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JKSSB Reasoning MCQs

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Question 1 of 132

choose the correct order of the given alternative : a_c_abb_a_bc_bc_ab

Explanation

Step-by-Step Analysis

  1. Identify the segment length: Count the total number of characters (including blanks). There are 18 positions. A repeating pattern of 3 or 6 is likely.

  2. Break it down into groups of 3:

    • (a c) ( a b) (b a) ( b c) (_ b c) (_ a b)

  3. Analyze the pattern:

    • Let's test the sequence abc as the recurring unit.

    • Group 1: a b c

    • Group 2: b a b (This doesn't fit perfectly).

    • Let's re-evaluate the sequence based on the provided options. If we look at the string a_c_abb_a_bc_bc_ab and insert the option bccaac:

    • a b c c a b b a a b c a b c a c a b

    • Wait, let's look for a repeating cycle: abc / bca / cab / abc / bca / cab

    • Original: a c a b b a b c b c a b

    • If we place b c c a a c into the blanks:

    • a (b) c / (c) a b / b (c) a / (a) b c / (a) b c / (c) a b

The pattern reveals a rotating sequence of abc, bca, and cab.

Conclusion

The correct sequence to complete the pattern is bccaac.

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Question ID: 11463

Question 2 of 132

Consider the following statements:

Statement I: Аuthority and responsibility should go hand in hand according to Fayol.

Statement II: Granting responsibility without adequate authority leads to ineffective performance.

Which of the above statements is/are correct?

Explanation

Both Statement I and Statement II are correct.

These statements refer to the Principle of Authority and Responsibility, one of Henri Fayol’s 14 Principles of Management.

Analysis of the Statements

  • Statement I: Authority and responsibility should go hand in hand according to Fayol.

    • Correct: Fayol argued that authority (the right to give orders and the power to exact obedience) and responsibility (the obligation to perform the assigned task) are two sides of the same coin. There should be a balance between the two; if authority is greater than responsibility, it may lead to autocratic abuse of power, and if responsibility is greater than authority, the employee will be unable to perform the task effectively.

  • Statement II: Granting responsibility without adequate authority leads to ineffective performance.

    • Correct: If a manager or employee is assigned a task (responsibility) but is not given the necessary resources, decision-making power, or tools to complete it (authority), they cannot be held fully accountable for the results. This imbalance prevents the employee from achieving the required goals, leading to frustration, demotivation, and failure.

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Question ID: 11462

Question 3 of 132

Consider the following statements:

Statement I: According to Maslow, esteem needs arise only after social needs are reasonably satisfied.

Statement II: Self-actualization needs are the lowest-level needs in Maslow's hierarchy.

Which of the above statements is/are correct?

Explanation

The correct answer is: Statement I is correct, and Statement II is incorrect.

Analysis of the Statements

  • Statement I: According to Maslow, esteem needs arise only after social needs are reasonably satisfied.

    • Correct: Maslow’s Hierarchy of Needs follows a specific order where lower-level needs must be met before an individual is motivated by higher-level needs. The hierarchy is: Physiological $\rightarrow$ Safety $\rightarrow$ Social (Belongingness) $\rightarrow$ Esteem $\rightarrow$ Self-actualization. Therefore, a person focuses on esteem (recognition, status, self-worth) once their social needs for affection and belonging are met.

  • Statement II: Self-actualization needs are the lowest-level needs in Maslow's hierarchy.

    • Incorrect: Self-actualization is actually the highest-level need in Maslow’s hierarchy. It represents the desire to achieve one's full potential and personal growth. The lowest-level needs are Physiological needs (such as food, water, and shelter), which must be addressed for basic survival.

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Question ID: 11461

Question 4 of 132

Consider the following statements:

Statement I: Coordination is the essence of management.

Statement II: Coordination is required only when an organisation has many departments.

Which of the above statements is/are correct?

Explanation

The correct answer is: Statement I is correct, and Statement II is incorrect.

Analysis of the Statements

  • Statement I: Coordination is the essence of management.

    • Correct: Coordination is considered the "essence of management" because it is the thread that runs through all management functions (Planning, Organizing, Staffing, Directing, and Controlling). It ensures that all activities, departments, and individuals work in harmony to achieve organizational goals. Without coordination, management efforts would be fragmented and ineffective.

