The volume (in cu.cm.) of a right circular cylinder with radius 1 cm and height 2 cm is: (Take π = \( \frac{22}{7} \))
To find the volume of a right circular cylinder, we use the standard formula for the volume of a cylinder, which is the area of its base multiplied by its height. The base is a circle, so its area is given by \( \pi r^2 \). We are given the radius and height, and a value for \( \pi \).
Correct Option: D) The calculated volume is \( \frac{44}{7} \) cu.cm.
This is a syllogism problem. We need to evaluate the given conclusions based on the provided statements, treating the statements as absolutely true, even if they contradict common knowledge. We can use Venn diagrams to visualize the relationships between the categories (Kings, Queens, Beautiful people) and determine which conclusions logically follow.
B) Neither Conclusion I nor II follows.
This problem involves substituting new meanings for mathematical operators and then evaluating the expression according to the order of operations (BODMAS/PEMDAS).
The original expression is \(20 \times 8 \div 8 - 4 + 2\).
Applying the substitutions:
So, the new expression is \(20 + 8 - 8 \div 4 \times 2\).
BODMAS/PEMDAS stands for Brackets, Orders (powers/roots), Division/Multiplication (from left to right), Addition/Subtraction (from left to right).
The expression is \(20 + 8 - 8 \div 4 \times 2\).
A) 24 is the correct answer, as derived by correctly substituting the operators and following the order of operations.
The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 is:
\( \frac{49}{7} \)
\( \frac{19}{7} \)
\( \frac{50}{7} \)
\( \frac{18}{7} \)
To find the mean deviation of a given set of data, we first need to calculate the mean of the data. Then, we find the absolute difference between each data point and the mean. Finally, we calculate the average of these absolute differences.
List the data points:
The given data is: \(3, 10, 10, 4, 7, 10, 5\).
Calculate the mean (\(\bar{x}\)) of the data:
The mean is the sum of all data points divided by the number of data points.
\[ \bar{x} = \frac{\sum x_i}{n} = \frac{3 + 10 + 10 + 4 + 7 + 10 + 5}{7} \]\[ \bar{x} = \frac{49}{7} = 7 \]Calculate the absolute deviations from the mean:
For each data point \(x_i\), calculate \(|x_i - \bar{x}|\).
Sum the absolute deviations:
Sum of absolute deviations \( = 4 + 3 + 3 + 3 + 0 + 3 + 2 = 18\).
Calculate the Mean Deviation (MD):
The mean deviation is the sum of the absolute deviations divided by the number of data points.
\[ \text{MD} = \frac{\sum |x_i - \bar{x}|}{n} = \frac{18}{7} \]D) \( \frac{18}{7} \) is the correct mean deviation calculated from the given data.
This is a blood relations problem. We need to trace the relationships described in the statement to find out how Anitha is related to the man in the photograph. We will break down the statement into smaller parts and establish the connections.
Correct Option: B) Niece
The question asks for the enactment year of the Environment (Protection) Act of India. This requires knowledge of key environmental legislation in India and their historical context.
Correct Option: B) 1986
The Environment (Protection) Act (EPA) was enacted by the Parliament of India in 1986. This Act was a direct outcome of the Bhopal Gas Tragedy and was designed to provide a general framework for environmental protection and improvement, coordinating the activities of various central and state authorities established under other laws.
The problem involves calculating the total distance traveled when an object covers equal distances at different speeds and the total time taken is given. We can use the relationship between distance, speed, and time (\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)) for each segment of the journey and sum the times to find the total time. Since the distances are equal, we can represent each segment's distance by a variable and solve for it.
Since speeds are in km/hr, we convert the total time from minutes to hours:
\[ T_{\text{total}} = 15.5 \text{ minutes} = \frac{15.5}{60} \text{ hours} = \frac{31}{120} \text{ hours} \]The time taken for each segment is:
The sum of the times for each segment must equal the total time:
\[ T_1 + T_2 + T_3 = T_{\text{total}} \] \[ \frac{D}{10} + \frac{D}{30} + \frac{D}{8} = \frac{31}{120} \]Find a common denominator for 10, 30, and 8, which is 120.
\[ \frac{12D}{120} + \frac{4D}{120} + \frac{15D}{120} = \frac{31}{120} \]Combine the terms on the left side:
\[ \frac{12D + 4D + 15D}{120} = \frac{31}{120} \] \[ \frac{31D}{120} = \frac{31}{120} \]Multiply both sides by 120:
\[ 31D = 31 \]Divide by 31:
\[ D = 1 \text{ km} \]Since Vishnu traveled three equal distances of \(D\) km each, the total distance is \(3D\).
\[ \text{Total Distance} = 3 \times D = 3 \times 1 = 3 \text{ km} \]Correct Option: B) 3
The question asks to identify the city that topped the 'Swachh Survekshan-2016' rankings. This requires knowledge of the results of the Swachh Survekshan survey conducted in 2016.
B) Mysore: Mysore topped the 'Swachh Survekshan-2016' rankings, being declared the cleanest city among the 73 cities surveyed.
This is a work and time problem. We need to determine the individual work rate of Kamal based on the combined work rate and the efficiency ratio between Ehsaan and Kamal. Once Kamal's work rate is known, we can calculate the time he would take to complete the work alone.
Let Kamal's one day's work be \(x\).
The problem states that Ehsaan is twice as good a worker as Kamal. This means Ehsaan's work rate is twice Kamal's work rate. So, Ehsaan's one day's work is \(2x\).
Together, Ehsaan and Kamal finish the work in 29 days. This means their combined one day's work is \(\frac{1}{29}\) of the total work.
The sum of their individual one day's work should equal their combined one day's work:
\[ x + 2x = \frac{1}{29} \]Combine the terms on the left side:
\[ 3x = \frac{1}{29} \]Solve for \(x\), which represents Kamal's one day's work:
\[ x = \frac{1}{3 \times 29} \]\[ x = \frac{1}{87} \]Kamal's one day's work is \(\frac{1}{87}\) of the total work. This implies that Kamal, working alone, will finish the entire work in 87 days.
Correct Option: C) 87
The question asks for the specific name of a semi-luxury train launched by IRCTC in 2015, covering Jaisalmer, Jodhpur, and Jaipur. This requires knowledge of specific IRCTC tourism initiatives.
C) Desert Circuit — The IRCTC launched the "Desert Circuit" train in 2015 as a semi-luxury service connecting key tourist destinations in Rajasthan, including Jaisalmer, Jodhpur, and Jaipur. This name accurately reflects the geographical and thematic focus of the train.