the digits with their new positions after arranging the digits in ascending order. We will list the original number, then sort its digits, and finally compare the positions digit by digit.
Original Number: \(5 \quad 3 \quad 8 \quad 4 \quad 9 \quad 7 \quad 2\)
Positions: \(\quad \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7\)
The digits in the number \(5384972\) are \(5, 3, 8, 4, 9, 7, 2\).
Arranging these digits in ascending order gives: \(2, 3, 4, 5, 7, 8, 9\).
New Number: \(\quad 2 \quad 3 \quad 4 \quad 5 \quad 7 \quad 8 \quad 9\)
Positions: \(\quad \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7\)
Only the digit \(3\) at position \(2\) remains in the same position.
Therefore, only one digit's position remains unchanged.
Correct Option: B) One
The question asks about the duration for which financial assistance is provided under the Maulana Azad Fellowship Scheme (MANF) for M.Phil. and Ph.D. studies. To answer this, one needs to recall the key features of the scheme, specifically its duration.
Correct Option: C) The Maulana Azad Fellowship Scheme (MANF) provides financial assistance for a 5-year period for M.Phil. and Ph.D. studies. This is the maximum duration for which the fellowship is granted.
This is a direction and distance problem. We need to track Punit's movements step-by-step, considering each turn and the distance covered. We will denote the initial unknown distance traveled north as \(x\). By analyzing the net displacement in the north-south direction, we can find the value of \(x\).
Initial Movement: Punit starts driving towards the north direction. Let the distance covered in this initial segment be \(x\) km.
First Turn: He turns left. Since he was going north, a left turn means he is now heading west. He drives 10 km in the west direction.
Second Turn: He again turns left. From west, a left turn means he is now heading south. He drives 20 km in the south direction.
Third Turn: He further takes a left turn. From south, a left turn means he is now heading east. He drives 10 km in the east direction.
Net Displacement Calculation:
East-West Displacement: He drove 10 km west and then 10 km east. These movements cancel each other out. So, the net displacement in the east-west direction is \(10 \text{ km (West)} - 10 \text{ km (East)} = 0 \text{ km}\).
North-South Displacement: He initially drove \(x\) km north and then 20 km south. The net displacement in the north-south direction is \(x \text{ km (North)} - 20 \text{ km (South)}\).
Final Position: The problem states that his present location is 10 km south of his starting point.
Formulating the Equation: The net north-south displacement must equal his final position relative to the starting point. Since his final position is 10 km south, we can write the equation:
\[ x \text{ (North)} - 20 \text{ (South)} = -10 \text{ (South)} \]Solving for \(x\):
\[ x - 20 = -10 \]\[ x = -10 + 20 \]\[ x = 10 \]So, Punit moved 10 km towards the north direction initially.
D) 10 km is the correct answer. The step-by-step calculation shows that the initial distance traveled north was 10 km for Punit to end up 10 km south of his starting point after the subsequent movements.
A) 18 km - This value would result in a different final position. If he moved 18 km north initially, his final position would be \(18 - 20 = -2\) km, meaning 2 km south, not 10 km south.
B) 20 km - If he moved 20 km north initially, his final position would be \(20 - 20 = 0\) km, meaning he would be at the same north-south level as his starting point, not 10 km south.
C) 15 km - If he moved 15 km north initially, his final position would be \(15 - 20 = -5\) km, meaning 5 km south, not 10 km south.
The problem requires us to apply specific letter transformation rules to the word "PAIR" and then arrange the resulting letters alphabetically. Finally, we need to identify the third letter from the right in the alphabetically ordered sequence.
C) J is the third letter from the right in the alphabetically arranged sequence B, J, O, Q.
This problem involves two trains moving towards each other. The key is to calculate the distance covered by the first train before the second train starts, then find the remaining distance, and finally use the concept of relative speed to determine the time taken for them to meet.
Calculate the head start distance: The first train starts from Chennai at 5:00 p.m. at 75 km/h. The second train starts from Trivandrum at 9:00 p.m. This means the first train travels for \(9:00 \text{ p.m.} - 5:00 \text{ p.m.} = 4\) hours before the second train starts.
Distance covered by the first train in 4 hours:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 75 \text{ km/h} \times 4 \text{ h} = 300 \text{ km} \]Calculate the remaining distance: The total distance between Chennai and Trivandrum is 915 km. After the first train covers 300 km, the remaining distance is:
\[ \text{Remaining Distance} = 915 \text{ km} - 300 \text{ km} = 615 \text{ km} \]Calculate the relative speed: Since the trains are moving towards each other, their speeds add up to give the relative speed.
Speed of first train = 75 km/h
Speed of second train = 60 km/h
\[ \text{Relative Speed} = 75 \text{ km/h} + 60 \text{ km/h} = 135 \text{ km/h} \]Calculate the time to meet: The time it takes for them to meet after 9:00 p.m. is the remaining distance divided by their relative speed.
\[ \text{Time to Meet} = \frac{\text{Remaining Distance}}{\text{Relative Speed}} = \frac{615 \text{ km}}{135 \text{ km/h}} \] \[ \text{Time to Meet} = \frac{615}{135} = \frac{41}{9} \text{ hours} \]Convert this fraction into hours and minutes:
\[ \frac{41}{9} \text{ hours} = 4 \frac{5}{9} \text{ hours} \]This is 4 hours and \(\frac{5}{9}\) of an hour.
