All practice questions

In a published civil services merit list, Rohan is ranked $14^{\text{th}}$ from the top, while Seema is ranked $33^{\text{rd}}$ from the bottom. After a re-evaluation of marks, Rohan and Seema interchange their positions, resulting in Rohan becoming $48^{\text{th}}$ from the top. A third candidate, Amit, holds a rank exactly halfway between Rohan's new position and Seema's new position. If $6$ candidates ranked above Amit withdraw their candidature and $4$ new candidates are placed below Amit in the updated list, what is Amit's final rank from the bottom of the modified merit list?

In a district administration office, a survey of $120$ officers was conducted regarding their proficiency in using three government portals: e-Office ($E$), CPGRAMS ($C$), and GeM ($G$). The survey revealed that $65$ officers are proficient in e-Office, $55$ in CPGRAMS, and $50$ in GeM. Furthermore, $25$ officers are proficient in both e-Office and CPGRAMS, $20$ in both CPGRAMS and GeM, and $22$ in both e-Office and GeM. If $10$ officers are proficient in all three portals, how many officers are proficient in none of these three portals?

If 1st January 2004 was a Thursday, what day of the week was 1st January 2005?

Five public welfare projects—Electrification, Reforestation, Sanitation, Transport, and Water Supply—are scheduled for administrative approval from 1st to 5th based on the following conditions:
- Water Supply is approved immediately after Electrification.
- Reforestation is approved before Sanitation, but after Transport.
- Sanitation is approved before Electrification.

Arrange the five projects in the correct sequential order of their approval from 1st to 5th.

If the six-digit number $45231x$ is completely divisible by $9$, what is the value of the digit $x$?

In a state administrative audit of $300$ urban development projects, participation across three infrastructure domains—Sanitation ($S$), Transport ($T$), and Green Space ($G$)—was analyzed. The audit revealed that $145$ projects involve Sanitation, $135$ involve Transport, and $125$ involve Green Space. Exactly $70$ projects involve precisely two domains, while $20$ projects involve all three domains. Furthermore, $45$ projects involve both Sanitation and Transport, and $35$ projects involve both Transport and Green Space. Which of the following statements are correct? (Select all correct options.)

Consider the following statements regarding administrative policy and environmental developments in an agricultural district:

Statement I: The district administration implemented a strict mandate requiring drip irrigation systems for all water-intensive commercial crops.
Statement II: Groundwater depletion rates in the district registered a 25% decrease over the subsequent three years.
Statement III: Surrounding river basins experienced severe seasonal flooding due to unseasonal upstream torrential rainfall.

Based on logical cause-and-effect reasoning, which of the following statements are correct?

A municipal corporation is distributing its annual infrastructure development fund. Exactly $0.\overline{5}$ of the total fund is allocated to urban housing projects. From the remaining fund, $\frac{3}{7}$ is assigned to public transportation. The rest of the fund is distributed equally between two sectors: renewable energy and public parks. If the amount allocated to renewable energy is $\$3.2$ million, what is the total annual infrastructure development fund?

A student is reviewing fundamental number properties and evaluating several arithmetic scenarios. Identify which of the following assertions regarding number classification are mathematically valid. (Select all that apply)

An inventory analyst is auditing two specific electronic components in a warehouse. He calculates that the product of their exact unit quantities is $32,175$, and the Highest Common Factor (HCF) of these two quantities is $15$. If there are more than $100$ units of each component currently in stock, what is the total combined quantity of both components?

Five executives—Ford, Greta, Harry, Ian, and Julia—are seated in a single straight row facing South during a board meeting.

Based on the following conditions, arrange the executives in the exact order they are seated from West to East (i.e., from the viewer's left to right):

1. Ford sits at the extreme left end of the row.
2. Julia sits immediately to the right of Ford.
3. Greta sits second to the right of Ian.
4. Harry sits adjacent to Ian, but does not sit next to Julia.

A mathematician is formally classifying a set of numbers and analyzing their properties. Evaluate the mathematical validity of the following three propositions:

I. The number $0$ is an even integer, but it is considered neither positive nor negative.
II. The fraction $\frac{22}{7}$ is an irrational number because it is commonly used to represent the constant $\pi$.
III. The absolute difference between any two distinct odd prime numbers is always an even composite number.

Which of the propositions given above is/are mathematically correct?

A digital signal processing unit transmits three distinct telemetry data packets in continuous periodic cycles. The transmission cycles for the three packets take $\frac{14}{15}$ seconds, $\frac{7}{5}$ seconds, and $\frac{63}{20}$ seconds, respectively. If all three packets are transmitted simultaneously at the beginning of a diagnostic test, after how many seconds will all three packets be transmitted together again for the first time?

During a system stress test, four data processing modules record their average latency per transaction (in seconds) as given below. Arrange the modules in ascending order based on their latency times (from fastest to slowest).

Consider all positive two-digit integers where the sum of their digits is exactly $10$. How many of these integers are prime numbers?

Six city planners—David, Elena, Felix, Grace, Hassan, and Iris—are sitting around a circular table for a development meeting. Some planners are facing the center of the table while others are facing outward.

Based on the following conditions, determine their exact seating arrangement:
1. David and Grace sit opposite each other, and both are facing the center.
2. Elena sits to the immediate left of David.
3. Iris sits second to the left of Elena.
4. Felix sits to the immediate right of Grace.
5. Elena, Hassan, and Iris all face the same direction.
6. Felix faces the opposite direction to Hassan.

Based on the seating arrangement, who sits to the immediate left of Hassan?

Under the governance and rural transformation framework of the Government of India, the SVAMITVA (Survey of Villages and Mapping with Improvised Technology in Village Areas) scheme was rolled out nationwide to reform land record management. Which of the following statements accurately characterizes the primary mandate and operational mechanism of this scheme?

A heated verbal altercation has erupted at a major construction site between field officers of the Public Works Department (PWD) and the Forest Department over the clearing of marked trees, bringing a sanctioned highway expansion to a complete halt. When a senior administrative mediator arrives to manage this escalating inter-departmental crisis, arrange the following actions in the most appropriate sequential order to assertively de-escalate and resolve the conflict.

Carefully review the categorical statements and the corresponding conclusion below.

Statements:
- All high-frequency trading algorithms are automated financial systems.
- Some automated financial systems are unregulated market tools.

Conclusion:
Consequently, some high-frequency trading algorithms are unregulated market tools.

Determine whether it is true or false that this conclusion is a logically valid deduction from the given statements.

Match the flagship state government welfare schemes in List-I with their corresponding primary policy objectives and target sectors in List-II: