All practice questions

What is the numerical value of the mathematical expression

80 - [15 + (12 \div 3 \times 2)]

when simplified using the standard BODMAS rule?

Show answer & explanation

Answer: 57

Answer

The simplified numerical value of the given expression is 57.

Evaluating the expression following the strict BODMAS order of operations: first simplify the innermost round brackets by doing division (

12 \div 3 = 4

) then multiplication (

4 \times 2 = 8

). Next, add the numbers inside the square brackets (

15 + 8 = 23

). Finally, subtract 23 from 80 to obtain 57.

Step-by-Step Solution

1

Perform division inside the round brackets.

12 \div 3 = 4

According to the BODMAS rule, division takes precedence over multiplication within brackets.

2

Perform multiplication to complete the round bracket evaluation.

4 \times 2 = 8

Complete the operations contained within the innermost parentheses.

3

Perform addition inside the square brackets.

15 + 8 = 23

Simplify the terms remaining inside the square brackets.

4

Subtract the result of the brackets from the outer value.

80 - 23 = 57

Perform final subtraction to determine the simplified answer.

Key Concept

BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

Question 322Question →

Three automated robotic arms in an assembly line complete their respective sorting cycles in $\frac{14}{15}$ minutes, $\frac{21}{20}$ minutes, and $\frac{42}{25}$ minutes. If all three robotic arms start a sorting cycle simultaneously at 9:00:00 AM, after what minimum time interval will all three arms simultaneously begin a new sorting cycle again?

8

minutes

24

seconds

1.4

seconds

42

minutes

51

seconds

42.86

seconds

Show answer & explanation

Answer: $8$ minutes $24$ seconds

Answer

8

minutes

24

seconds

To find the time when events with fractional period lengths coincide again, we compute the LCM of the fraction time intervals. The formula for the LCM of fractions is

\frac{\text{LCM of numerators}}{\text{HCF of denominators}}

. Finding

\text{LCM}(14, 21, 42) = 42

and

\text{HCF}(15, 20, 25) = 5

yields

\frac{42}{5} = 8.4

minutes, which equals

8

minutes

24

seconds.

Step-by-Step Solution

1

Identify the mathematical operation required for simultaneous recurrence

The required minimum time interval is the Least Common Multiple (LCM) of the three cycle times:

\text{LCM}\left(\frac{14}{15}, \frac{21}{20}, \frac{42}{25}\right)

minutes.

Simultaneous future events occurring at periodic intervals require finding the LCM of the given time periods.

2

Apply the formula for the LCM of fractions

\text{LCM}\left(\frac{a}{b}, \frac{c}{d}, \frac{e}{f}\right) = \frac{\text{LCM}(a, c, e)}{\text{HCF}(b, d, f)}

For simplified fractions, the LCM is determined by dividing the LCM of all numerators by the HCF of all denominators.

3

Calculate the LCM of the numerators

(14, 21, 42)

14 = 2 \times 7

,

21 = 3 \times 7

,

42 = 2 \times 3 \times 7

. Thus,

\text{LCM}(14, 21, 42) = 2 \times 3 \times 7 = 42

.

The smallest positive integer divisible by 14, 21, and 42 is 42.

4

Calculate the HCF of the denominators

(15, 20, 25)

15 = 3 \times 5

,

20 = 2^2 \times 5

,

25 = 5^2

. Thus,

\text{HCF}(15, 20, 25) = 5

.

The greatest integer that divides 15, 20, and 25 without remainder is 5.

5

Combine the results and convert to minutes and seconds

\text{LCM} = \frac{42}{5} = 8.4

minutes. Converting

0.4

minutes to seconds gives

0.4 \times 60 = 24

seconds. Total time =

8

minutes

24

seconds.

Multiplying the fractional minute by 60 converts it into exact seconds.

Key Concept

LCM of Fractions

Question 323Question →

In an agricultural extension survey conducted across three blocks—Block A, Block B, and Block C—a total of $800$ farmers were interviewed regarding their adoption of organic farming practices. Out of the total interviewed farmers, $40\%$ were from Block A. The remaining farmers were equally divided between Block B and Block C. How many farmers were interviewed from Block B?

240

320

480

160

Show answer & explanation

Answer: $240$

Answer

The number of farmers interviewed from Block B is

240

.

The total number of interviewed farmers is

800

. Block A accounts for

40\%

of

800

, which equals

320

farmers. The remaining farmers across Block B and Block C combined total

800 - 320 = 480

. Since these remaining farmers are divided equally between Block B and Block C, Block B has

480 \div 2 = 240

farmers.

Step-by-Step Solution

1

Calculate the number of farmers in Block A

40\% \text{ of } 800 = 0.40 \times 800 = 320

farmers.

