To solve this problem, we need to compare the positions of digits in the original number with their positions after the digits are rearranged in descending order. We will list the original number and its digits, then rearrange them, and finally compare the positions.
Correct Option: D) None
To determine the nature of the roots of a quadratic equation of the form \( ax^2 + bx + c = 0 \), we use the discriminant, denoted by \(\Delta\) or \(D\). The discriminant is given by the formula \( \Delta = b^2 - 4ac \). The nature of the roots depends on the value of the discriminant:
Here, we have:
Since \( \Delta = -23 \), which is less than \( 0 \) (i.e., \( \Delta < 0 \)), the roots of the quadratic equation are imaginary.
Correct Option: C) Imaginary roots
The question asks for the easiest way to sort files by name in File Explorer in Windows 11. This involves understanding the basic functionalities of File Explorer for sorting items.
A) Click the Name column header in File Explorer
This is the most straightforward and common method to sort files by name in File Explorer. Clicking the 'Name' column header toggles between ascending and descending alphabetical order.
The question asks to identify the tax reform implemented in 2017 that aimed to unify India's indirect tax structure, following the spirit of the 1991 economic reforms. We need to recall major tax reforms and their objectives.
Correct Option: B) GST. The Goods and Services Tax (GST), implemented in 2017, was a monumental tax reform designed to unify India's fragmented indirect tax structure, replacing multiple central and state taxes with a single, comprehensive tax. This aligns perfectly with the question's description of a reform aimed at boosting efficiency and compliance by unifying the indirect tax system.
This is a linear arrangement puzzle. We need to deduce the exact seating order of the seven people (A, B, C, D, S, T, U) based on the given clues and then determine the number of people between A and S.
B) Two. As derived, B and C sit between A and S.
The question asks for the location of the Bagh caves, known for their Buddhist mural paintings. This is a factual question related to Indian art and culture, specifically ancient cave architecture and paintings. To answer this, one needs to recall the geographical location of prominent historical sites in India.
A) Madhya Pradesh — The Bagh caves, famous for their Buddhist mural paintings, are indeed located in the state of Madhya Pradesh. They are a significant archaeological site reflecting the rich Buddhist heritage of ancient India.
The question asks for the original language of Yōko Ogawa's novel "Mina's Matchbox." This is a factual question about a well-known author and her works. To answer this, one needs to identify the nationality and primary writing language of Yōko Ogawa.
A) Japanese. Yōko Ogawa is a celebrated Japanese author, and all her original works, including "Mina's Matchbox," are written in Japanese.
Anushka walks to her office 5 km away from home. In the morning she covers the distance in 1 hour, whereas while returning home in the evening, she takes 15 more minutes to cover the same distance. Find her average speed (in km/hr) during the two-way journey.
\( \frac{38}{9} \)
\( \frac{40}{9} \)
\( \frac{40}{11} \)
\( \frac{41}{9} \)
To find the average speed for the two-way journey, we need to calculate the total distance covered and the total time taken. The average speed is then the total distance divided by the total time.
Anushka walks 5 km to her office and 5 km back home. So, the total distance covered is:
\[ \text{Total Distance} = 5 \text{ km} + 5 \text{ km} = 10 \text{ km} \]Time taken to go to the office = 1 hour.
While returning, she takes 15 more minutes than the morning journey. So, the time taken is:
\[ \text{Time (evening)} = 1 \text{ hour} + 15 \text{ minutes} \]Convert 15 minutes to hours:
\[ 15 \text{ minutes} = \frac{15}{60} \text{ hours} = \frac{1}{4} \text{ hours} = 0.25 \text{ hours} \]So, the time taken in the evening is:
\[ \text{Time (evening)} = 1 \text{ hour} + 0.25 \text{ hours} = 1.25 \text{ hours} \]We can also write 2.25 hours as \(2 \frac{1}{4}\) hours or \(\frac{9}{4}\) hours.
The formula for average speed is:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]Substitute the values:
\[ \text{Average Speed} = \frac{10 \text{ km}}{\frac{9}{4} \text{ hours}} \] \[ \text{Average Speed} = 10 \times \frac{4}{9} \text{ km/hr} \] \[ \text{Average Speed} = \frac{40}{9} \text{ km/hr} \]Correct Option: B) \( \frac{40}{9} \)
This problem involves calculating ages at different points in time based on given average ages. We will first determine the sum of ages at the present time for the given groups and then use these sums to find the individual age of B.
The problem asks us to identify the letter-cluster that does not follow the same pattern as the other three, based on the English alphabetical order. We need to find the positional values of the letters in each cluster and look for a consistent mathematical relationship or sequence.
For options B, C, and D:
Let's re-examine Option A with this pattern:
Therefore, KQN does not follow the pattern of the other three clusters.
A) KQN is the letter-cluster that does not belong to the group. The pattern observed in options B, C, and D is that the second letter is 6 positions after the first, and the third letter is 4 positions before the second. In KQN, K (+6) = Q, but Q (-4) = M, not N.