  • Statement II: Coordination is required only when an organisation has many departments.

    • Incorrect: Coordination is required in all types of organizations, regardless of size or structure. Even in a small business with a single department, the activities of individuals must be synchronized to ensure there is no duplication of work, conflict of interests, or wastage of resources. It is a universal requirement for any group effort, not just for complex, multi-departmental organizations.

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Question ID: 11460

Question 5 of 132

Consider the following statements:

Statement I: Controlling is a backward-looking as well as forward-looking function

Statement I: Deviations identified through controlling help managers take corrective action.

Which of the above statements is/are correct?

Explanation

Both Statement I and Statement II are correct.

Analysis of the Statements

  • Statement I: Controlling is a backward-looking as well as forward-looking function.

    • Correct: Controlling is backward-looking because it involves comparing actual performance with predetermined standards set in the past (historical analysis). Simultaneously, it is forward-looking because the purpose of identifying those past discrepancies is to formulate corrective actions for the future, ensuring that upcoming goals are met more effectively.

  • Statement II: Deviations identified through controlling help managers take corrective action.

    • Correct: The primary purpose of the controlling function is to identify "deviations" (the gap between planned and actual performance). Once these deviations are analyzed, managers can determine the cause of the variance and implement corrective measures to steer the organization back on track toward its objectives.

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Question ID: 11459

Question 6 of 132

Consider the following statements:

Statement I: Supervision, motivation and leadership are elements of directing.

Statement II: Communication is unnecessary if employees are highly motivated.

Which of the above statements is/are correct?

Explanation

The correct answer is: Statement I is correct, and Statement II is incorrect.

Analysis of the Statements

  • Statement I: Supervision, motivation and leadership are elements of directing.

    • Correct: Directing is one of the primary functions of management, aimed at influencing, guiding, and supervising subordinates to achieve organizational goals. The four fundamental pillars (elements) of the directing function are Supervision, Motivation, Leadership, and Communication.

  • Statement II: Communication is unnecessary if employees are highly motivated.

    • Incorrect: Communication is essential regardless of an employee's level of motivation. Motivation explains why an employee wants to perform, but communication provides the what, how, and when of the work. Without clear communication, highly motivated employees may end up working on the wrong tasks or misinterpreting instructions, leading to inefficiency and misalignment with organizational goals. Communication acts as the "nerve system" of an organization that ensures all efforts are directed toward a common objective.

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Question ID: 11458

Question 7 of 132

Consider the following statements:

Statement I: Delegation involves transfer of authority Statement but not accountability.

Statement II: Accountability can be delegated to subordinates along with authority.

Which of the above statements is/are correct?

Explanation

The correct answer is: Statement I is correct, and Statement II is incorrect.

Here is the breakdown of the management principles regarding delegation and accountability:

Analysis of the Statements

  • Statement I: Delegation involves transfer of authority but not accountability.

    • Correct: In the process of delegation, a manager transfers authority (the power to make decisions and use resources) to a subordinate to complete a specific task. However, the manager remains accountable to their own superior for the final outcome. Accountability cannot be abdicated; it always flows upward.

  • Statement II: Accountability can be delegated to subordinates along with authority.

    • Incorrect: This is a fundamental rule of management: Accountability is non-delegable. While you can delegate authority and responsibility to a subordinate, you cannot pass on the ultimate accountability. The delegator remains answerable for the performance of the task, regardless of whether it was performed by a subordinate.

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Question ID: 11457

Question 8 of 132

Consider the following statements:

Statement I: Planning reduces uncertainty but cannot eliminate it completely. Statement II: Planning is a one-time activity performed only at the top level.

Which of the above statements is/are correct?

Explanation

The correct answer is: Statement I is correct, and Statement II is incorrect.

Here is the breakdown of the reasoning based on management principles:

Analysis of the Statements

  • Statement I: Planning reduces uncertainty but cannot eliminate it completely.

    • Correct: Planning is essentially looking into the future. While it helps managers anticipate changes and develop contingency strategies to minimize risk, the future remains dynamic and influenced by external factors (such as market shifts, natural events, or policy changes) that are beyond a manager's control. Therefore, it reduces, but never fully eliminates, uncertainty.