Block A accounts for

40\%

of the total

800

farmers.

2

Calculate the remaining number of farmers for Block B and Block C combined

800 - 320 = 480

farmers.

The paragraph states that the remaining farmers belong to Block B and Block C.

3

Divide the remaining farmers equally to find the count for Block B

480 \div 2 = 240

farmers.

Block B and Block C share the remaining farmers equally.

Key Concept

Paragraph Data Extraction and Simple Multi-Step Calculation

Estimated Time:45s

Question 324Question →

If $x = \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$ and $y = \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}$ , what is the value of $x^2 + y^2$ ?

Show answer & explanation

Answer: 23

Answer

The value of

x^2 + y^2

is 23.

By rationalizing the denominators of

x

and

y

, we obtain

x = \frac{5+\sqrt{21}}{2}

and

y = \frac{5-\sqrt{21}}{2}

. Adding these gives

x+y=5

, and multiplying them gives

xy=1

. Using the identity

x^2+y^2 = (x+y)^2 - 2xy

, we calculate

5^2 - 2(1) = 23

.

Step-by-Step Solution

1

Rationalize the expressions for

x

and

y

by multiplying the numerator and denominator by their respective conjugates.

x = \frac{(\sqrt{7}+\sqrt{3})^2}{7-3} = \frac{10 + 2\sqrt{21}}{4} = \frac{5 + \sqrt{21}}{2}

and

y = \frac{(\sqrt{7}-\sqrt{3})^2}{7-3} = \frac{10 - 2\sqrt{21}}{4} = \frac{5 - \sqrt{21}}{2}

Eliminating surds from the denominator simplifies addition and multiplication.

2

Calculate the sum

(x + y)

and the product

(x \cdot y)

of

x

and

y

.

x + y = \frac{5 + \sqrt{21}}{2} + \frac{5 - \sqrt{21}}{2} = 5

and

x \cdot y = \frac{(5 + \sqrt{21})(5 - \sqrt{21})}{4} = \frac{25 - 21}{4} = 1

Simplifying the symmetric expressions reduces computation complexity.

3

Apply the algebraic identity

x^2 + y^2 = (x + y)^2 - 2xy

.

x^2 + y^2 = (5)^2 - 2(1) = 25 - 2 = 23

Using the identity avoids evaluating complex squares directly.

Key Concept

Rationalization of surds and application of symmetric algebraic identities

Question 325Question →

If $2^{x-1} + 2^{x+1} = 320$ , what is the value of $x$ ?

5

6

7

8

Show answer & explanation

Answer: $7$

Answer

7

Factoring

2^{x-1}

from the left side gives

2^{x-1}(1 + 2^2) = 5 \cdot 2^{x-1} = 320

. Dividing both sides by

5

yields

2^{x-1} = 64 = 2^6

. Equating the powers gives

x - 1 = 6

, which solves to

x = 7

.

Step-by-Step Solution

1

Factor out the common exponential term from the left-hand side

2^{x-1}(1 + 2^2) = 320 \implies 2^{x-1}(1 + 4) = 320 \implies 5 \cdot 2^{x-1} = 320

Applying the distributive law of exponents to simplify the sum.

2

Divide both sides by 5

2^{x-1} = \frac{320}{5} = 64

Isolate the exponential term with base 2.

3

Express 64 as a power of 2 and equate the exponents

64 = 2^6 \implies x - 1 = 6 \implies x = 7

Since the bases are equal (

2

), the exponents must be equal.

Key Concept

Laws of Indices and Exponential Equations

Question 326Question →

In a university central library, a survey was conducted on $500$ students who visited on Monday. Out of the total $500$ students, $300$ students borrowed books, while the remaining $200$ students used the reading room only. Among the students who borrowed books, $180$ were undergraduate students and the rest were postgraduate students. Among the students who used the reading room only, $120$ were undergraduate students and the rest were postgraduate students.

Based on the information provided in the paragraph above, which of the following statements are correct?

Select all that apply

The total number of postgraduate students surveyed is

200

.

The ratio of undergraduate students to postgraduate students who borrowed books is

3 : 2

.

The percentage of postgraduate students among those using the reading room only is

50\%

.

The total number of undergraduate students surveyed is

250

.

Show answer & explanation

Answer: The total number of postgraduate students surveyed is $200$ .; The ratio of undergraduate students to postgraduate students who borrowed books is $3 : 2$ .

Answer

The correct statements are that the total number of postgraduate students surveyed is 200, and the ratio of undergraduate students to postgraduate students who borrowed books is 3 : 2.

