The question asks us to identify the relationship between the first pair of terms and apply the same relationship to the second pair. The first pair is "Sun : Earth". We need to find a term that relates to "Moon" in the same way.
Correct Option: B) Earth. The relationship is that the Sun is orbited by the Earth (a planet), and the Moon orbits the Earth (a planet). Alternatively, the Sun is the central body for Earth, and Earth is the central body for the Moon.
The question asks to identify the specific book written by Ernest Mackay concerning his archaeological work, particularly at Mohenjo-daro. This requires knowledge of prominent archaeological publications related to the Indus Valley Civilization.
D) Further Excavations at Mohenjo-daro — Ernest Mackay authored the seminal work titled "Further Excavations at Mohenjo-daro" which was published in 1938. This two-volume publication detailed his extensive archaeological findings and interpretations from the site of Mohenjo-daro, providing crucial insights into the Indus Valley Civilization.
This is a syllogism problem that can be solved using Venn diagrams or by applying rules of logical deduction. We need to determine which conclusions logically follow from the given statements.
Analyze Statement 1: All chocolates are candies.
This means that the set of 'chocolates' is entirely contained within the set of 'candies'. If we draw a Venn diagram, the circle for chocolates would be inside the circle for candies.
Analyze Statement 2: All candies are toffees.
This means that the set of 'candies' is entirely contained within the set of 'toffees'. In a Venn diagram, the circle for candies would be inside the circle for toffees.
Combine the statements:
From statement 1, we have: Chocolates \(\subset\) Candies.
From statement 2, we have: Candies \(\subset\) Toffees.
Combining these, we get: Chocolates \(\subset\) Candies \(\subset\) Toffees. This implies that the set of 'chocolates' is also entirely contained within the set of 'toffees'.
Evaluate Conclusion 1: All chocolates are toffees.
Based on our combined analysis (Chocolates \(\subset\) Toffees), this conclusion logically follows. If all chocolates are candies, and all candies are toffees, then it must be true that all chocolates are toffees.
Evaluate Conclusion 2: All toffees are chocolates.
This conclusion does not logically follow. While all chocolates are toffees, it does not mean that all toffees are chocolates. There can be toffees that are not candies, and therefore not chocolates. For example, if there are 10 chocolates, 20 candies (including the 10 chocolates), and 30 toffees (including the 20 candies), then not all 30 toffees are chocolates (only 10 are). This is a common fallacy of reversing the implication.
Correct Option: A) Only conclusion 1 follows.
The question asks about a fundamental discovery in biology and the scientist credited with it. We need to recall the contributions of Robert Hooke to cellular biology.
Correct Option: C) Robert Hooke discovered the Cell in 1665 while observing cork under a microscope.
This problem involves the relationship between mean, median, and mode, which are measures of central tendency. For a moderately skewed distribution, there's an empirical relationship known as the "Empirical Formula" or "Karl Pearson's Empirical Formula" that connects these three measures. We will use this formula to find the required ratio.
Recall the Empirical Formula:
For a moderately skewed distribution, the relationship between mean, median, and mode is given by:
Given Ratio:
We are given that the ratio of mean and median is \(4:5\). Let's denote Mean as \(M_e\) and Median as \(M_d\).
Express Median in terms of Mean:
From the given ratio, we can write:
Substitute into the Empirical Formula:
Now, substitute the expression for \(M_d\) into the empirical formula:
Simplify the expression for Mode:
To simplify, find a common denominator:
Find the ratio of Mean and Mode:
We need to find the ratio of Mean to Mode, which is \(\frac{M_e}{\text{Mode}}\).
State the ratio:
The ratio of its mean and mode is \(4:7\).
Correct Option: D) 4 : 7
This question tests knowledge about blood groups and their compatibility for transfusions. The concept of a "universal recipient" refers to a blood group that can safely receive blood from any other blood group without an adverse immune reaction. This is determined by the presence or absence of specific antigens on red blood cells and antibodies in the plasma.
Correct Option: B) AB+
Individuals with AB+ blood are considered universal recipients because their red blood cells have both A and B antigens, and the Rh antigen. Crucially, their plasma does not contain anti-A, anti-B, or anti-Rh antibodies. This means they can receive red blood cells from any ABO and Rh type without causing an immune reaction.
