The question asks to identify a game where an opponent is eliminated by touching them. We need to recall the basic rules of each game listed in the options.
Based on this analysis, Kho Kho is the game that fits the description.
Correct Option: A) Kho Kho is a traditional Indian tag game where players from the chasing team (chasers) try to tag and eliminate opponents from the defending team (runners) by touching them.
This problem involves calculating the mean of observations. We will use the formula for the mean, which is the sum of observations divided by the number of observations. We will first find the total sum of the initial observations, then the total sum after including new observations, and finally deduce the sum of the new observations to find their mean.
Calculate the sum of the initial 22 observations:
Given that the mean of 22 observations is 10.
The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]So, the sum of the initial 22 observations (\(S_{22}\)) can be calculated as:
\[ S_{22} = \text{Mean} \times \text{Number of observations} \]\[ S_{22} = 10 \times 22 = 220 \]
Calculate the sum of all observations after including two new ones:
Two more observations are included, so the total number of observations becomes \(22 + 2 = 24\).
The new mean of these 24 observations is 11.
The sum of these 24 observations (\(S_{24}\)) is:
\[ S_{24} = \text{New Mean} \times \text{New Number of observations} \]\[ S_{24} = 11 \times 24 = 264 \]
Calculate the sum of the two new observations:
The sum of the two new observations (\(S_{\text{new}}\)) is the difference between the total sum of 24 observations and the sum of the initial 22 observations.
\[ S_{\text{new}} = S_{24} - S_{22} \]
\[ S_{\text{new}} = 264 - 220 = 44 \]
Calculate the mean of the two new observations:
The mean of the two new observations is their sum divided by their number (which is 2).
\[ \text{Mean of new observations} = \frac{S_{\text{new}}}{\text{Number of new observations}} \]
\[ \text{Mean of new observations} = \frac{44}{2} = 22 \]
D) 22 is the correct mean of the two new observations.
The problem involves finding an angle given a relationship between the angle and its complement. We will use the definition of complementary angles, which states that two angles are complementary if their sum is 90 degrees. We will set up an algebraic equation based on the given information and solve for the unknown angle.
Correct Option: C) 50° is the greater angle, as calculated.
When two objects move in the same direction, their relative speed is the difference between their individual speeds. We can use this relative speed to calculate the time taken to achieve a certain distance apart.
Since they are moving in the same direction, the relative speed is the difference between their speeds. Manisha is faster, so her speed minus Neelam's speed will give the rate at which the distance between them increases.
\[ \text{Relative Speed} = S_M - S_N = 9 \text{ kmph} - 7 \text{ kmph} = 2 \text{ kmph} \]Using the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\), we can find the time it takes for them to be 12 km apart.
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{12 \text{ km}}{2 \text{ kmph}} = 6 \text{ hours} \]Correct Option: B) 6 hours
This problem involves the relationship between speed, distance, and time. Since the distance covered by the Delhi metro is constant, we can use the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) to find the distance and then calculate the new speed required to cover the same distance in a reduced time.
The initial time is given in minutes, so we need to convert it to hours for consistency with the speed unit (kmph).
\[ \text{Time}_1 = 40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours} \]Given the initial speed and time, we can find the total distance covered.
\[ \text{Speed}_1 = 48 \text{ kmph} \]\[ \text{Distance} = \text{Speed}_1 \times \text{Time}_1 \]\[ \text{Distance} = 48 \text{ kmph} \times \frac{2}{3} \text{ hours} \]\[ \text{Distance} = 16 \times 2 \text{ km} \]\[ \text{Distance} = 32 \text{ km} \]The desired new time is 32 minutes.
\[ \text{Time}_2 = 32 \text{ minutes} = \frac{32}{60} \text{ hours} = \frac{8}{15} \text{ hours} \]To find the speed required to cover the same distance (32 km) in the new time (32 minutes), we use the formula \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\).
\[ \text{Speed}_2 = \frac{\text{Distance}}{\text{Time}_2} \]\[ \text{Speed}_2 = \frac{32 \text{ km}}{\frac{8}{15} \text{ hours}} \]\[ \text{Speed}_2 = 32 \times \frac{15}{8} \text{ kmph} \]\[ \text{Speed}_2 = 4 \times 15 \text{ kmph} \]\[ \text{Speed}_2 = 60 \text{ kmph} \]A) 60 kmph is the correct speed required to reduce the journey time to 32 minutes.
To find the coefficient of variation (CV), we use its definition which relates the standard deviation to the mean of a distribution. The formula for the coefficient of variation is the ratio of the standard deviation to the mean, usually expressed as a percentage.
The mean of the distribution, denoted by \(\bar{x}\) or \(\mu\), is 13.
\[ \bar{x} = 13 \]
The standard deviation, denoted by \(\sigma\), is 7.
\[ \sigma = 7 \]
The coefficient of variation is given by the formula:
\[ \text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\% \]
Or, in symbols:
\[ \text{CV} = \frac{\sigma}{\bar{x}} \times 100\% \]
\[ \text{CV} = \frac{7}{13} \times 100\% \]
\[ \text{CV} = 0.5384615... \times 100\% \]
\[ \text{CV} \approx 53.85\% \]
C) 53.85% — This is the calculated value of the coefficient of variation.
The question asks about the primary force responsible for a car stopping when brakes are applied. We need to identify the force that opposes the motion of the car and brings it to rest.
Correct Option: C) Frictional — When brakes are applied, the brake pads create friction with the brake discs/drums, which slows down the wheels. Simultaneously, the static friction between the tires and the road surface provides the necessary force to decelerate the entire vehicle, bringing it to a stop. This is the primary force responsible for stopping the car.
We need to analyze the given statements and determine which of the conclusions logically follows from them. This involves understanding the definitions and relationships presented in the statements and checking if the conclusions are direct inferences.
Correct Option: B) Only conclusion II follows.
This question requires us to analyze the given statements and determine which of the conclusions logically follow from them. We need to evaluate each conclusion based on the information provided in the statements, without introducing outside knowledge.
A) Only conclusion I follows. Conclusion I directly infers from the statements that depleting resources (specifically energy resources due to population burden) will impact the quality of life, as stated in Statement 2 and supported by Statement 1.
The question asks for the chemical composition of quartz, specifically the type used in clocks. This requires knowledge of common minerals and their chemical formulas.
Correct Option: B) Silicon dioxide
Quartz is a mineral composed of silicon and oxygen atoms in a continuous framework of \(\text{SiO}_4\) silicon-oxygen tetrahedra, with each oxygen atom being shared between two tetrahedra. This gives an overall chemical formula of \(\text{SiO}_2\), which is silicon dioxide. Its piezoelectric property, where it generates an electric charge when subjected to mechanical stress and vice-versa, makes it ideal for use in quartz clocks and watches to maintain precise time.