The total number of postgraduate students surveyed is

200

(

120

who borrowed books and

80

who used the reading room only). Furthermore, the ratio of undergraduate borrowers (

180

) to postgraduate borrowers (

120

) simplifies correctly to

3 : 2

.

Step-by-Step Solution

1

Extract data for students who borrowed books

Total borrowing books =

300

. Undergraduate borrowers =

180

. Postgraduate borrowers =

300 - 180 = 120

.

Separating the borrowing group into undergraduate and postgraduate categories.

2

Extract data for students using the reading room only

Total reading room only =

200

. Undergraduate reading room users =

120

. Postgraduate reading room users =

200 - 120 = 80

.

Separating the reading room group into undergraduate and postgraduate categories.

3

Calculate total postgraduate and undergraduate counts across both categories

Total postgraduate students =

120 + 80 = 200

. Total undergraduate students =

180 + 120 = 300

.

Summing values across both activity categories to verify totals.

4

Verify ratios and percentages

Ratio of UG borrowers to PG borrowers =

180 : 120 = 3 : 2

. Percentage of PG students in reading room =

\frac{80}{200} \times 100 = 40\%

.

Testing each option statement against computed values.

Key Concept

Data Extraction and Tabulation from Caselets

Question 327Question →

Evaluate the following mathematical expression using the standard BODMAS (VBODMAS) rule:

40\% \text{ of } 250 - \left[ 15 + \left\{ 45 \div \left( 2 + \frac{1}{4} \text{ of } \left( 18 - \overline{8 - 2} \right) \right) \right\} \right]

What is the final simplified value of the expression?

76

88

94

24

Show answer & explanation

Answer: 76

Answer

The simplified value of the expression is 76.

Following the strict hierarchical order of operations (VBODMAS), resolving the bar vinculum first gives 6, then the inner parenthesis yields 12. Taking 1/4 of 12 gives 3, and adding 2 yields 5. Dividing 45 by 5 yields 9, and adding 15 yields 24 inside the main bracket. Subtracting 24 from 40% of 250 (which equals 100) gives the correct answer of 76.

Step-by-Step Solution

1

Evaluate the expression under the vinculum bar:

\overline{8 - 2}

.

\overline{8 - 2} = 6

According to VBODMAS, operations under a vinculum take highest priority.

2

Evaluate the innermost round bracket:

(18 - 6)

.

18 - 6 = 12

Resolve terms within the round parentheses.

3

Evaluate the 'of' operation inside the round bracket context:

\frac{1}{4} \text{ of } 12

.

\frac{1}{4} \times 12 = 3

'Of' precedes basic addition and division.

4

Complete the addition inside the innermost bracket:

(2 + 3)

.

2 + 3 = 5

Finalize inner parentheses.

5

Evaluate the division inside the curly brackets:

\{45 \div 5\}

.

45 \div 5 = 9

Perform division inside curly brackets.

6

Evaluate the addition inside the square brackets:

[15 + 9]

.

15 + 9 = 24

Resolve the square brackets.

7

Evaluate the percentage term:

40\% \text{ of } 250

.

\frac{40}{100} \times 250 = 100

Calculate the percentage value independently.

8

Perform the final subtraction:

100 - 24

.

100 - 24 = 76

Subtract the bracket result from the percentage value.

Key Concept

BODMAS / VBODMAS Order of Operations

Alternative Method

Calculate the percentage term 40% of 250 = 100 first, then systematically simplify the bracket from innermost (vinculum) to outermost to subtract from 100.

Estimated Time:1m 15s

Question 328Question →

During a public health immunization drive in a rural district, a total of $1,500$ vaccines were administered across three primary health centers: PHC Alpha, PHC Beta, and PHC Gamma. PHC Alpha administered $550$ vaccines, while PHC Beta administered $600$ vaccines. The remaining vaccines were administered by PHC Gamma. What is the total number of vaccines administered by PHC Gamma?

350

1,150

550

450

Show answer & explanation

Answer: $350$

Answer

The total number of vaccines administered by PHC Gamma is

350

.

The total number of vaccines administered across all three health centers is

1,500

. Adding the vaccines administered by PHC Alpha (

550

) and PHC Beta (

600

) yields a total of

1,150

. Subtracting

1,150

from

1,500

gives

350

vaccines administered by PHC Gamma.

Step-by-Step Solution

1

Calculate the total vaccines administered by PHC Alpha and PHC Beta combined.

550 + 600 = 1,150

vaccines

To find the remaining amount for PHC Gamma, first aggregate the given counts of the other two health centers.

2

Subtract the combined count from the grand total of vaccines administered.

1,500 - 1,150 = 350

vaccines

Subtracting the known portions from the total gives the remaining vaccines administered by PHC Gamma.

