The problem asks us to find the mode of a data set given its mean and median, using the empirical relation between these three measures of central tendency. The empirical relation states that for a moderately skewed distribution, the relationship between mean, median, and mode is approximately given by:
\[ \text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean} \]We will substitute the given values of mean and median into this formula to calculate the mode.
A) 62 is the correct answer. By applying the empirical formula relating mean, median, and mode, we calculated the mode to be 62.
The problem involves decoding a pattern in a given code language. We need to identify the rule applied to transform the letters of the given words and then apply the same rule to the target word.
A) NFMLC is the correct option as derived by applying the consistent pattern of subtracting 2 from the alphabetical position of each letter.
Muscle cramps are involuntary and painful contractions of muscles. Understanding the physiological processes involved in muscle contraction and relaxation helps identify the primary cause of cramps. We will analyze each option to determine its relevance to muscle cramps.
Correct Option: B) Insufficiency of oxygen supply to muscles
When muscles are overused or exercised intensely, the oxygen supply may not be sufficient to meet the metabolic demands. This forces the muscles to switch to anaerobic respiration, producing lactic acid. The accumulation of lactic acid, along with other metabolic byproducts, can lead to muscle fatigue, pain, and involuntary contractions known as cramps.
The question asks to identify the part of the human excretory system that connects the kidney to the urinary bladder. This requires knowledge of the basic anatomy and function of the urinary system.
C) Ureters are the tubes that carry urine from the kidneys to the urinary bladder. This perfectly matches the function described in the question.
The surface area (in cm²) of a sphere of radius 14 cm is: Take π=\( \frac{22}{7} \)
To find the surface area of a sphere, we use the standard formula for the surface area of a sphere, which is \(4\pi r^2\), where \(r\) is the radius of the sphere. We are given the radius and the value of \(\pi\).
A) 2464 — The calculated surface area of the sphere is \(2464 \text{ cm}^2\), which matches this option.
The problem involves finding the total profit of a company given the ratio of profit distribution among three partners and the difference between the smallest and largest shares. We will use the concept of ratios to represent the shares and then use the given difference to find the value of one unit of the ratio, which will allow us to calculate the total profit.
Represent the shares: Let the shares of the three partners be \(1x\), \(3x\), and \(5x\), where \(x\) is a common multiplier for the ratio.
Identify the smallest and largest shares: The smallest share is \(1x\) and the largest share is \(5x\).
Use the given difference: The difference between the largest and smallest share is Rs 80,000. So, we can write the equation:
\[ 5x - 1x = 80,000 \]Solve for \(x\):
\[ 4x = 80,000 \]\[ x = \frac{80,000}{4} \]\[ x = 20,000 \]Calculate the total profit: The total profit is the sum of all shares, which is \(1x + 3x + 5x\).
\[ \text{Total Profit} = (1 + 3 + 5)x \]\[ \text{Total Profit} = 9x \]Substitute the value of \(x\):
\[ \text{Total Profit} = 9 \times 20,000 \]\[ \text{Total Profit} = 180,000 \]Thus, the total profit of the company is Rs 1,80,000.
Correct Option: B) 1,80,000As calculated, the total profit is Rs 1,80,000.
The question asks about the purpose of different-coloured dustbins, specifically the blue one, provided by municipalities for waste collection. This is a common practice in urban waste management to facilitate segregation at the source. Understanding the standard colour codes for waste segregation is key to answering this question.
C) reusable wastes. In many waste segregation systems, particularly in India, blue dustbins are designated for dry waste, which includes recyclable and reusable materials such as plastic, paper, metal, and glass. This helps in efficient recycling and resource recovery.
To find the total resistance of the circuit, we need to determine how the components are connected. Since the problem states that an electric bulb and a conductor are connected to a battery without specifying parallel connection, it is assumed they are connected in series. In a series circuit, the total resistance is the sum of individual resistances.
The voltage of the battery (10 V) is additional information not required to calculate the total resistance of the circuit, but it would be needed if the total current or power were asked.
C) 50 Ω — The total resistance in a series circuit is the sum of the individual resistances, which is \(40 \, \Omega + 10 \, \Omega = 50 \, \Omega\).
The problem asks us to find a relationship between pairs of numbers. We need to identify a pattern that connects the first number to the second, and the third number to the fourth. Once this pattern is established, we apply it to the fifth number to find the missing sixth number.
D) 64 — The pattern observed is that the second number is the square of (the first number plus one). For the pair \(3 : 16\), \( (3+1)^2 = 4^2 = 16 \). For the pair \(5 : 36\), \( (5+1)^2 = 6^2 = 36 \). Applying this to \(7 : ?\), we get \( (7+1)^2 = 8^2 = 64 \).
To determine the location of the principal focus of a convex mirror, we need to recall the definition of the principal focus and how light rays interact with a convex mirror.
Correct Option: D) behind the mirror