The problem presents two sets of numbers and states that a consistent set of mathematical operations transforms the first number into the second, the second into the third, and so on. We need to identify this pattern of operations and then find an option that follows the exact same pattern.
C) 4 - 8 - 16 - 17
All operations match the established pattern.
The question asks to identify the official responsible for the implementation of decisions made by the Municipal Corporation's council and standing committees. This requires knowledge of the administrative structure and roles within urban local bodies in India.
C) Municipal Commissioner is the chief executive and administrative head of the Municipal Corporation. They are responsible for the implementation of all decisions and policies made by the council and its standing committees, as well as the day-to-day functioning of the urban local body.
If a + b = 33, and a - b = 37, find the value of (a + b)2.
The problem provides two linear equations with two variables, \(a\) and \(b\), and asks for the value of \((a+b)^2\). We are given the values of \(a+b\) and \(a-b\). We can directly use the given value of \(a+b\) to find \((a+b)^2\).
We are given two equations:
We need to find the value of \((a + b)^2\).
The expression we need to evaluate is \((a + b)^2\). We are directly given the value of \(a + b\) from Equation 1.
Substitute the value of \(a + b = 33\) into the expression \((a + b)^2\):
\[ (a + b)^2 = (33)^2 \]Now, calculate the square of 33:
\[ 33^2 = 33 \times 33 \]\[ 33 \times 33 = 1089 \]The value of \((a + b)^2\) is 1089.
C) 1089 — The value of \(a+b\) is directly given as 33. Squaring this value gives \(33^2 = 1089\).
This is a coding-decoding problem where letters are assigned specific numerical codes. To find the code for 'D', we need to compare the given coded words and identify the common letters and their corresponding common codes.
| Letter | Possible Code from 'PEAR' | Possible Code from 'DEAR' |
|---|---|---|
| E | {4, 8, 1} | {7, 1, 5, 4} |
| A | {4, 8, 1} | {7, 1, 5, 4} |
| R | {4, 8, 1} | {7, 1, 5, 4} |
Correct Option: D) 5
The question asks to identify the individual who first coined the term 'judicial activism'. This is a factual question related to the history and terminology of legal systems, particularly in the context of judicial roles.
D) Arthur Schlesinger Jr. is widely credited with coining the term 'judicial activism' in a 1947 article titled "The Supreme Court: 1947" published in Fortune magazine. He used the term to describe the judicial philosophy of certain Supreme Court justices who were seen as actively shaping public policy through their rulings.
A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/Symbol | 3 | # | 8 | $ | 7 | & | 6 | * | 4 | ^ | 2 | 9 | @ |
| Code | B | S | D | F | G | H | J | K | L | P | R | U | C |
Conditions:
i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.
ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©.
iii) If both the second and third elements are perfect squares, then the code of the second element will be the code for the third element.
What will be the code for the following group?
849@
A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/Symbols | 3 | # | 4 | $ | 7 | & | 6 | * | 8 | ^ | 2 |
| Code | H | A | J | B | K | C | L | D | M | E | N |
Conditions:
i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.
ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©.
iii) If both the second and third elements are perfect cubes, the code of the second element will be the code of third element.
What will be the code for the following group?
3$72
The problem requires us to code a given group of numbers and symbols based on a provided table and a set of conditions. We need to evaluate each condition in order to determine which one applies, and then apply the coding rules accordingly.
This is a logical reasoning problem involving the arrangement of boxes. We need to deduce the exact order of the seven boxes (A, B, C, D, E, F, G) based on the given conditions and then determine how many boxes are kept above B.
This means F is the topmost box.
Order: F
Since F is at the top, B must be below F with three boxes in between.
Order: F
Box 1
Box 2
Box 3
B
This accounts for 5 boxes. Since there are 7 boxes in total, there must be 2 more boxes below B.
Current arrangement (from top to bottom):
1. F
2. _
3. _
4. _
5. B
6. _
7. _
This fills the 4th position.
Current arrangement:
1. F
2. _
3. _
4. E
5. B
6. _
7. _
Since E is at position 4, A can be either at position 2 (above E) or position 6 (below E).
Case 1: A is above E.
1. F
2. A
3. _ (This box is between A and E)
4. E
5. B
6. _
7. _
Case 2: A is below E.
1. F
2. _
3. _
4. E
5. B
6. A (This box is between E and A, but E is immediately above B, so A cannot be below E with one box between them if B is at 5. If A is at 6, then there is 1 box (B) between E and A. Let's check this possibility.)
If A is at 6, then B is at 5, and E is at 4. The condition states "Only one box is kept between A and E". If A is at 6 and E is at 4, then B (at 5) is the only box between them. This is a valid interpretation.
Let's re-evaluate Case 2 with the full set of conditions.
If A is at 6, then:
1. F
2. _
3. _
4. E
5. B
6. A
7. _
Now let's check Condition 2 again: "Only three boxes are kept between F and B." F is at 1, B is at 5. Boxes at 2, 3, 4 are between F and B. That's 3 boxes. This is consistent.
Let's proceed with Case 1 first, as it seems more straightforward to fill from the top.
Case 1 (A at position 2):
1. F
2. A
3. _
4. E
5. B
6. _
7. _
In Case 1, A is at position 2. If there are four boxes between A and C, then C must be at position \(2+4+1 = 7\).
Current arrangement:
1. F
2. A
3. _
4. E
5. B
6. _
7. C
The remaining boxes are D and G. The remaining empty slots are 3 and 6.
If G is above D, then G must be at position 3 and D at position 6.
Final arrangement:
1. F
2. A
3. G
4. E
5. B
6. D
7. C
Let's verify all conditions:
This arrangement is consistent with all conditions.
From the final arrangement, the boxes above B (position 5) are F, A, G, E.
There are 4 boxes above B.
B) 4
As determined from the step-by-step deduction, there are 4 boxes (F, A, G, E) kept above B.
Jitesh and Kamal can complete a certain piece of work in 5 and 18 days, respectively. They started to work together, and after 3 days, Kamal left. In how many days will Jitesh complete the remaining work?
\( \frac{11}{6} \)
\( \frac{13}{6} \)
\( \frac{7}{6} \)
\( \frac{25}{6} \)
This problem involves work and time. We need to calculate the individual work rates, the combined work done, the remaining work, and finally the time taken by Jitesh to complete the remaining work.
Correct Option: C) \( \frac{7}{6} \)
The question asks about a specific amendment, the Waqf (Amendment) Act, 2025. This requires knowledge of the provisions introduced or changed by this particular legislation. Since the year 2025 is in the future, this question is likely testing knowledge of a hypothetical or proposed amendment, or it might be a trick question based on a non-existent act. However, assuming it refers to a real or proposed legislative change, we need to identify which option accurately reflects a change made by such an act.
Given that the Waqf (Amendment) Act, 2025 is a hypothetical act, we must infer the most likely progressive change that such an act would introduce, aligning with modern governance principles and social inclusion. The inclusion of Muslim women in boards aligns with such principles.
D) Added Muslim women to boards. While the Waqf (Amendment) Act, 2025, is a hypothetical act (as no such act has been passed or even widely proposed with that specific year), the inclusion of Muslim women in Waqf boards is a progressive reform that has been a subject of discussion and is aligned with principles of inclusive governance. The Waqf (Amendment) Act, 2013, already aimed at improving the management and administration of Waqf properties, and future reforms would likely continue this trend, including better representation for all sections of the community, including women. Therefore, among the given choices, this represents the most plausible and positive reform that a future amendment might introduce.