Key Concept

Data extraction and simple subtraction from paragraph-based caselets

Question 329Question →

With reference to the Ahom Revolt of 1828 in the regional history of Assam, consider the following statements:

1. It erupted primarily due to the non-fulfillment of the British pledge to withdraw from Assam after the First Anglo-Burmese War.
2. Gomdhar Konwar was proclaimed king by the insurgents during the uprising.
3. The movement received official military backing from the East India Company under the Treaty of Yandabo.

Which of the statements given above is/are correct?

1 and 2 only

2 and 3 only

1 and 3 only

1, 2, and 3

Show answer & explanation

Answer: 1 and 2 only

Answer

Statements 1 and 2 are correct. The Ahom Revolt (1828) occurred after the First Anglo-Burmese War when the British failed to withdraw from Assam as previously implied, attempting instead to incorporate Ahom territories into Company possessions. The rebels declared Gomdhar Konwar as their king. The movement was suppressed by the East India Company.

The option stating '1 and 2 only' is correct because the Ahom Revolt of 1828 broke out when the British East India Company reneged on its implied pledge to evacuate Assam after defeating the Burmese in 1826. Ahom nobles raised the standard of rebellion and crowned Gomdhar Konwar as king near Jorhat. The movement was directed entirely against Company rule, rendering the assertion of British military backing completely false.

Step-by-Step Solution

1

Analyze Statement 1 regarding the cause of the revolt.

Statement 1 is correct. After the conclusion of the First Anglo-Burmese War (1824–26) and the Treaty of Yandabo (1826), the British had promised to retreat, but instead attempted to incorporate the Ahom kingdom into British territory, triggering discontent.

Understanding the geopolitical context following the Treaty of Yandabo clarifies the primary trigger of the rebellion.

2

Analyze Statement 2 regarding the leadership of the revolt.

Statement 2 is correct. In 1828, Ahom nobility led by Gomdhar Konwar and Dhananjay Borgohain rebelled and formally proclaimed Gomdhar Konwar as King at Jorhat.

Identifying the key leaders of regional resistance movements confirms the validity of the second statement.

3

Analyze Statement 3 regarding British involvement.

Statement 3 is incorrect. The revolt was an anti-British resistance; the East India Company dispatched troops under Lieutenant Rutherford to suppress the uprising, leading to Gomdhar Konwar's arrest.

Distinguishing between opposing factions avoids misattributing colonial treaty terms to rebel support.

Key Concept

Ahom Revolt of 1828 and early anti-colonial uprisings in North-East India

Estimated Time:1m 15s

Question 330Question →

Arrange the following Indian environmental institutions and bodies in chronological order of their establishment, from the earliest to the latest:

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct chronological sequence from earliest to latest is: Botanical Survey of India (1890), Central Pollution Control Board (1974), National Biodiversity Authority (2003), and National Green Tribunal (2010).

The correct sequence begins with the Botanical Survey of India, established in 1890. Next is the Central Pollution Control Board, constituted in 1974 under the Water (Prevention and Control of Pollution) Act. This is followed by the National Biodiversity Authority, established in 2003 under the Biological Diversity Act, 2002. Finally, the National Green Tribunal was created in 2010 under the NGT Act. Thus, the proper order from earliest to latest is BSI (1890) → CPCB (1974) → NBA (2003) → NGT (2010).

Step-by-Step Solution

1

Determine the founding year of each environmental organization or body.

Botanical Survey of India (1890), Central Pollution Control Board (1974), National Biodiversity Authority (2003), and National Green Tribunal (2010).

Knowing the statutory or historical establishment year allows for accurate timeline construction.

2

Sort the institutions sequentially from the oldest establishment date to the most recent.

1890 (BSI) → 1974 (CPCB) → 2003 (NBA) → 2010 (NGT).

Arranging the years in ascending numerical order provides the requested chronological order.

Key Concept

Establishment Timeline of Key Indian Environmental Institutions

Question 331Question →

The seminal definition of Sustainable Development as 'development that meets the needs of the present without compromising the ability of future generations to meet their own needs' was formally introduced by which of the following reports?

Our Common Future (Brundtland Commission Report, 1987)

The Limits to Growth (Club of Rome Report, 1972)

Agenda 21 (Rio Earth Summit Document, 1992)

Caring for the Earth (IUCN/UNEP/WWF Strategy, 1991)

Show answer & explanation

Answer: Our Common Future (Brundtland Commission Report, 1987)

Answer

The report 'Our Common Future', released by the World Commission on Environment and Development (Brundtland Commission) in 1987, formally defined Sustainable Development.

The report 'Our Common Future', published in 1987 by the World Commission on Environment and Development (popularly known as the Brundtland Commission), coined and popularized the standard definition of Sustainable Development.

