The problem asks us to identify a set of three numbers that follow the same relationship as the given sets: (144, 12, 6) and (210, 15, 7). We need to find a mathematical operation or pattern connecting the three numbers in each set.
Let the numbers be \(A\), \(B\), and \(C\). So, \(A = 144\), \(B = 12\), \(C = 6\).
We look for a relationship between \(A\), \(B\), and \(C\). Let's try operations involving \(B\) and \(C\) to get \(A\).
If the relationship is \(A = B^2\), then \(C\) seems to be extra. Let's see if \(C\) is related to \(B\).
Let's combine these observations. The relationship could be:
Let's verify this pattern with the second given set.
Here, \(A = 210\), \(B = 15\), \(C = 7\).
Let's re-evaluate the relationship for the first set. What if the relationship involves all three numbers in a different way?
Consider the product of the second and third numbers, and then some operation on that product.
So, the pattern could be: \(A = (B \times C) \times 2\).
Let's verify this pattern with the second given set.
This matches the first number \(A = 210\). So, the established relationship is: The first number is equal to twice the product of the second and third numbers, i.e., \(A = 2 \times B \times C\).
A) (96, 8, 6)
The question asks to identify the specific book for which Gaurav Pandey received the Sahitya Akademi Yuva Puraskar in 2024. This requires knowledge of recent literary awards and their recipients.
Gaurav Pandey was indeed awarded the Sahitya Akademi Yuva Puraskar in 2024 for his Hindi poetry collection.
The specific book for which Gaurav Pandey won the Sahitya Akademi Yuva Puraskar in 2024 is titled "Smritiyon Ke Beech Ghiri Hai Prithvi" (स्मृतियों के बीच घिरी है पृथ्वी).
A) Smritiyon Ke Beech Ghiri Hai Prithvi — This is the correct title of the Hindi poetry collection by Gaurav Pandey that won the Sahitya Akademi Yuva Puraskar in 2024.
The question asks for the raw material used in the preparation of calcium sulphate hemihydrate, commonly known as Plaster of Paris. This involves recalling the chemical process for its manufacturing.
C) Gypsum — Gypsum (calcium sulphate dihydrate) is the direct precursor to calcium sulphate hemihydrate (Plaster of Paris) through a controlled heating process.
The problem presents a numerical series, and we need to find the missing term. We will analyze the differences between consecutive terms to identify a pattern. If the first differences do not reveal a clear pattern, we will look at the second differences.
7, 15, 24, 34, 45, ?
The differences are 8, 9, 10, 11. This is an arithmetic progression where each subsequent difference increases by 1.
Following the pattern, the next difference should be \(11 + 1 = 12\).
Add the next difference to the last known term in the series:
\[ \text{Missing Term} = 45 + 12 = 57 \]C) 57 — The pattern of differences between consecutive terms is an arithmetic progression (8, 9, 10, 11, ...). The next difference is 12, so the next term is \(45 + 12 = 57\).
This is a coding-decoding problem where letters are assigned specific numerical codes. We need to identify the code for a particular letter by comparing the given coded words.
The word 'NICE' is coded as '2468'.
The word 'CARS' is coded as '1235'.
The letter 'C' is present in both words.
This indicates that the coding is not a direct, fixed mapping for each letter across all words. Instead, it's a positional coding within each word, or there's an error in the question's premise if it expects a single, universal code for 'C'. However, in competitive exams, if a letter appears in multiple coded words with different codes, it usually means we need to find a consistent pattern or identify if one of the codes is the intended one based on the options. Let's re-examine the question and options.
Upon re-evaluation, the question asks for the code for 'C' in the given code language. This implies a consistent mapping. The discrepancy (C=6 in NICE, C=1 in CARS) suggests that the question might be flawed or it's a trick. However, if we assume a direct mapping from the first instance of 'C' encountered in the options or the most straightforward interpretation, we look at the options.
Let's consider the possibility that the question intends for us to pick one of the codes associated with 'C' from the given information. The options are 2, 1, 5, 6.
Both '1' and '6' are available as options. This is a poorly constructed question if it expects a unique answer. However, if we look at the provided correct answer, it is 'A) 2'. Neither '1' nor '6' is '2'. This implies there might be a misunderstanding of the problem or a typo in the question or the provided correct answer.
Let's assume there's a typo in the question and the intended code for 'NICE' was something like '2418' or 'CARS' was '6235' to make 'C' consistent. Without that, we cannot definitively determine a unique code for 'C'.
However, if we strictly follow the provided correct answer (A) which is '2', we need to find how 'C' could be '2'.
The letter 'A' is coded as '2' in 'CARS'. The letter 'N' is coded as '2' in 'NICE'. The letter 'C' is never coded as '2' in the given information.
Given the provided solution 'A) 2', it suggests that the question might have intended to ask for the code of 'A' or 'N', or there's a significant error in the question's data or the provided correct answer. If we are forced to choose '2' as the answer for 'C', it contradicts the given coding schemes.
Let's re-examine the problem assuming a direct positional mapping and that the question is well-formed, and there might be a common letter that gives the answer '2'.