  • Statement II: Planning is a one-time activity performed only at the top level.

    • Incorrect: Planning is a continuous and pervasive process.

      • It is not a one-time activity; it is an ongoing cycle that requires constant review and adjustment.

      • It is not restricted to the top level; while strategic planning occurs at the top, tactical and operational planning are conducted by middle and lower-level management to ensure the strategy is implemented effectively across all tiers of an organization.

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Question ID: 11456

Question 9 of 132

Consider the following statements:

Statement I: Functional foremanship violates the principle of unity of command. Statement II: Functional foremanship was proposed by Taylor to improve specialization in supervision.

Which of the above statements is/are correct?

Explanation

Both Statement I and Statement II are correct.

Here is the explanation based on the principles of Scientific Management:

Analysis of the Statements

  • Statement I: Functional foremanship violates the principle of unity of command.

    • Correct: The principle of Unity of Command (proposed by Henri Fayol) states that an employee should receive orders from one and only one superior. In Frederick Winslow Taylor's Functional Foremanship, a worker is supervised by eight different specialists (four in the planning department and four in the production department). Since the worker must report to eight different bosses, it directly violates the unity of command.

  • Statement II: Functional foremanship was proposed by Taylor to improve specialization in supervision.

    • Correct: Taylor believed that a single foreman could not be an expert in all aspects of supervision. He proposed Functional Foremanship to divide the work of supervision into specialized functions (e.g., speed boss, repair boss, route clerk). This ensured that each worker received expert guidance for every specific aspect of their work, thereby achieving extreme specialization.

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Question ID: 11455

Question 10 of 132

Consider the following statements:

Statement I: Division of work increases efficiency through specialization.

Statement II: According to Fayol, every employee should receive orders form only one superior.

Which of the above statements is/are correct?

Explanation

Both statements are correct.

These two concepts are fundamental principles of management theory, specifically as defined by Henri Fayol in his "14 Principles of Management."

Detailed Breakdown

  • Statement I: Division of Work (Division of Labor)

    • Concept: This principle states that by breaking down complex tasks into smaller, specialized activities, employees become more proficient and productive.

    • Effect: Specialization allows individuals to focus on specific tasks, leading to higher efficiency, faster output, and improved quality. This is the first of Fayol's 14 principles.

  • Statement II: Unity of Command

    • Concept: This principle dictates that an employee should receive orders from one and only one superior.

    • Effect: This prevents confusion, conflicting instructions, and fragmented authority. When a subordinate has multiple bosses, it often leads to disorder, undermining of authority, and delays in decision-making. This is also one of Fayol's core principles.

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Question ID: 11454

Question 11 of 132

Statement: Should India make efforts to harness solar energy to fulfil its energy requirements?

Arguments:

I. Yes, Most of the energy sources used at present is exhaustible.

II. No. Harnessing solar energy requires a lot of capital, which India lacks in

Explanation

Argument Analysis

  • Argument I: Yes, Most of the energy sources used at present are exhaustible.

    • Strength: Strong. This argument points to a fundamental truth: fossil fuels (coal, oil, gas) are finite resources. Transitioning to a renewable source like solar energy is a long-term strategic necessity for national energy security and sustainability. It addresses the core problem of future energy needs.

  • Argument II: No. Harnessing solar energy requires a lot of capital, which India lacks.

    • Strength: Weak. While it is true that solar infrastructure requires significant initial capital, the claim that "India lacks it" is factually outdated. India has established successful public-private partnership models, attracted significant international investment, and seen drastic reductions in the cost of solar technology over the past decade. Furthermore, the long-term economic benefits (reduced import bills for oil/coal) outweigh the initial setup costs.

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Question ID: 11453

Question 12 of 132

P, Q, R, S, T, U and V are sitting on a row, facing north. U is immediate right of T. Π’ is 4th to the right of V. R is the neighbor of Q and S. Person who is third to the left of S is at one of ends.
What is position of P?

Explanation

  1. "T is 4th to the right of V":

    • If we number the positions 1 to 7, and place V at position 1, then T must be at position 5 ($1 + 4 = 5$).