Step-by-Step Solution

1

Identify the core definition given in the question stem.

The definition 'development that meets the needs of the present without compromising the ability of future generations to meet their own needs' is the classic definition of sustainable development.

Tracing international environmental landmarks requires identifying key publication origins.

2

Correlate the definition with historical environmental commission reports.

The United Nations convened the World Commission on Environment and Development (WCED), chaired by Gro Harlem Brundtland, which published its report 'Our Common Future' in 1987.

This report bridged economic development and environmental protection under the framework of sustainable development.

Key Concept

Brundtland Commission Report and the Origin of Sustainable Development

Question 332Question →

In a regional agricultural seed bank's categorization system, crop names are converted into numerical codes for database entry. Under this specific protocol, the crop name "WHEAT" is coded as "4-19-5-1-7", and the crop name "BARLEY" is coded as "25-1-9-15-5-2". Following the exact same logical pattern, how will the crop name "MAIZE" be coded?

14-1-9-1-5

14-26-18-1-22

13-1-9-26-5

13-26-18-26-22

Show answer & explanation

Answer: 14-1-9-1-5

Answer

14-1-9-1-5

The correct answer is derived by observing that all consonants are transformed into their reverse alphabetical positions (e.g., M=13 becomes 14, Z=26 becomes 1), while all vowels maintain their standard forward alphabetical positions (e.g., A=1, I=9, E=5). Combining these values in sequence produces 14-1-9-1-5.

Step-by-Step Solution

1

Determine the standard alphabetical positions of the letters in the first example, 'WHEAT'.

W=23, H=8, E=5, A=1, T=20.

Establishing the base numerical values is the first step in identifying coding transformations.

2

Compare the base numerical values of 'WHEAT' with its given code: '4-19-5-1-7'.

W(23) becomes 4. H(8) becomes 19. E(5) remains 5. A(1) remains 1. T(20) becomes 7.

This comparison reveals the specific mathematical or logical transformation applied to each letter.

3

Identify the underlying logical rule governing the transformations.

Consonants (W, H, T) are assigned their reverse alphabetical positions (calculated as 27 - forward position). Vowels (E, A) retain their standard forward alphabetical positions.

Defining the conditional rule is required before it can be reliably applied to other words.

4

Verify the identified rule using the second example, 'BARLEY'.

Forward positions: B=2, A=1, R=18, L=12, E=5, Y=25. Applying the rule: B(consonant) -> 25, A(vowel) -> 1, R(consonant) -> 9, L(consonant) -> 15, E(vowel) -> 5, Y(consonant) -> 2. Code is 25-1-9-15-5-2, which perfectly matches the given code.

Testing the hypothesis against a second dataset confirms the logic is universally applied within the system.

5

Apply the verified rule to the target word 'MAIZE'.

M(13, consonant) -> 27-13 = 14. A(1, vowel) -> 1. I(9, vowel) -> 9. Z(26, consonant) -> 27-26 = 1. E(5, vowel) -> 5.

Translating the target string using the established algorithm yields the final answer.

Key Concept

Mixed Alphanumeric Substitution using Vowel/Consonant Conditional Logic and Reverse Indexing

Question 333Question →

You are a District Civil Supplies Officer in a drought-hit tribal block. A severe food shortage is reported, and you discover that a cartel of ration shop dealers is illegally diverting subsidized government grains to the open market. Desperate and hungry villagers have gathered to protest outside the block administrative office. Rank the following administrative actions from the most ethically sound and procedurally correct to the least appropriate.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence begins with immediate relief and lawful enforcement, followed by standard bureaucratic procedure, then unethical negotiation, and ends with the disproportionate use of force.

The most appropriate response must balance immediate public welfare (food distribution) with strict enforcement of the law (suspending licenses). Relying solely on bureaucratic notices fails to address the urgency, while negotiating with corrupt dealers compromises institutional integrity. Using state force against starving citizens is the ultimate administrative failure and must be ranked last.

Step-by-Step Solution

1

Evaluate the primary administrative duty in the scenario.

The immediate priority is preventing starvation and stopping the theft of public resources.

In crisis management, humanitarian needs take precedence over routine paperwork.

2

Identify the most ethically sound action.

Suspending licenses and arranging alternative distribution addresses both the corruption and the food crisis simultaneously.

It upholds both the rule of law and public welfare.

3

Identify the least appropriate action.

Using police force against starving villagers is the worst possible choice.

It penalizes the victims and represents a gross misuse of state power (extreme administrative action).

4

Rank the remaining two intermediate actions.

Issuing notices is ranked higher than negotiating immunity.

Bureaucratic delay, while flawed in an emergency, is still legally permissible; offering immunity to corrupt officials actively violates statutory duties.

