Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster.
ADJUST : BEKWUV :: BACKED : CBDMGF :: PACKUP :?
The problem presents a letter-cluster analogy. We need to identify the pattern or rule that transforms the first letter-cluster into the second, and the third into the fourth. Once the rule is found, apply it to the fifth letter-cluster to find the missing sixth letter-cluster.
The pattern for the first pair is: the first three letters are shifted by +1 position, and the next three letters are shifted by +2 positions in the English alphabet.
The pattern for the second pair is consistent with the first: the first three letters are shifted by +1 position, and the next three letters are shifted by +2 positions.
Therefore, PACKUP transforms to QBDMWR.
B) QBDMWR is the correct option as it follows the established pattern of shifting the first three letters by +1 and the next three letters by +2.
This is a syllogism problem. We need to determine which conclusions logically follow from the given statements. We can use Venn diagrams or logical deductions to solve this. We will represent each category as a circle and show the relationships between them based on the statements.
From (1) and (2), we can deduce a transitive relationship:
Since all Capes are Scholars, and all Scholars are Trip Advisors, it logically follows that all Capes are Trip Advisors. \(\text{Capes} \subset \text{Scholars} \subset \text{Trip Advisors} \implies \text{Capes} \subset \text{Trip Advisors}\)
From (3), we know that Hats are completely separate from Trip Advisors. Since Capes are a subset of Trip Advisors, Hats must also be completely separate from Capes.
This contradicts Statement 2 ("All scholars are trip advisors"). If all scholars are trip advisors, then it's impossible that no trip advisor is a scholar. Some trip advisors are scholars (specifically, all the scholars are also trip advisors). So, Conclusion I does not follow.
As deduced in step 2, since all capes are scholars and all scholars are trip advisors, it logically follows that all capes are trip advisors. So, Conclusion II follows.
Since Statement 2 says "All scholars are trip advisors," it implies that the set of Scholars is a subset of Trip Advisors. If all scholars are trip advisors, then certainly some trip advisors are scholars (specifically, all of them). So, Conclusion III follows.
From Statement 3, "No hat is a trip advisor." From our deduction, "All capes are trip advisors." If capes are trip advisors and hats are not trip advisors, then no cape can be a hat. They are mutually exclusive. So, Conclusion IV follows.
Conclusions II, III, and IV logically follow from the statements.
C) Only conclusions II, III and IV follow.
The problem describes the relative positions of students in a single row, all facing north. We need to determine the total number of students. We can establish the position of each student relative to the starting point (Pranavi, as no one is to her left) and then find the position of the rightmost student to get the total count.
A) 22 — Based on the step-by-step calculation, Vipanchi is at position 22, and since she is the last student, the total number of students is 22.
Suppose in a circuit, a silver wire of length L and cross-sectional area A is replaced by an aluminium wire of length 5L and cross-sectional area 9A. The resistance of the circuit will ______.
(Given that ρ silver = 1.6×10−8 Ω·m and ρ aluminium = 2.6×10−8 Ω·m)
increase to 1.1 times of itself
increase to 1.2 times of itself
decrease to 0.9 times of itself
decrease to 0.8 times of itself
The resistance of a wire depends on its resistivity, length, and cross-sectional area. We will calculate the initial resistance of the silver wire and the final resistance of the aluminium wire using the given parameters and then determine the ratio of the final resistance to the initial resistance to find out how the resistance changes.
Recall the formula for resistance:
The resistance \(R\) of a wire is given by the formula:
where \(\rho\) is the resistivity of the material, \(L\) is the length, and \(A\) is the cross-sectional area.
Calculate the initial resistance (silver wire):
For the silver wire:
So, the initial resistance \(R_1\) is:
\[ R_1 = \rho_{\text{silver}} \frac{L}{A} = 1.6 \times 10^{-8} \frac{L}{A} \]Calculate the final resistance (aluminium wire):
For the aluminium wire:
So, the final resistance \(R_2\) is:
\[ R_2 = \rho_{\text{aluminium}} \frac{5L}{9A} = 2.6 \times 10^{-8} \frac{5L}{9A} \]Determine the ratio of final resistance to initial resistance:
To find out how the resistance changes, we calculate the ratio \(\frac{R_2}{R_1}\):
Cancel out the common terms \((10^{-8})\), \(L\), and \(A\):
\[ \frac{R_2}{R_1} = \frac{2.6 \times 5}{1.6 \times 9} \]Perform the multiplication:
\[ \frac{R_2}{R_1} = \frac{13}{14.4} \]Calculate the decimal value:
\[ \frac{R_2}{R_1} \approx 0.9027 \]Rounding to one decimal place, \(\frac{R_2}{R_1} \approx 0.9\).
Interpret the result:
Since \(\frac{R_2}{R_1} \approx 0.9\), the new resistance \(R_2\) is approximately \(0.9\) times the original resistance \(R_1\). This means the resistance decreases to \(0.9\) times of itself.