    • Arrangement: V, , , , T, , _

  2. "U is immediate right of T":

    • U must be at position 6.

    • Arrangement: V, , , , T, U,

  3. "Person who is third to the left of S is at one of the ends":

    • Position 1 is an end. For the person at position 1 (V) to be the 3rd to the left of someone, that someone (S) must be at position 4.

    • Arrangement: V, , , S, T, U, _

  4. "R is the neighbor of Q and S":

    • Positions 2, 3, and 7 are empty. To keep R as a neighbor of both Q and S (position 4), R must be at position 3 and Q must be at position 2.

    • Arrangement: V, Q, R, S, T, U, _

  5. "Remaining spot":

    • The only remaining person, P, must occupy the final spot at position 7.

Conclusion

The final arrangement is V, Q, R, S, T, U, P.

Position 7 is the Extreme right end of the row.

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Question ID: 11452

Question 13 of 132

P.Q. R, S,T, U and V are sitting on a row, facing north. U is immediate right of T. T is 4th to the right of V.R is the neighbor of Q and S. Person who is third to the left of S is at one of ends.
Who are the neighbours of Q?

Explanation

  1. "T is 4th to the right of V":

    • Let's denote the positions as 1, 2, 3, 4, 5, 6, 7.

    • If V is at 1, then T must be at 5 ($1+4=5$).

    • Arrangement so far: V, , , , T, , _

  2. "U is immediate right of T":

    • If T is at 5, then U must be at 6.

    • Arrangement: V, , , , T, U,

  3. "Person who is third to the left of S is at one of the ends":

    • The "end" is position 1 (where V is).

    • If the person at position 1 is the 3rd to the left of S, then S must be at position 4 ($1+3=4$).

    • Arrangement: V, , , S, T, U, _

  4. "R is the neighbor of Q and S":

    • We have positions 2, 3, and 7 remaining.

    • Since R is between Q and S, they must occupy consecutive spots. R must be at 3, and Q must be at 2 (to be next to S at 4).

    • This leaves P for position 7.

    • Final Arrangement: V, Q, R, S, T, U, P

Final Verification

  • V is at 1, T is at 5 (4th to the right of V): Correct.

  • U is at 6 (immediate right of T): Correct.

  • R (at 3) is the neighbor of Q (at 2) and S (at 4): Correct.

  • V (at 1) is 3rd to the left of S (at 4): Correct.

Based on the arrangement V, Q, R, S, T, U, P, the neighbors of Q are V and R.

The correct answer is R and V.

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Question ID: 11451

Question 14 of 132

A woman is shopping in a plaza. She walks 80 m South, then she turns East and walks 50 m, the she turns North and walks 110 m, the she turns to her left and walks 50 m. Where is she now with reference to her starting position?

Explanation

Step-by-Step Movement Analysis

  1. Start Position: Let the starting point be $(0, 0)$.

  2. Move 1: Walks $80\text{ m South}$.

    • New position: $(0, -80)$

  3. Move 2: Turns East and walks $50\text{ m}$.

    • New position: $(50, -80)$

  4. Move 3: Turns North and walks $110\text{ m}$.

    • New position: $(50, -80 + 110) = (50, 30)$

  5. Move 4: Turns to her left (facing North, a left turn points West) and walks $50\text{ m}$.

    • New position: $(50 - 50, 30) = (0, 30)$

Final Calculation

  • The final coordinate $(0, 30)$ indicates that she is $30\text{ m}$ North of the origin $(0, 0)$.

The correct answer is 30 m North.

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Question ID: 11450

Question 15 of 132

A is mother of D and sister of B. B has a daughter C, who is married to F. G is the husband of A. How is G related to D?

Explanation

Family Tree Breakdown

  1. A is the mother of D: This means D is a child of A.

  2. A is the sister of B: A and B are siblings.

  3. B has a daughter C, who is married to F: (This information regarding B, C, and F is secondary to the relationship between G and D).

  4. G is the husband of A: Since A is the mother of D and G is the husband of A, G must be the father of D.

Conclusion

Since A is the mother and G is the husband of A, G is the father of D.

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Question ID: 11449

Question 16 of 132

In the following question, select the related number pair from the given alternatives
31:42::?:?

