The question asks to identify the scientist credited with discovering the fundamental laws of inheritance. This requires knowledge of key figures in the history of genetics.
Correct Option: D) Gregor Mendel is widely recognized as the "Father of Genetics" for his pioneering work on pea plants. He discovered the fundamental laws of inheritance: the Law of Segregation, the Law of Independent Assortment, and the Law of Dominance. His findings, though initially overlooked, were rediscovered in the early 20th century and became the cornerstone of modern genetics.
To solve this problem, we first need to calculate the original cost price (CP) of the TV set using the given selling price (SP) and profit percentage. Then, we will calculate the new production cost by increasing the original CP by 15%. Finally, we will determine the new selling price required to achieve a 15% profit on this new production cost.
Calculate the original Cost Price (CP):
Given:
The formula for SP with profit is: \[\text{SP} = \text{CP} \times (1 + \frac{\text{Profit Percentage}}{100})\]
So, \(24750 = \text{CP} \times (1 + \frac{10}{100})\)
\(24750 = \text{CP} \times (1 + 0.10)\)
\(24750 = \text{CP} \times 1.10\)
Therefore,
\[ \text{CP} = \frac{24750}{1.10} = 22500 \]
The original Cost Price is ₹22,500.
Calculate the new production cost:
The production cost is increased by 15%.
New Production Cost = Original CP + 15% of Original CP
\[ \text{New Production Cost} = 22500 + \left( \frac{15}{100} \times 22500 \right) \]
\[ \text{New Production Cost} = 22500 + (0.15 \times 22500) \]
\[ \text{New Production Cost} = 22500 + 3375 \]
\[ \text{New Production Cost} = 25875 \]
The new production cost is ₹25,875.
Calculate the new Selling Price (SP) for a 15% profit:
We want to gain a profit of 15% on the new production cost.
New SP = New Production Cost \[\times (1 + \frac{\text{Desired Profit Percentage}}{100})\]
\[ \text{New SP} = 25875 \times \left(1 + \frac{15}{100}\right) \]
\[ \text{New SP} = 25875 \times (1 + 0.15) \]
\[ \text{New SP} = 25875 \times 1.15 \]
\[ \text{New SP} = 29756.25 \]
The new selling price should be ₹29,756.25.
Correct Option: B) ₹29,756.25
The question asks to identify one of the leaders of the Khilafat Movement. This requires knowledge of prominent figures associated with this historical movement in India.
Correct Option: D) Shaukat Ali was one of the prominent leaders of the Khilafat Movement, along with his brother Maulana Mohammad Ali Jauhar. They are collectively known as the 'Ali Brothers' and played a crucial role in organizing and leading the movement in India.
The question asks to identify the odd one out from a given list of celestial bodies. To solve this, we need to categorize each item and find the one that doesn't fit the category of the others.
A) Iapetus is a moon of Saturn, whereas Venus, Mars, and Jupiter are all planets.
This question asks to arrange the life stages of an insect undergoing complete metamorphosis in a meaningful, chronological order. Complete metamorphosis involves four distinct stages: egg, larva, pupa, and adult (imago).
Therefore, the correct sequence is Egg \(\to\) Larva \(\to\) Pupa \(\to\) Imago.
Correct Option: C) D \(\to\) C \(\to\) A \(\to\) B
The question asks to identify India's first dedicated astronomy mission designed for simultaneous multi-wavelength observations (X-ray, optical, UV). This requires knowledge of India's space missions, specifically those related to astronomy.
Correct Option: B) AstroSat is indeed India's first dedicated astronomy mission. Launched by ISRO in 2015, it is designed to study celestial sources in X-ray, optical, and UV spectral bands simultaneously. It carries five primary payloads for this purpose, making it a unique multi-wavelength observatory.
The question asks for the correct full form of the acronym MPEG. This is a common acronym in the field of digital media and computer science, often encountered in competitive exams. The approach is to recall the standard full form of MPEG.