To find the sum of all numbers between 100 and 200 that are divisible by 12, we first need to identify these numbers. These numbers form an arithmetic progression (AP). We will find the first term, the last term, and the number of terms in this AP. Then, we will use the formula for the sum of an arithmetic progression.
The first number greater than 100 that is divisible by 12 can be found by dividing 100 by 12:
\[ 100 \div 12 = 8 \text{ with a remainder of } 4 \]This means \(12 \times 8 = 96\). The next multiple of 12 is \(12 \times 9 = 108\). So, the first term \(a = 108\).
The last number less than 200 that is divisible by 12 can be found by dividing 200 by 12:
\[ 200 \div 12 = 16 \text{ with a remainder of } 8 \]This means \(12 \times 16 = 192\). So, the last term \(l = 192\).
The terms form an arithmetic progression: 108, 120, ..., 192. The common difference \(d = 12\).
Using the formula for the \(n\)-th term of an AP, \(l = a + (n-1)d\):
\[ 192 = 108 + (n-1)12 \] \[ 192 - 108 = (n-1)12 \] \[ 84 = (n-1)12 \] \[ \frac{84}{12} = n-1 \] \[ 7 = n-1 \] \[ n = 7 + 1 \] \[ n = 8 \]There are 8 numbers between 100 and 200 that are divisible by 12.
The sum of an arithmetic progression is given by the formula:
\[ S_n = \frac{n}{2}(a + l) \]Substitute the values of \(n\), \(a\), and \(l\):
\[ S_8 = \frac{8}{2}(108 + 192) \] \[ S_8 = 4(300) \] \[ S_8 = 1200 \]Correct Option: D) 1200
If \(\sqrt{4624}\) = 68, then the value of:
\(\sqrt{46.24}\) + \(\sqrt{0.4624}\)+ \(\sqrt{0.004624}\)
The problem asks us to calculate the sum of three square roots: \(\sqrt{46.24}\), \(\sqrt{0.4624}\), and \(\sqrt{0.004624}\). We are given that \(\sqrt{4624} = 68\). We can use this information to find the values of the individual square roots by adjusting the decimal places.
Calculate \(\sqrt{46.24}\):
We know that \(\sqrt{4624} = 68\).
To find \(\sqrt{46.24}\), we can write \(46.24\) as \(\frac{4624}{100}\).
So, \[\sqrt{46.24} = \sqrt{\frac{4624}{100}} = \frac{\sqrt{4624}}{\sqrt{100}} = \frac{68}{10} = 6.8\].
Calculate \(\sqrt{0.4624}\):
To find \(\sqrt{0.4624}\), we can write \(0.4624\) as \(\frac{4624}{10000}\).
So, \[\sqrt{0.4624} = \sqrt{\frac{4624}{10000}} = \frac{\sqrt{4624}}{\sqrt{10000}} = \frac{68}{100} = 0.68\].
Calculate \(\sqrt{0.004624}\):
To find \(\sqrt{0.004624}\), we can write \(0.004624\) as \(\frac{4624}{1000000}\).
So, \[\sqrt{0.004624} = \sqrt{\frac{4624}{1000000}} = \frac{\sqrt{4624}}{\sqrt{1000000}} = \frac{68}{1000} = 0.068\].
Sum the calculated values:
Now, we need to add the three values we found:
\(6.8 + 0.68 + 0.068\)
\(6.800\)
\(0.680\)
+ \(0.068\)
----------
\(7.548\)
The sum is \(7.548\).
B) 7.548 — The step-by-step calculation shows that the sum of the three square roots is \(7.548\).
The question asks to identify the Viceroy of India who took the initiative to create elected local government bodies. This requires knowledge of the administrative reforms undertaken by various Viceroys during British rule in India, specifically focusing on local self-government.
D) Lord Ripon
Lord Ripon (1880-1884) is widely regarded as the 'Father of Local Self-Government in India'. His Resolution of 1882 on Local Self-Government was a landmark step. It advocated for the establishment of local boards (district and sub-district level) consisting largely of non-official members, who were to be elected. This initiative aimed at decentralization of administration and political education of the people, laying the foundation for modern municipal administration in India.
The problem involves ratios of fares and ratios of the number of passengers for different modes of transportation (train, bus, air). We need to find the total fare collected from air passengers given the total fare collected from all modes of transportation. We will use the given ratios to determine the relative contribution of each mode to the total fare collected.
B) ₹60,000 is the total fare collected from the air passengers.