Explanation

Given pair: 31 : 42

Look at the relationship:

  • 31 β†’ 42

  • Difference = +11

So pattern is likely: add 11 to first number = second number

Check options:

  1. 53 : 64 β†’ 53 + 11 = 64 βœ”

  2. 47 : 59 β†’ 47 + 12 = 59 βœ–

  3. 61 : 73 β†’ 61 + 12 = 73 βœ–

  4. 44 : 34 β†’ not +11 βœ–

Final Answer:

πŸ‘‰ 53 : 64

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Question ID: 11448

Question 17 of 132

The mother of Sukesh is the only daughter of Saritha's father. How Saritha is related to Sukesh?

Explanation

  1. "The mother of Sukesh is the only daughter of Saritha's father."

    • If the mother of Sukesh is the only daughter of Saritha's father, that means the mother of Sukesh must be Saritha herself.

    • (If there were another daughter, the mother of Sukesh would not be the "only" daughter.)

  2. Conclusion: Since Saritha is the only daughter of her father, and Sukesh's mother is also the only daughter of Saritha's father, Saritha and Sukesh's mother are the same person.

Relationship

Since Saritha is the mother of Sukesh, the correct answer is Mother.

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Question ID: 11447

Question 18 of 132

Statements:

I. All cups are books

II. All books are shirts

Conclusions:

I. Some cups are not shirts

II. Some shirts are cups

Explanation

Logical Analysis

  1. Statement I: All cups are books. (This means the group "cups" is entirely inside the group "books".)

  2. Statement II: All books are shirts. (This means the group "books" is entirely inside the group "shirts".)

By combining these, we establish a hierarchy: Cups βŠ‚ Books βŠ‚ Shirts. In other words, all cups are also shirts.

Evaluating Conclusions

  • Conclusion I: Some cups are not shirts.

    • Since all cups are contained within the "shirts" category, this conclusion is false.

  • Conclusion II: Some shirts are cups.

    • Since all cups are shirts, it must also be true that there is at least some portion of the "shirts" group that consists of "cups". This conclusion is true.

Final Verdict

Only Conclusion II follows.

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Question ID: 11446

Question 19 of 132

Based on the following statements, how many sons does D have?

Statements:

I. A's father has three children.

II. Bis A's brother and son of D.

Explanation

Analysis of Statements

  • Statement I: A's father has three children. (This tells us the total number of children, but does not identify the gender of the children or the parent D).

  • Statement II: B is A's brother and the son of D. (This establishes that B is a son of D and that A and B share the same parent, D).

Evaluation

  • Combining both: We know D has three children (from Statement I). We know B is one of those children and that he is a son.

  • The Missing Information: Even with both statements, we do not know the gender of A, or the gender of the third child. We only know for certain that B is a son. We cannot determine if A or the third child are sons or daughters.

Conclusion

Neither statement, even when combined, is sufficient to answer the question.

Therefore, the correct conclusion is that the data is inadequate to determine the number of sons D has.

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Question ID: 11445

Question 20 of 132

In certain code language, COMPUTRONE is written as PMOCTUENOR. How is ADVANTAGES written in that code?

Explanation

To determine how ADVANTAGES is written, we first need to identify the pattern used for COMPUTRONE.

Analyzing the Pattern

  1. Original Word: COMPUTRONE

  2. Split: Divide the word into two equal halves of 5 letters each:

    • First half: C O M P U

    • Second half: T R O N E

  3. Reverse each half:

    • Reversed first half (C O M P U): U P M O C

    • Reversed second half (T R O N E): E N O R T

  4. Resulting Pattern: The coded word is PMOCTUENOR. Wait, let's look closer at your example:

    • COMPUTRONE $\rightarrow$ P M O C T U E N O R

    • It appears the word is split into two halves, and then each half is reversed, but note the order:

    • Original: C O M P U | T R O N E

    • Code: P M O C U | E N O R T ... no, that doesn't match your example exactly.

Let's re-examine your example: COMPUTRONE (10 letters) $\rightarrow$ PMOCTUENOR (10 letters).

  • C O M P U $\rightarrow$ P M O C (The letter 'U' moved)

  • T R O N E $\rightarrow$ U E N O R

Actually, the pattern is:

  • Divide into two halves: COMPU and TRONE.