Key Concept

Administrative Proportionality, Public Interest, and Crisis Management

Question 334Question →

What is the Highest Common Factor (HCF) of the fractions $\frac{8}{15}$ and $\frac{14}{25}$ ?

\frac{2}{75}

\frac{56}{5}

\frac{2}{5}

\frac{56}{75}

Show answer & explanation

Answer: $\frac{2}{75}$

Answer

The Highest Common Factor (HCF) is

\frac{2}{75}

.

The correct answer is found by taking the Highest Common Factor (HCF) of the numerators (

8

and

14

), which is

2

, and dividing it by the Least Common Multiple (LCM) of the denominators (

15

and

25

), which is

75

. This yields exactly

\frac{2}{75}

.

Step-by-Step Solution

1

Identify the numerators and denominators of the given fractions.

The numerators are

8

and

14

. The denominators are

15

and

25

.

The formula for the HCF of fractions requires processing numerators and denominators separately.

2

Calculate the Highest Common Factor (HCF) of the numerators.

The HCF of

8

and

14

is

2

.

According to the formula, the numerator of the final answer must be the HCF of the original numerators.

3

Calculate the Least Common Multiple (LCM) of the denominators.

The LCM of

15

and

25

is

75

.

According to the formula, the denominator of the final answer must be the LCM of the original denominators.

4

Combine the results into a single fraction.

The resulting fraction is

\frac{2}{75}

.

The HCF of fractions is defined as

\frac{\text{HCF of numerators}}{\text{LCM of denominators}}

.

Key Concept

Highest Common Factor (HCF) of Fractions

Question 335Question →

Select the letter-cluster that is related to the third letter-cluster in the same way that the second letter-cluster is related to the first letter-cluster.

TASK : XYWI :: POND : ?

TMRB

TSRH

LQJF

RKPZ

Show answer & explanation

Answer: TMRB

Answer

The correct letter-cluster is TMRB.

The relationship between the first and second letter-clusters follows an alternating alphabetical shift pattern. The first and third letters are shifted forward by 4 positions (+4), while the second and fourth letters are shifted backward by 2 positions (-2), with standard circular alphabetical wrap-around. Applying this identical +4, -2, +4, -2 sequence to the letters P, O, N, and D yields T, M, R, and B respectively.

Step-by-Step Solution

1

Analyze the positional shifts between the first pair of letter-clusters: TASK and XYWI.

T(20) to X(24) is +4. A(1 or 27) to Y(25) is -2. S(19) to W(23) is +4. K(11) to I(9) is -2.

Establishing the underlying logical rule requires checking the step interval for every individual letter to ensure the full pattern is identified.

2

Determine the unified rule governing the analogy.

The alternating shift sequence is +4, -2, +4, -2.

This confirms that the transformation is not a uniform shift, but an alternating forward and backward arithmetic progression.

3

Apply the identical +4, -2, +4, -2 pattern to the target letter-cluster: POND.

P(16) + 4 = T(20). O(15) - 2 = M(13). N(14) + 4 = R(18). D(4) - 2 = B(2).

To maintain the analogical relationship, the exact sequence of operations must be applied to the new group.

Key Concept

Alphabetical Positional Alternating Shifts

Question 336Question →

A family of six individuals—Kiran, Rahul, Priya, Dev, Sam, and Alex—are traveling together. The family's structure is defined by the following facts:

1. Dev is the mother of Priya, and is married to Alex.
2. Rahul is the father of both Alex and Kiran.
3. Rahul is the paternal grandfather of Sam.
4. Priya is the sister of Sam.
5. Within this specific group of six, there are exactly two fathers, three brothers, and one mother.

Based on this information, how is Kiran related to Priya?

Paternal aunt

Paternal uncle

Maternal uncle

Brother

Show answer & explanation

Answer: Paternal uncle

Answer

Paternal uncle

Based on the given clues, Alex and Dev are the parents of Priya and Sam. Rahul is the father of Alex and Kiran, making Alex and Kiran siblings. To satisfy the condition that there are exactly three brothers in the group, we must count Alex (brother to Kiran), Kiran (brother to Alex), and Sam (brother to Priya). This strictly defines Kiran as male. Since Kiran is the brother of Priya's father (Alex), Kiran is Priya's paternal uncle.

Step-by-Step Solution

1

Determine the parents of Priya and Sam.

Alex is the father and Dev is the mother.

Dev is the mother of Priya and is married to Alex. Since Priya is Sam's sister, Alex and Dev are parents to both.

2

Determine the generational relationship of Rahul, Alex, and Kiran.

Rahul is the father of both Alex and Kiran (Generation 1). Alex and Kiran are siblings (Generation 2).