Correct Option: C) Moving Picture Experts Group is the correct full form of MPEG. It refers to a working group of experts formed by ISO and IEC to set standards for audio and video compression and transmission.
To find the difference between the median and mode of the given data, we first need to arrange the data in ascending order. Then, we will identify the median (the middle value) and the mode (the most frequently occurring value). Finally, we will calculate their difference.
The given data set is: 2, 3, 5, 7, 2, 3, 3, 5, 7, 9.
Arranging it in ascending order, we get:
2, 2, 3, 3, 3, 5, 5, 7, 7, 9
The median is the middle value of a data set when it is ordered. Since there are 10 data points (an even number), the median will be the average of the two middle values.
The number of data points \(n = 10\).
The middle terms are the \((\frac{n}{2})\)-th term and the \((\frac{n}{2} + 1)\)-th term.
Here, the \((\frac{10}{2})\)-th term is the 5th term, which is 3.
And the \((\frac{10}{2} + 1)\)-th term is the 6th term, which is 5.
The median is the average of these two terms:
\[ \text{Median} = \frac{5\text{th term} + 6\text{th term}}{2} = \frac{3 + 5}{2} = \frac{8}{2} = 4 \]The mode is the value that appears most frequently in the data set.
In the ordered data set (2, 2, 3, 3, 3, 5, 5, 7, 7, 9):
The value 3 appears most frequently (3 times).
So, the Mode is 3.
Difference = Median - Mode
\[ \text{Difference} = 4 - 3 = 1 \]D) 1 — The median of the data is 4 and the mode is 3. Their difference is \(4 - 3 = 1\).
This is a blood relation problem. We need to break down the statement made by Raman step-by-step to establish the relationship between the lady and Raman.
B) Wife's father's sister: As derived, the lady's only brother is Raman's wife's father, making the lady the sister of Raman's wife's father.
This problem involves successive percentage decreases. When an amount is decreased by a certain percentage, and then the new amount is decreased by another percentage, the total percentage decrease is not simply the sum of the individual percentages. We need to calculate the effect of each decrease sequentially on the current value of the expenses.
Assume an initial expense: Let the initial expenses be \(P\). For simplicity in percentage calculations, it's often helpful to assume \(P = 100\).
Calculate the first decrease: Sohan decreased his expenses by 25%.
\[ \text{First decrease} = 25\% \text{ of } P = 0.25P \]New expenses after the first decrease:
\[ \text{Expenses}_1 = P - 0.25P = 0.75P \]If \(P = 100\), then \(\text{Expenses}_1 = 0.75 \times 100 = 75\).
Calculate the second decrease: He then decreased them further by 10%. This 10% decrease is applied to the new expenses (\(\text{Expenses}_1\)), not the original expenses (\(P\)).
\[ \text{Second decrease} = 10\% \text{ of } \text{Expenses}_1 = 0.10 \times (0.75P) = 0.075P \]Final expenses after the second decrease:
\[ \text{Expenses}_2 = \text{Expenses}_1 - 0.10 \times \text{Expenses}_1 = 0.90 \times \text{Expenses}_1 \] \[ \text{Expenses}_2 = 0.90 \times (0.75P) = 0.675P \]If \(P = 100\), then \(\text{Expenses}_2 = 0.675 \times 100 = 67.5\).
Calculate the total percentage decrease: The total decrease is the difference between the initial expenses and the final expenses, expressed as a percentage of the initial expenses.
\[ \text{Total decrease} = P - \text{Expenses}_2 = P - 0.675P = 0.325P \]Percentage decrease:
\[ \text{Percentage decrease} = \frac{\text{Total decrease}}{P} \times 100\% \] \[ \text{Percentage decrease} = \frac{0.325P}{P} \times 100\% = 0.325 \times 100\% = 32.5\% \]Alternatively, using \(P=100\):
\[ \text{Percentage decrease} = \frac{100 - 67.5}{100} \times 100\% = \frac{32.5}{100} \times 100\% = 32.5\% \]A) The total percentage decrease is 32.5%.