The problem presents a number series, and we need to find the next term. We will analyze the differences between consecutive terms to identify a pattern. If the first differences don't reveal a clear pattern, we will look at the differences of the differences (second differences) or try to find a multiplicative or combined pattern.
Thus, the missing number in the series is 2045.
Correct Option: A) 2045 is the correct number that replaces the question mark, following the identified pattern where the difference between consecutive terms is multiplied by 3.
To find the smallest four-digit number exactly divisible by 24, 40, and 56, we first need to find the Least Common Multiple (LCM) of these three numbers. The smallest number divisible by all three will be their LCM. Then, we find the smallest multiple of this LCM that is a four-digit number.
The LCM is found by taking the highest power of all prime factors present in the numbers.
\[\text{LCM}(24, 40, 56) = 2^3 \times 3^1 \times 5^1 \times 7^1\] \[\text{LCM}(24, 40, 56) = 8 \times 3 \times 5 \times 7\] \[\text{LCM}(24, 40, 56) = 24 \times 35\] \[\text{LCM}(24, 40, 56) = 840\]The smallest four-digit number is 1000. We need to find the smallest multiple of 840 that is greater than or equal to 1000.
Divide 1000 by 840:
\[1000 \div 840 = 1 \text{ with a remainder of } 160\]This means \(1 \times 840 = 840\), which is a three-digit number.
The next multiple of 840 will be the smallest four-digit number divisible by 840 (and thus by 24, 40, and 56).
\[2 \times 840 = 1680\]1680 is a four-digit number and is the smallest such number divisible by 24, 40, and 56.
Correct Option: B) 1680
This problem involves analyzing logical statements and conclusions, a common type of question in competitive exams. We will use Venn diagrams to visually represent the given statements and then check the validity of each conclusion based on these diagrams.
B) Only conclusion (II) follows
Conclusion (I) is not necessarily true, as beds might intersect only with the part of tables that are not chairs. Conclusion (II) is a direct logical consequence of the statement "All chairs are tables." If all chairs are tables, then it must be true that some tables are chairs.
This is a work and time problem. We can solve it by determining the individual work rates of a man and a boy. Once we have their individual efficiencies, we can calculate the total work done by the new group (15 men and 20 boys) and then find the time taken.
Let \(M\) be the amount of work one man can do in one day.
Let \(B\) be the amount of work one boy can do in one day.
The total work done is constant. We use the formula: \(\text{Work} = \text{Number of people} \times \text{Efficiency per person} \times \text{Time}\).
From the first statement: 6 men and 8 boys can do the work in 10 days.
\[ (6M + 8B) \times 10 = \text{Total Work} \quad (1) \]From the second statement: 26 men and 48 boys can do the same work in 2 days.
\[ (26M + 48B) \times 2 = \text{Total Work} \quad (2) \]This means one man's work rate is equal to the work rate of two boys.
Substitute \(M = 2B\) into equation (1):
\[ \text{Total Work} = (6(2B) + 8B) \times 10 \] \[ \text{Total Work} = (12B + 8B) \times 10 \] \[ \text{Total Work} = 20B \times 10 \] \[ \text{Total Work} = 200B \]Convert the men into equivalent boys using \(M = 2B\):
\[ 15M + 20B = 15(2B) + 20B \] \[ = 30B + 20B \] \[ = 50B \]So, 15 men and 20 boys are equivalent to 50 boys in terms of work rate.
Let \(D\) be the number of days taken by 15 men and 20 boys.
\[ (15M + 20B) \times D = \text{Total Work} \] \[ 50B \times D = 200B \] \[ D = \frac{200B}{50B} \] \[ D = 4 \]Therefore, 15 men and 20 boys can do the work in 4 days.
Correct Option: C) 4 days
The problem asks us to find a relationship between two sets of letters based on their positions in the English alphabet. We need to identify the pattern in the given pairs (KGFL to OJHM and ASNP to EVPQ) and then apply the same pattern to MBTS to find its related set of letters.
To solve this problem, we need to follow a sequence of steps:
Original word: GROUPS
Let's identify vowels and consonants:
Apply the transformation rule: Each letter is changed to the letter following it in the English alphabetical order.
The new group of letters formed is H, S, P, V, Q, T.
Arrange the new group of letters in English alphabetical order:
The letters are H, S, P, V, Q, T.
Arranging them alphabetically gives: H, P, Q, S, T, V.
Identify the third letter from the left:
In the alphabetically ordered group (H, P, Q, S, T, V), the third letter from the left is Q.
Correct Option: D) Q
The third letter from the left in the alphabetically arranged group is Q.
The question asks to identify the institute responsible for developing the 'Investor Information and Analytics Platform' in 2024. This requires knowledge of recent collaborations and projects undertaken by prominent Indian educational institutions, specifically the IITs, in the financial technology sector.
In February 2024, the National Stock Exchange (NSE) announced a collaboration with IIT Madras to develop an 'Investor Information and Analytics Platform'. This platform is intended to enhance investor education and provide data analytics tools for investors.
C) IIT Madras — IIT Madras, in collaboration with the National Stock Exchange (NSE), developed the 'Investor Information and Analytics Platform' in 2024. This initiative aims to provide investors with better access to information and analytical tools to make informed decisions.
The problem presents a series of three-letter combinations based on the English alphabetical order. We need to identify the pattern in the series to find the missing term. The pattern can be observed by analyzing the position of each letter in the alphabet and the relationship between consecutive terms.
The next term in the series is formed by combining the letters found in steps 1, 2, and 3: JKI.
D) JKI is the correct option because it follows the established pattern where each letter in the three-letter combination decreases by 3 positions compared to the corresponding letter in the previous term.
The problem requires us to perform a series of transformations on the letters of the word "RELATION". First, we change vowels to the next letter and consonants to the previous letter. Then, we arrange the resulting letters in reverse alphabetical order. Finally, we identify the fourth letter from the right in this new arrangement.
First, arrange them in alphabetical order: B, F, J, K, M, P, Q, S.
Then, arrange them in reverse alphabetical order: S, Q, P, M, K, J, F, B.
The letters in reverse alphabetical order are: S, Q, P, M, K, J, F, B.
Counting from the right:
C) K is the fourth letter from the right in the group of letters thus formed.
The question asks to identify the biological process where a fully differentiated organism can regenerate new individuals from its body parts. This refers to a specific type of asexual reproduction or restorative process.
D) Regeneration is the process where an organism can regrow lost or damaged body parts, and in some cases, a complete new individual can develop from a fragment of the parent organism. This is a characteristic feature of organisms like Planaria and starfish, which are fully differentiated but possess remarkable regenerative capabilities.