This is explicitly stated in the second clue, and it aligns perfectly with Rahul being the paternal grandfather of Sam.

3

Deduce the genders of the remaining members using the role count conditions.

Sam is male, and Kiran is male.

We must have exactly 3 brothers. Alex is a brother (to Kiran). To get two more brothers, Kiran must be a brother (to Alex), and Sam must be a brother (to Priya). Thus, both are logically deduced to be male.

4

Identify Kiran's relationship to Priya.

Kiran is the paternal uncle of Priya.

Kiran is the male sibling of Alex, who is Priya's father.

Key Concept

Logical Deduction of Gender in Blood Relations

Estimated Time:1m 30s

Question 337Question →

Analyze the provided administrative announcement and evaluate the candidate assumptions.

Announcement:
"The Department of Urban Development has launched a new web platform for residents to report road defects, guaranteeing that maintenance teams will resolve any verified complaint within 48 hours of submission."

Assumptions:
I. The local residents are equipped with the digital devices and internet connectivity required to submit complaints through the web platform.
II. The department has adequate operational capacity and manpower to repair the reported road defects within the promised two-day timeframe.

Based on the announcement above, which of the given assumptions is implicit?

Only Assumption I is implicit

Only Assumption II is implicit

Either Assumption I or Assumption II is implicit

Neither Assumption I nor Assumption II is implicit

Both Assumption I and Assumption II are implicit

Show answer & explanation

Answer: Both Assumption I and Assumption II are implicit

Answer

Both Assumption I and Assumption II are implicit

An assumption is an unstated premise that must be true for a statement to hold logical ground. When a government body launches a digital reporting system, it inherently assumes that the target demographic possesses the means to access and utilize it, making the first assumption valid. Furthermore, by publicly guaranteeing a specific 48-hour resolution window, the department logically assumes it has the logistical and workforce resources to fulfill that exact promise, making the second assumption valid as well. Therefore, both candidate premises are logically implicit.

Step-by-Step Solution

1

Analyze the core premise of the announcement.

The announcement introduces a digital reporting tool and guarantees a 48-hour resolution timeframe.

Identifying the main actions (launching a web platform, setting a deadline) helps isolate the unstated conditions required for those actions to make sense.

2

Evaluate Assumption I.

Assumption I is implicit because introducing a web-based platform inherently relies on the unstated condition that the target audience can access and use it.

An action intended for public use logically assumes public accessibility.

3

Evaluate Assumption II.

Assumption II is implicit because guaranteeing a specific timeframe (48 hours) relies on the unstated condition that the department has the resources to meet this strict deadline.

A public commitment to a timeline logically assumes the operational capacity to honor it.

Key Concept

Identifying Implicit Premises in Administrative Statements

Question 338Question →

As the District Magistrate, you are assigned to resolve a rapidly escalating conflict over the redevelopment of a defunct riverside warehouse district. The state government plans to build a subsidized housing complex on the site. However, local neighborhood associations are demanding the space be converted into a high-end commercial park, while environmental groups have initiated blockades, protesting over alleged industrial soil contamination that they claim has not been addressed.

Arrange the following conflict de-escalation and negotiation steps in the optimal administrative sequence to resolve the crisis effectively.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The optimal sequence is: immediate de-escalation (standstill directive), individual stakeholder mapping (confidential sessions), objective fact-finding (independent technical study), joint mediation (multi-party forum), and formalization of the agreement (binding memorandum).

A structured administrative negotiation follows a standard progression designed to minimize volatility and maximize rational problem-solving. It must begin with immediate de-escalation to ensure safety and order. Once the situation is stable, the administrator must explore individual stakeholder interests privately, as public forums encourage rigid posturing. Following this, commissioning an independent technical study provides the objective criteria necessary to neutralize emotional disputes over unverified claims (such as contamination). Only when these facts are established should stakeholders be brought together in a joint forum to negotiate solutions based on a shared reality. Finally, any consensus reached must be codified into a formal agreement to ensure long-term accountability.

Step-by-Step Solution

1

Issue an immediate standstill directive

Protests are halted, the site is secured, and physical escalation is prevented.

Administrative conflict resolution cannot proceed during active unrest; securing public order is always the baseline prerequisite.

2

Conduct confidential listening sessions

The core interests and non-negotiables of each conflicting party are identified.

Bringing hostile parties together immediately often deepens divisions. Private mapping allows the negotiator to understand the true drivers of the conflict.

3

Commission an independent technical study

Objective, verified data regarding the soil contamination and urban impact is produced.

Disputes over facts (like contamination levels) must be resolved by neutral experts before stakeholders can meaningfully negotiate.