Convert \(\frac{5}{9}\) of an hour to minutes:
\[ \frac{5}{9} \times 60 \text{ minutes} = \frac{300}{9} \text{ minutes} = \frac{100}{3} \text{ minutes} = 33 \frac{1}{3} \text{ minutes} \]This is 33 minutes and \(\frac{1}{3}\) of a minute.
Convert \(\frac{1}{3}\) of a minute to seconds:
\[ \frac{1}{3} \times 60 \text{ seconds} = 20 \text{ seconds} \]So, the time taken to meet is 4 hours, 33 minutes, and 20 seconds.
Determine the meeting time: The trains start moving towards each other effectively from 9:00 p.m. They meet 4 hours, 33 minutes, and 20 seconds later.
Meeting time = 9:00 p.m. + 4 hours 33 minutes 20 seconds = 01:33:20 a.m.
Correct Option: D) 01:33:20 a.m.
The question asks to identify the recipient of the 2020 Tenzing Norgay National Award for land adventure, who received it from then President Ram Nath Kovind during the 2021 National Sports Awards function. This requires knowledge of specific award recipients for a given year.
A) Priyanka Mangesh Mohite was indeed one of the 7 recipients of the 2020 Tenzing Norgay National Award for land adventure. She is a renowned Indian mountaineer known for scaling several high peaks, including Mount Annapurna I in 2021, becoming the first Indian woman to do so. She received this award for her significant contributions to land adventure sports.
An open water drum is in the form of a cylinder. The height of the drum is 7 m and its internal diameter is 21 m. Find the area (in m²) that needs to be painted if one wants to paint the inside of the drum.
(Take π = \( \frac{22}{7} \))
The problem asks for the area to be painted inside an open cylindrical water drum. Since the drum is open, only the inner curved surface and the inner base need to be painted. We need to calculate these two areas and sum them up.
The radius \(r\) is half of the diameter.
\[ r = \frac{D}{2} = \frac{21}{2} = 10.5 \text{ m} \]The formula for the curved surface area of a cylinder is \(2\pi rh\).
\[ \text{Curved Surface Area} = 2 \times \frac{22}{7} \times 10.5 \text{ m} \times 7 \text{ m} \\ \text{Curved Surface Area} = 2 \times 22 \times 10.5 \text{ m}^2 \\ \text{Curved Surface Area} = 44 \times 10.5 \text{ m}^2 \\ \text{Curved Surface Area} = 462 \text{ m}^2 \]Since the drum is open, there is no top. The base is a circle, and its area is given by \(\pi r^2\).
\[ \text{Base Area} = \frac{22}{7} \times (10.5 \text{ m})^2 \\ \text{Base Area} = \frac{22}{7} \times 10.5 \text{ m} \times 10.5 \text{ m} \\ \text{Base Area} = 22 \times 1.5 \text{ m} \times 10.5 \text{ m} \\ \text{Base Area} = 33 \times 10.5 \text{ m}^2 \\ \text{Base Area} = 346.5 \text{ m}^2 \]The total area to be painted is the sum of the curved surface area and the base area.
\[ \text{Total Area} = \text{Curved Surface Area} + \text{Base Area} \\ \text{Total Area} = 462 \text{ m}^2 + 346.5 \text{ m}^2 \\ \text{Total Area} = 808.5 \text{ m}^2 \]Correct Option: D) 808.5
To find the profit percentage, we need to calculate the total cost price (CP) and the total selling price (SP) of the apples. Since the man purchased an equal number of apples of each variety, we can assume a convenient number of apples (like the least common multiple of the quantities given in the rates) to simplify calculations. Then, we calculate the profit and express it as a percentage of the total cost price.
Calculate the Cost Price (CP) for Variety 1:
The rate for the first variety is Rs 2 for 3 apples. Let's assume the man purchased \(N\) apples of this variety. To make calculations easier, let \(N\) be a multiple of 3. Let's assume \(N = 3\) apples for Variety 1.
Cost of 3 apples of Variety 1 = Rs 2.
Calculate the Cost Price (CP) for Variety 2:
The rate for the second variety is Rs 1 per apple. Since he purchased an equal number of apples of each variety, he also purchased 3 apples of Variety 2.
Cost of 3 apples of Variety 2 = \(3 \times \text{Rs } 1 = \text{Rs } 3\).
Calculate the Total Cost Price (CP):
Total number of apples purchased = \(3 (\text{Variety 1}) + 3 (\text{Variety 2}) = 6\) apples.
Total Cost Price (CP) = Cost of Variety 1 + Cost of Variety 2
\[ \text{Total CP} = \text{Rs } 2 + \text{Rs } 3 = \text{Rs } 5 \]
Calculate the Total Selling Price (SP):
He sold all his apples at Rs 1 per apple. He has a total of 6 apples.
Total Selling Price (SP) = \(6 \times \text{Rs } 1 = \text{Rs } 6\).
Calculate the Profit:
Profit = Total SP - Total CP
\[ \text{Profit} = \text{Rs } 6 - \text{Rs } 5 = \text{Rs } 1 \]
Calculate the Profit Percentage:
Profit percentage is calculated as \[\left( \frac{\text{Profit}}{\text{Total CP}} \times 100 \right)\].
\[ \text{Profit Percentage} = \left( \frac{1}{5} \times 100 \right)\% = 20\% \]
Correct Option: B) 20%