Correct Option: C) decrease to 0.9 times of itself
The problem requires us to determine the class schedule for six professors over six days (Monday to Saturday) based on a series of clues. We will use a table or a linear arrangement to map professors to days of the week, filling in information as it becomes available.
Let's represent the schedule:
| Day | Professor |
|---|---|
| Monday | |
| Tuesday | Jayanth |
| Wednesday | |
| Thursday | |
| Friday | |
| Saturday | Omprakash |
| Day | Professor |
|---|---|
| Monday | |
| Tuesday | Jayanth |
| Wednesday | |
| Thursday | Mythili |
| Friday | |
| Saturday | Omprakash |
| Day | Professor |
|---|---|
| Monday | |
| Tuesday | Jayanth |
| Wednesday | |
| Thursday | Mythili |
| Friday | Kiran |
| Saturday | Omprakash |
| Day | Professor |
|---|---|
| Monday | Nischal |
| Tuesday | Jayanth |
| Wednesday | |
| Thursday | Mythili |
| Friday | Kiran |
| Saturday | Omprakash |
| Day | Professor |
|---|---|
| Monday | Nischal |
| Tuesday | Jayanth |
| Wednesday | Lasya |
| Thursday | Mythili |
| Friday | Kiran |
| Saturday | Omprakash |
C) Nischal
The question asks about the trend of boiling points in a homologous series. A homologous series is a series of organic compounds with the same functional group but differing by a \(\text{CH}_2\) unit. We need to understand how molecular mass influences intermolecular forces, which in turn affect the boiling point.
Correct Option: A) The boiling points increase with increasing molecular mass. This statement is correct because higher molecular mass leads to stronger intermolecular forces (specifically London dispersion forces) which require more energy to overcome, thus resulting in a higher boiling point.
To identify an example of revenue expenditure, it's important to understand the distinction between revenue and capital expenditure in government budgeting. Revenue expenditure refers to expenses that do not create assets or reduce liabilities, and are generally recurring in nature. Capital expenditure, on the other hand, creates assets or reduces liabilities and is typically non-recurring.
D) Salaries of government employees are recurring expenses for the normal functioning of the government and do not create assets or reduce liabilities. Hence, they are a clear example of revenue expenditure.
The question asks to identify which of the given rivers originates in Nepal and flows into India. This requires knowledge of the geographical origins and courses of major rivers in the Indian subcontinent.
A) Karnali — The Karnali River (known as Ghaghara in India) originates in the Tibetan Himalayas, flows through Nepal, and then enters India, making it the correct answer.
To find the selling price after two successive discounts, we first calculate the price after the first discount, and then apply the second discount to this new price. Alternatively, we can use a direct formula for successive discounts.
The marked price is Rs 7,200.
The first discount is 9%.
Amount of first discount \( = 9\% \text{ of } 7,200 \)
\[ = \frac{9}{100} \times 7,200 \]\[ = 9 \times 72 \]\[ = 648 \]Price after first discount \( = \text{Marked Price} - \text{First Discount} \)
\[ = 7,200 - 648 \]\[ = 6,552 \]The second discount is 15% on the price after the first discount (Rs 6,552).
Amount of second discount \( = 15\% \text{ of } 6,552 \)
\[ = \frac{15}{100} \times 6,552 \]\[ = 0.15 \times 6,552 \]\[ = 982.80 \]Selling Price \( = \text{Price after first discount} - \text{Second Discount} \)
\[ = 6,552 - 982.80 \]\[ = 5,569.20 \]When two successive discounts of \(d_1\%\) and \(d_2\%\) are given, the effective discount percentage \(D\%\) can be calculated as:
\[ D = d_1 + d_2 - \frac{d_1 \times d_2}{100} \]\[ D = 9 + 15 - \frac{9 \times 15}{100} \]\[ D = 24 - \frac{135}{100} \]\[ D = 24 - 1.35 \]\[ D = 22.65\% \]Now, calculate the selling price using this effective discount:
Selling Price \[= \text{Marked Price} \times \left(1 - \frac{D}{100}\right)\]
\[ = 7,200 \times \left(1 - \frac{22.65}{100}\right) \]\[ = 7,200 \times (1 - 0.2265) \]\[ = 7,200 \times 0.7735 \]\[ = 5,569.20 \]B) The selling price of the article is Rs 5,569.20.
The question asks about the type of nutrition observed in mushrooms. To answer this, we need to understand the different modes of nutrition and how mushrooms obtain their food.
Correct Option: B) Saprotrophic — Mushrooms are fungi, and fungi are heterotrophic organisms that obtain their nutrients by secreting digestive enzymes onto dead or decaying organic matter and then absorbing the digested products. This process is known as saprotrophic nutrition.