4

Facilitate a multi-party mediation forum

Stakeholders collaboratively design a revised redevelopment plan using the technical data.

Joint problem-solving is most effective when parties share a common baseline of facts and feel their individual concerns have been heard.

5

Institutionalize the consensus

A binding memorandum of understanding is signed with clear compliance metrics.

Verbal agreements are fragile; a formal administrative mechanism ensures all parties are legally and procedurally bound to the negotiated outcome.

Key Concept

Sequential Administrative Conflict Resolution and Interest-Based Negotiation

Question 339Question →

You are the Director of a State Transport Corporation. To improve profitability, the state government has issued a strict mandate to phase out all consistently loss-making rural bus routes before the upcoming budget session. Upon reviewing the data, you discover that cancelling these specific routes will completely sever several remote villages from the nearest district hospital and secondary schools. The local political representatives are pressing you to implement the mandate quickly to demonstrate financial turnaround, while village panchayats have sent frantic petitions highlighting their impending isolation. Which of the following is the most appropriate and ethically sound administrative action to resolve this dilemma?

Execute the government mandate immediately to ensure financial compliance and demonstrate administrative efficiency, advising the affected villagers to rely on alternative private transport.

Refuse to cancel the routes and unilaterally suspend the government mandate, publicly stating that the transport corporation must prioritize rural welfare over financial metrics.

Implement a restructured timetable that reduces frequency but maintains daily essential connectivity to the villages, while formally submitting a proposal to the government for a public service obligation subsidy for these routes.

Secretly divert operational funds from profitable urban routes to subsidize the rural routes without informing the government, thereby satisfying both the financial targets on paper and the villagers' needs.

Show answer & explanation

Answer: Implement a restructured timetable that reduces frequency but maintains daily essential connectivity to the villages, while formally submitting a proposal to the government for a public service obligation subsidy for these routes.

Answer

Implement a restructured timetable that reduces frequency but maintains daily essential connectivity to the villages, while formally submitting a proposal to the government for a public service obligation subsidy for these routes.

The correct answer demonstrates the principle of proportionality and adherence to due process. By reducing the frequency of buses rather than cancelling them outright, the administrator minimizes financial losses while preserving critical access to hospitals and schools. Furthermore, by formally petitioning the government for a subsidy, the administrator respects the chain of command and seeks a transparent, policy-based resolution rather than relying on insubordination or deception.

Step-by-Step Solution

1

Analyze the competing interests and administrative duties in the scenario.

The primary conflict is between the government's mandate for financial profitability and the state's ethical obligation to provide essential services (healthcare and education access) to remote citizens.

Identifying the core tension is necessary to find a balanced solution that does not completely sacrifice one priority for the other.

2

Evaluate the proposed courses of action against principles of administrative propriety and public interest.

Immediate cancellation harms the public; unilateral suspension violates administrative hierarchy; fund diversion is unethical and illegal. Only a compromise involving reduced frequency and formal appeals aligns with both duty and procedure.

Administrative decisions must be proportional, transparent, and adhere to established protocols while striving to protect vulnerable stakeholders.

Key Concept

Balancing statutory directives with public welfare through proportional action and proper procedural channels.

Question 340Question →

What is the remainder when the mathematical expression $14 \times 47^{55} - 63$ is divided by $48$ ?

29

16

19

1

Show answer & explanation

Answer: 19

Answer

The correct remainder is 19.

The correct answer is found by applying modular arithmetic properties. First, simplify the base:

47 \equiv -1 \pmod{48}

. Raising this to an odd power gives

47^{55} \equiv (-1)^{55} = -1 \pmod{48}

. Substituting this back into the expression yields

14 \times (-1) - 63

. We can also simplify

63 \pmod{48}

to

15

. The expression then becomes

-14 - 15 = -29 \pmod{48}

. Because standard remainders cannot be negative, we add the divisor (48) to find the true positive remainder:

-29 + 48 = 19

.

Step-by-Step Solution

1

Simplify the base of the exponent modulo 48.

47 \equiv -1 \pmod{48}

Using negative remainders makes calculating large powers manageable.

2

Evaluate the exponentiated term modulo 48.

(-1)^{55} = -1

An odd power of -1 remains -1.

3

Simplify the constant term modulo 48.

63 \equiv 15 \pmod{48}

To keep all terms within the modulo base before finalizing the expression.

4

Substitute the simplified values back into the expression.

14 \times (-1) - 15 = -14 - 15 = -29

To find the overall remainder of the expression, which currently results in a negative value.

5

Convert the negative remainder to a valid positive remainder.

-29 + 48 = 19

Remainders must be strictly positive integers less than the divisor.

Key Concept

Divisibility Rules and Remainder Theorem

Answer

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