The problem involves identifying a pattern in letter relationships based on their positions in the English alphabet. We need to find the numerical difference in alphabetical positions between corresponding letters in the given pairs and then apply the same pattern to the target word.
The pattern observed is that each letter in the first word is shifted backward by 8 positions to get the corresponding letter in the second word.
This pair also follows the same pattern: a backward shift of 8 positions for each letter.
Now, we apply the "shift backward by 8 positions" rule to each letter of UNQK:
So, UNQK is related to MFIC.
Correct Option: D) MFIC
There are two pumps to fill a tank with water. The first pump can fill the empty tank in 6 hours, while the second in 8 hours. If both the pumps are opened at the same time and kept open for 2 hours, the part of tank that will be filled up is:
\( \frac{9}{10} \)
\( \frac{9}{12} \)
\( \frac{7}{12} \)
\( \frac{7}{10} \)
To solve this problem, we need to determine the individual filling rates of each pump and then combine them to find their combined filling rate. Finally, we multiply the combined rate by the time they are both open to find the fraction of the tank filled.
The first pump can fill the tank in 6 hours. So, in 1 hour, it fills \(\frac{1}{6}\) of the tank.
The second pump can fill the tank in 8 hours. So, in 1 hour, it fills \(\frac{1}{8}\) of the tank.
When both pumps are opened together, their individual rates add up.
\[ \text{Combined rate} = \frac{1}{6} + \frac{1}{8} \]To add these fractions, find a common denominator, which is 24.
\[ \text{Combined rate} = \frac{4}{24} + \frac{3}{24} = \frac{4+3}{24} = \frac{7}{24} \]So, both pumps together fill \(\frac{7}{24}\) of the tank in 1 hour.
Since both pumps are kept open for 2 hours, multiply their combined rate by 2.
\[ \text{Part filled in 2 hours} = \text{Combined rate} \times 2 \text{ hours} \] \[ \text{Part filled in 2 hours} = \frac{7}{24} \times 2 = \frac{14}{24} \]The fraction \(\frac{14}{24}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\[ \frac{14 \div 2}{24 \div 2} = \frac{7}{12} \]Thus, \(\frac{7}{12}\) of the tank will be filled in 2 hours.
Correct Option: C) \( \frac{7}{12} \)
The question asks for the city that hosted the inaugural Women's Hockey India League in 2025. This requires knowledge of recent sports events and their venues in India.
Correct Option: D) Ranchi
Ranchi, the capital of Jharkhand, has been chosen to host the inaugural edition of the Women's Hockey India League in 2025. This decision highlights Ranchi's growing prominence as a hub for hockey in India, building on its history of hosting major national and international hockey events.
What is the mode of the data given below? [Give your answer correct to 2 decimal places.]
| Age in years | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| No. of patients | 29 | 35 | 25 | 10 | 18 | 34 | 17 |
To find the mode for grouped data, we first identify the modal class, which is the class interval with the highest frequency. Then, we use the formula for calculating the mode of grouped data.
The given data is:
The highest frequency is 35, which corresponds to the class interval 20-30. Therefore, the modal class is 20-30.
The formula for the mode of grouped data is:
\[ \text{Mode} = L + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h \]Where:
The mode of the data is 23.75.
Correct Option: C) 23.75
The question asks to identify which European East India Company established its factory in Petapuli on the North Coromandel Coast in 1606. This requires knowledge of the early European trading posts in India and their respective founding dates and locations.
C) Dutch East India Company
The Dutch East India Company (VOC) established its factory at Petapuli (Nizampatnam) on the North Coromandel Coast in 1606. This was a significant early trading post for the Dutch in India, primarily for the procurement of textiles.
The problem asks us to identify the letter-cluster that does not follow the same pattern as the other three, based on English alphabetical order. We need to find the positional values of each letter in the alphabet and then look for a consistent relationship or pattern within each cluster.
Therefore, PRS is the letter-cluster that does not belong to the group.
Correct Option: D) PRS
This is a logical reasoning problem involving the arrangement of boxes. We need to deduce the exact order of the seven boxes based on the given clues and then identify the box that is fourth from the top.
The problem presents a series of letter-number clusters. To find the missing cluster, we need to identify the pattern in the letters and the numbers separately.
E (5), H (8), K (11), N (14), ?
The pattern is an increment of 3 in alphabetical position:
So, the first letter of the next cluster will be N + 3 = Q (17).
F (6), I (9), L (12), O (15), ?
The pattern is an increment of 3 in alphabetical position:
So, the second letter of the next cluster will be O + 3 = R (18).
R (18), U (21), X (24), A (1), ?
The pattern is an increment of 3 in alphabetical position, wrapping around from Z to A:
So, the third letter of the next cluster will be A + 3 = D (4).
7, 12, 17, 22, ?
The pattern is an increment of 5:
So, the next number in the series will be 22 + 5 = 27.
The next cluster will be QRD27.
B) QRD27 is the correct option as it matches all the patterns identified for the letters and the number.
To find the average speed, we need to calculate the total distance covered and the total time taken for the entire journey. The journey is divided into two parts with different speeds and durations. We will calculate the distance for each part and then sum them up, along with the total time, to find the average speed.
Correct Option: D) 79
The problem presents a series of three-letter codes. We need to identify the pattern in the letters of each code and the progression from one code to the next to determine the missing code.
The pattern for the first letter is an increase of 2 in alphabetical position: \(12 + 2 = 14\), \(14 + 2 = 16\), \(16 + 2 = 18\). Following this pattern, the next first letter should be \(18 + 2 = 20\), which corresponds to the letter T.
The pattern for the second letter is also an increase of 2 in alphabetical position: \(9 + 2 = 11\), \(11 + 2 = 13\), \(13 + 2 = 15\). Following this pattern, the next second letter should be \(15 + 2 = 17\), which corresponds to the letter Q.
The pattern for the third letter is also an increase of 2 in alphabetical position: \(16 + 2 = 18\), \(18 + 2 = 20\), \(20 + 2 = 22\). Following this pattern, the next third letter should be \(22 + 2 = 24\), which corresponds to the letter X.
Combining the next first, second, and third letters (T, Q, X) gives us TQX.
B) TQX — This option correctly follows the established pattern of adding 2 to the alphabetical position of each corresponding letter in the sequence.