If the question intended to ask for the code of 'A', then 'A' is coded as '2' in 'CARS'. This matches option A.
If the question intended to ask for the code of 'N', then 'N' is coded as '2' in 'NICE'. This also matches option A.
Since the question explicitly asks for 'C', and 'C' is coded as '6' in 'NICE' and '1' in 'CARS', and neither of these is '2', there is a clear inconsistency. However, in competitive exams, sometimes questions have errors. If we must pick an option, and the provided correct answer is A (2), it implies that '2' is the code for some letter that the question *intended* to ask about, or there's a pattern not immediately obvious.
Without further information or clarification, and given the options and the provided correct answer, the most plausible scenario is that the question contains a typo and was meant to ask for the code of 'A' or 'N', both of which are coded as '2'. Since the question asks for 'C', and '2' is the correct option, it implies a flawed question where 'C' is somehow meant to be '2'.
However, if we strictly follow the provided data:
Neither of these is 2. Therefore, based on the given data, the code for 'C' cannot be '2'. There seems to be an error in the question or the provided answer key.
Assuming the question is flawed and the intended answer is '2' for some other letter (like 'A' or 'N'):
If the question intended to ask for 'N' or 'A', then '2' would be the correct answer. Since the question asks for 'C' and the correct option is 'A', we must conclude there's an error in the question's premise or the provided answer.
Let's proceed with the assumption that the question is flawed and the intended answer is '2', possibly for a different letter.
Correct Option: A) 2
Based on the provided information:
The letter 'C' is coded as '6' in 'NICE' and '1' in 'CARS'. Neither of these is '2'. However, if we assume there is a typo in the question and it was meant to ask for the code of 'A' or 'N', then '2' would be the correct answer. Given that 'A' is the correct option and its value is '2', this indicates a likely error in the question itself, where 'C' is incorrectly stated instead of 'A' or 'N'.
The question asks for India's unemployment rate in June 2024 as reported by the Centre for Monitoring Indian Economy (CMIE). This requires knowledge of recent economic data from a specific source.
D) 9.2% — According to CMIE data, India's unemployment rate in June 2024 was 9.2%. This is a key economic indicator often tracked by competitive exam aspirants.
The problem presents a proportion in the format \(a : b :: c : d\), which means that the ratio \(a/b\) is equal to the ratio \(c/d\). We need to find the value of \(x\) by setting up the proportion as an equation and solving for \(x\).
The given proportion is \(8 : 4 :: 3.2 : x\).
This can be written as an equation of ratios:
\[ \frac{8}{4} = \frac{3.2}{x} \]Simplify the left side of the equation:
\[ 2 = \frac{3.2}{x} \]To solve for \(x\), multiply both sides by \(x\):
\[ 2x = 3.2 \]Divide both sides by 2:
\[ x = \frac{3.2}{2} \]Perform the division:
\[ x = 1.6 \]Correct Option: B) 1.6
The problem presents a series of three-letter combinations. We need to identify the pattern in the English alphabetical order for each position of the letters within the combinations to find the next term in the series.
Correct Option: B) VRU
The first letter of each term follows the sequence N (+2) P (+2) R (+2) T (+2) V. The second letter follows J (+2) L (+2) N (+2) P (+2) R. The third letter follows M (+2) O (+2) Q (+2) S (+2) U. Therefore, the next term is VRU.
We need to find Mr. Hari's monthly income. We are given his annual savings and the percentages of his income spent on various categories. We will work backward from his annual savings to find his monthly savings, then his income before savings, and finally his total monthly income.
Mr. Hari saves ₹1,80,000 annually. To find his monthly savings, we divide the annual savings by 12 (months in a year).
\[ \text{Monthly Savings} = \frac{\text{Annual Savings}}{12} = \frac{1,80,000}{12} = \text{₹}15,000 \]He saves half of the remaining amount every month. This means his monthly savings of ₹15,000 represent 50% of the amount remaining before savings.
\[ \text{Amount remaining before saving} = \frac{\text{Monthly Savings}}{0.50} = \frac{15,000}{0.50} = \text{₹}30,000 \]He spends 25% of the remaining amount on clothes, medical, and conveyance. The amount remaining before saving (₹30,000) is what's left after these expenses. So, ₹30,000 represents \(100\% - 25\% = 75\%\) of the amount remaining after spending on food.
\[ \text{Amount remaining after spending on food} = \frac{30,000}{0.75} = \text{₹}40,000 \]He spends 36% of his income on food items. The amount remaining after spending on food (₹40,000) represents \(100\% - 36\% = 64\%\) of his total monthly income.
\[ \text{Total Monthly Income} = \frac{40,000}{0.64} = \text{₹}62,500 \]D) ₹62,500 is the correct monthly income calculated based on the given percentages and annual savings.
What is the purpose of making urine in the human body?
To empty the urinary bladder
To filter out waste products from the blood
To clean the impure blood coming to the heart
To remove CO2 from the blood in the lungs
The question asks about the primary purpose of urine formation in the human body. This relates to the excretory system's function, specifically the kidneys.
Correct Option: B) To filter out waste products from the blood