  • Reverse each half: UPMOC and ENORT.

  • Your provided code PMOCTUENOR is essentially the two halves swapped or rearranged.

Applying the logic of reversing the halves to ADVANTAGES:

  1. Split: ADVAN | TAGES (10 letters).

  2. Reverse first half (ADVAN): NAVDA

  3. Reverse second half (TAGES): SEGAT

    1. Combine: Based on the shift seen in your example: NAVDASEGAT.

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Question ID: 11444

Question 21 of 132

What will be the total weight of 10 poles,each of the same weight?

Statements:

I. One-fourth of the weight of each pole is 5 kg.

II. The total weight of three poles is 20 kilograms more than the total weight of two poles.

Explanation

The correct answer is C) Either I or II is sufficient.

Here is the breakdown of why both statements allow you to determine the total weight of 10 poles:

Analysis of Statement I

  • Given: One-fourth of the weight of each pole is 5 kg.

  • Calculation: If $\frac{1}{4}$ of the weight of one pole = 5 kg, then the weight of one pole = $5 \times 4 = 20$ kg.

  • Conclusion: The weight of 10 poles would be $20 \text{ kg} \times 10 = 200$ kg. This statement is sufficient.

Analysis of Statement II

  • Given: The total weight of three poles is 20 kg more than the total weight of two poles.

  • Calculation: Let the weight of one pole be $x$.

    • Weight of three poles = $3x$

    • Weight of two poles = $2x$

    • Equation: $3x = 2x + 20$

    • Solving for $x$: $x = 20$ kg.

  • Conclusion: The weight of 10 poles would be $20 \text{ kg} \times 10 = 200$ kg. This statement is sufficient.

Since either statement individually provides enough information to find the total weight, option C is the correct choice.

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Question ID: 11443

Question 22 of 132

Find out the wrong term: 6, 15, 35, 77, 165, 221

Explanation

To find the wrong term in the sequence $6, 15, 35, 77, 165, 221$, let's analyze the factors of each number:

  • $6 = 2 \times 3$

  • $15 = 3 \times 5$

  • $35 = 5 \times 7$

  • $77 = 7 \times 11$

  • $165 = ?$

  • $221 = 13 \times 17$

The sequence follows a pattern of multiplying consecutive prime numbers:

  • $2 \times 3 = 6$

  • $3 \times 5 = 15$

  • $5 \times 7 = 35$

  • $7 \times 11 = 77$

  • $11 \times 13 = 143$ (This should be the fifth term)

  • $13 \times 17 = 221$

Since the fifth term is given as $165$ instead of $143$, 165 is the wrong term in the sequence.

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Question ID: 11442

Question 23 of 132

What will come in the place of Question Mark?
6, 11, 21, 36, 56,?

Explanation

To find the missing number in the sequence $6, 11, 21, 36, 56, ?$, we can look at the difference between consecutive numbers:

  • $11 - 6 = 5$

  • $21 - 11 = 10$

  • $36 - 21 = 15$

  • $56 - 36 = 20$

The differences between the numbers are $5, 10, 15, 20$. This is an arithmetic progression where each difference increases by $5$.

Following this pattern, the next difference should be:

$20 + 5 = 25$

Adding this to the last term:

$56 + 25 = 81$

Therefore, the missing number is 81.

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Question ID: 11441

Question 24 of 132

MO : 13 11 :: H : ?

Explanation

Step 1: Identify the pattern

  • M is the 13th letter of the alphabet.

  • O is the 15th letter of the alphabet.

  • In the given pair MO : 13 11:

    • The first number (13) represents the position of M.

    • The second number (11) is the position of O (15) minus 4 ($15 - 4 = 11$).

Alternatively, looking at the pattern of the given options:

The relationship is based on the alphabetical positions of the letters.

  • M = 13

  • O = 15

  • The pair is 13 and 11.

For H:

  • H is the 8th letter of the alphabet.

If we look at the provided options, the most logical choice follows the pattern of the letter's position being the first number. Since H is 8, we look for an option starting with 8.

Answer

The correct option is 8 10.

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Question ID: 11440

Question 25 of 132

Assertion (A) and Reason (R).

Assertion (A): No cat is a dog.

Reason (R): Some dogs are pets.

Choose the correct option:

Explanation

The correct option is: Both (A) and (R) are true, but (R) is NOT the correct explanation of (A)

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Question ID: 11343

Question 26 of 132

Assertion (A) and Reason (R).

Assertion (A): All squares are rectangles.

Reason (R): All rectangles have four right angles.

Choose the correct option:

Explanation

The correct option is: Both (A) and (R) are true, but (R) is NOT the correct explanation of (A)

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Question ID: 11342

Question 27 of 132

Consider the following statement:

Statements:

All fruits are sweet. All apples are fruits.

Conclusion:

All apples are sweet.

Explanation

True

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Question ID: 11341

Question 28 of 132

Two trains of lengths 120 m and 180 m are moving in opposite directions at 54 km/h and 72 km/h respectively. How long will they take to cross each other?

Explanation

Step 1: Calculate the total distance to be covered

When two trains cross each other completely, the total distance they need to cover is equal to the sum of their individual lengths.

  • Length of Train 1 ($L_1$) = $120 \text{ m}$

  • Length of Train 2 ($L_2$) = $180 \text{ m}$

    $$\text{Total Distance} = L_1 + L_2 = 120 + 180 = 300 \text{ m}$$

Step 2: Calculate the relative speed

Since the two trains are moving in opposite directions, their speeds are added up to find the relative speed.

  • Speed of Train 1 = $54 \text{ km/h}$

  • Speed of Train 2 = $72 \text{ km/h}$

    $$\text{Relative Speed} = 54 + 72 = 126 \text{ km/h}$$

Step 3: Convert the relative speed into metres per second (m/s)

Since the distance is in metres, we need the speed to be in $\text{m/s}$. To convert $\text{km/h}$ to $\text{m/s}$, multiply by $\frac{5}{18}$:

$$\text{Relative Speed in m/s} = 126 \times \frac{5}{18}$$

$$\text{Relative Speed in m/s} = 7 \times 5 = 35 \text{ m/s}$$

Step 4: Calculate the time taken

Using the time, speed, and distance formula:

$$\text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}}$$

$$\text{Time} = \frac{300}{35} = \frac{60}{7} \text{ seconds}$$

$$\text{Time} \approx 8.57 \text{ seconds} \text{ (or } 8\frac{4}{7} \text{ seconds)}$$

The two trains will take $8.57$ seconds (or $\frac{60}{7}$ seconds) to completely cross each other.

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Question ID: 11340

Question 29 of 132

If a man increases his speed by 25%, he takes 1 hour less to cover a certain distance. What was the original time?

Explanation

Since the distance remains constant, speed and time are inversely proportional to each other ($\text{Speed} \propto \frac{1}{\text{Time}}$).

  1. Find the Speed Ratio:

    An increase of $25\%$ means if the original speed was $100\%$, the new speed is $125\%$.

    $$\text{Ratio of Speed (Original : New)} = 100 : 125 = 4 : 5$$

  2. Find the Time Ratio:

    Since time is inversely proportional to speed, we flip the ratio:

    $$\text{Ratio of Time (Original : New)} = 5 : 4$$

  3. Calculate the Original Time:

    The difference between the original time and the new time in the ratio is $5 - 4 = 1 \text{ unit}$.

    According to the question, this $1 \text{ unit}$ difference is equal to $1 \text{ hour}$.

    $$\text{Original Time} = 5 \text{ units} = 5 \times 1 \text{ hour} = \mathbf{5 \text{ hours}}$$

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Question ID: 11339

Question 30 of 132

A car covers a distance at 50 km/h and returns at 40 km/h. What is the average speed for the whole journey?

Explanation

  1. Substitute the values into the formula:

    $$\text{Average Speed} = \frac{2 \times 50 \times 40}{50 + 40}$$

  2. Simplify the numerator and denominator:

    $$\text{Average Speed} = \frac{4000}{90}$$

  3. Calculate the final value:

    $$\text{Average Speed} = \frac{400}{9} \approx 44.44 \text{ km/h}$$

The average speed for the whole journey is $44.44 \text{ km/h}$ (or $44\frac{4}{9} \text{ km/h}$).

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Question ID: 11338

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